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authorMatt Strapp <matt@mattstrapp.net>2022-05-24 11:18:46 -0500
committerMatt Strapp <matt@mattstrapp.net>2022-05-24 11:19:55 -0500
commit7a73162607544204032aa66cce755daf21edebda (patch)
tree58578e01f15f34a855d99c32898db9d7a1603e67 /math2373
parentdo some stuff (diff)
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Graduate
Signed-off-by: Matt Strapp <matt@mattstrapp.net>
Diffstat (limited to 'math2373')
-rw-r--r--math2373/FinalGraph.pngbin0 -> 20876 bytes
-rw-r--r--math2373/lab1.txt466
-rw-r--r--math2373/lab2.txt1024
-rw-r--r--math2373/lab3.txt12
-rw-r--r--math2373/lab4.txt173
-rw-r--r--math2373/lab4/graph2lab5.pngbin0 -> 10005 bytes
-rw-r--r--math2373/lab4/graph3lab5.pngbin0 -> 8743 bytes
-rw-r--r--math2373/lab4/graph4lab5.pngbin0 -> 12039 bytes
-rw-r--r--math2373/lab4/graph5lab5.pngbin0 -> 10633 bytes
-rw-r--r--math2373/lab4/graph6lab5.pngbin0 -> 18185 bytes
-rw-r--r--math2373/lab4/testt.pngbin0 -> 16175 bytes
-rw-r--r--math2373/lab5/lab4.txt59
-rw-r--r--math2373/lab5/multseries.m4
-rw-r--r--math2373/lab5/sum_of_fourths.m4
-rw-r--r--math2373/lab5/sum_of_nn.m4
-rw-r--r--math2373/lab6/alltogethernow.pngbin0 -> 17136 bytes
-rw-r--r--math2373/lab6/approx.m6
-rw-r--r--math2373/lab6/badEstimate.pngbin0 -> 12681 bytes
-rw-r--r--math2373/lab6/euler5.m5
-rw-r--r--math2373/lab6/eulerN.m5
-rw-r--r--math2373/lab6/fullEuler.pngbin0 -> 12127 bytes
-rw-r--r--math2373/lab6/lab6.txt3337
-rw-r--r--math2373/lab6/partialEuler.pngbin0 -> 9611 bytes
-rw-r--r--math2373/lab7/lab7.txt135
-rw-r--r--math2373/lab7/p100.m20
-rw-r--r--math2373/lab7/p100OG.m19
-rw-r--r--math2373/lab8.txt148
-rw-r--r--math2373/lab9.txt323
28 files changed, 5744 insertions, 0 deletions
diff --git a/math2373/FinalGraph.png b/math2373/FinalGraph.png
new file mode 100644
index 0000000..5303c6b
--- /dev/null
+++ b/math2373/FinalGraph.png
Binary files differ
diff --git a/math2373/lab1.txt b/math2373/lab1.txt
new file mode 100644
index 0000000..75b2264
--- /dev/null
+++ b/math2373/lab1.txt
@@ -0,0 +1,466 @@
+27+48
+
+
+ 75
+
+27-48
+
+
+ -21
+
+27*48
+
+
+ 1296
+
+sqrt(16)
+
+
+ 4
+
+27/48
+
+
+ 0.5625
+
+16.5*(38.5+71/40)
+
+
+ 664.5375
+
+2^5
+
+
+ 32
+
+5*3^2
+
+
+ 45
+
+(5*3)^2
+
+
+ 225
+
+5*(3^2)
+
+
+ 45
+
+x=7
+
+
+ 7
+
+y=9
+
+
+ 9
+
+x+y
+
+
+
+ 16
+
+x*y
+
+
+
+ 63
+
+x/y
+
+
+
+ 0.7778
+
+x^2
+
+
+
+ 49
+
+x=25
+
+
+ 25
+
+y=40
+
+
+ 40
+
+x+y
+
+
+
+ 65
+
+x*y
+
+
+
+ 1000
+
+x/y
+
+
+
+ 0.6250
+
+(8*x)/5
+
+
+ 40
+
+6*x+9*y
+
+
+ 510
+
+4+5
+
+ 9
+
+ans+10
+
+
+ 19
+
+ans+100
+
+
+ 119
+
+x=1, y=3, 3*x+7*y, 9*y, (5*y)/(2*x+y)
+
+ 1
+
+
+ 3
+
+
+ 24
+
+
+ 27
+
+
+ 3
+
+who
+
+ans x y
+
+dog=3
+
+DOG=7
+
+
+who
+
+DOG ans dog x y
+
+clear dog
+
+who
+
+Your variables are:
+
+DOG ans x y
+
+clear
+
+who
+
+pi
+
+
+
+ 3.1416
+
+5+pi
+
+
+
+ 8.1416
+
+5*pi
+
+
+
+ 15.7080
+
+sqrt(25)
+
+
+
+ 5
+
+sqrt(24)
+
+
+
+ 4.8990
+
+sqrt(-9)
+
+
+
+ 0.0000 + 3.0000i
+
+exp(1)
+
+
+
+ 2.7183
+
+exp(5)
+
+
+
+ 148.4132
+
+sinh(3)
+
+
+
+ 10.0179
+
+cosh(5)
+
+
+
+ 74.2099
+
+sinh(sqrt(5))
+
+
+
+ 4.6248
+
+tan(sqrt(5))
+
+
+
+ -1.2746
+
+cos(pi)
+
+
+
+ -1
+
+sin(pi/3)
+
+
+
+ 0.8660
+
+x=sin(1), y=cos(2)
+
+x =
+
+ 0.8415
+
+
+y =
+
+ -0.4161
+
+x+y, x*y
+
+
+
+ 0.4253
+
+
+
+
+ -0.3502
+
+log(8),log(100),asin(.5)+log(5)
+
+
+
+ 2.0794
+
+
+
+
+ 4.6052
+
+
+
+
+ 2.1330
+
+w=5-8i, z=3+4i
+
+w =
+
+ 5.0000 - 8.0000i
+
+
+z =
+
+ 3.0000 + 4.0000i
+
+4*z+w,z/w
+
+
+
+ 17.0000 + 8.0000i
+
+
+
+
+ -0.1910 + 0.4944i
+
+pi
+
+
+
+ 3.1416
+
+format long
+pi
+
+
+
+ 3.141592653589793
+
+format short
+pi
+
+
+
+ 3.1416
+
+6/14
+
+
+
+ 0.4286
+
+format rational
+6/14
+
+
+
+ 3/7
+
+format short
+2^20
+
+
+
+ 1048576
+
+2^20;
+[4 3 7 8 10 13]
+
+
+
+ 4 3 7 8 10 13
+
+[4; 3; 7; 8; 10; 13]
+
+
+
+ 4
+ 3
+ 7
+ 8
+ 10
+ 13
+
+[4 3 7; 8 10 13]
+
+
+
+ 4 3 7
+ 8 10 13
+
+[4 3; 7 8; 10 13]
+
+
+
+ 4 3
+ 7 8
+ 10 13
+
+x=[3 12 7], y=[-2 4 9]
+
+x =
+
+ 3 12 7
+
+
+y =
+
+ -2 4 9
+
+x+y,3*x
+
+
+
+ 1 16 16
+
+
+
+
+ 9 36 21
+
+clear
+
+a=[3 5 7 9]
+
+a =
+
+ 3 5 7 9
+
+b=[8,-2,4,11]
+
+b =
+
+ 8 -2 4 11
+
+a-5*b
+
+
+
+ -37 15 -13 -46
+
+dot(a,b)
+
+
+
+ 141
+
+x=[4 3 2 9], y=[7 5 11 6]
+
+x =
+
+ 4 3 2 9
+
+
+y =
+
+ 7 5 11 6
+
+x.*y
+
+
+
+ 28 15 22 54
+
+x.^2
+
+
+
+ 16 9 4 81
+
+diary off
diff --git a/math2373/lab2.txt b/math2373/lab2.txt
new file mode 100644
index 0000000..689a36b
--- /dev/null
+++ b/math2373/lab2.txt
@@ -0,0 +1,1024 @@
+format rational
+A=[2 -1 4 -5 19; -1 3 -2 -1 -18; 0 1 5 -6 12; 3 -8 1 0 29]
+
+A =
+
+ 2 -1 4 -5 19
+ -1 3 -2 -1 -18
+ 0 1 5 -6 12
+ 3 -8 1 0 29
+
+
+
+A(1,:)=A(1,:)+A(2,:)
+
+A =
+
+ 1 2 2 -6 1
+ -1 3 -2 -1 -18
+ 0 1 5 -6 12
+ 3 -8 1 0 29
+
+
+A(2,:)=A(2,:)+A(1,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 5 0 -7 -17
+ 0 1 5 -6 12
+ 3 -8 1 0 29
+
+A(4,:)=A(4,:)-3*A(1,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 5 0 -7 -17
+ 0 1 5 -6 12
+ 0 -14 -5 18 26
+
+A(2,:)=A(2,:)-4*A(3,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 1 5 -6 12
+ 0 -14 -5 18 26
+
+A(3,:)=A(2,:)-A(3,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 -25 23 -77
+ 0 -14 -5 18 26
+
+
+A(4,:)=A(2,:)+14*A(2,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 -25 23 -77
+ 0 15 -300 255 -975
+
+A(4,:)=A(2,:)-14*A(2,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 -25 23 -77
+ 0 -13 260 -221 845
+
+A =
+ A =
+ ↑
+{Error: Invalid expression. Check for missing or extra characters.
+}
+A = Aog
+
+A =
+
+ 2 -1 4 -5 19
+ -1 3 -2 -1 -18
+ 0 1 5 -6 12
+ 3 -8 1 0 29
+
+A(1,:)=A(1,:)+A(2,:)
+
+A =
+
+ 1 2 2 -6 1
+ -1 3 -2 -1 -18
+ 0 1 5 -6 12
+ 3 -8 1 0 29
+
+A(2,:)=A(2,:)+A(1,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 5 0 -7 -17
+ 0 1 5 -6 12
+ 3 -8 1 0 29
+
+A(4,:)=A(4,:)-3*A(1,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 5 0 -7 -17
+ 0 1 5 -6 12
+ 0 -14 -5 18 26
+
+Aog2=a
+{Undefined function or variable 'a'.
+}
+Aog2=A
+
+Aog2 =
+
+ 1 2 2 -6 1
+ 0 5 0 -7 -17
+ 0 1 5 -6 12
+ 0 -14 -5 18 26
+
+A(2,:)=A(2,:)-4*A(3,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 1 5 -6 12
+ 0 -14 -5 18 26
+
+A(3,:)=A(2,:)-A(3,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 -25 23 -77
+ 0 -14 -5 18 26
+
+A(4,:)=A(4,:)+14*A(2,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 -25 23 -77
+ 0 0 -285 256 -884
+
+Aog3=A
+
+Aog3 =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 -25 23 -77
+ 0 0 -285 256 -884
+
+A(3,:)=A(3,:)/-25
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 1 -23/25 77/25
+ 0 0 -285 256 -884
+
+A(4,:)=A(4,:)+285*A(3,:)
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 1 -23/25 77/25
+ 0 0 0 -31/5 -31/5
+
+A(4,:)=A(4,:)*5
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 1 -23/25 77/25
+ 0 0 0 -31 -31
+
+A(4,:)=A(4,:)/-31
+
+A =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+Aref=A
+
+Aref =
+
+ 1 2 2 -6 1
+ 0 1 -20 17 -65
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(1,:)=A(1,:)-2*A(2,:)
+
+A =
+
+ 1 0 42 -40 131
+ 0 1 -20 17 -65
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(1,:)=A(1,:)-42*A(3,:)
+
+A =
+
+ 1 0 0 -34/25 41/25
+ 0 1 -20 17 -65
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(2,:)=A(2,:)-20*A(3,:)
+
+A =
+
+ 1 0 0 -34/25 41/25
+ 0 1 -40 177/5 -633/5
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(2,:)=A(2,:)+20*A(3,:)
+
+A =
+
+ 1 0 0 -34/25 41/25
+ 0 1 -20 17 -65
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(2,:)=A(2,:)+20*A(3,:)
+
+A =
+
+ 1 0 0 -34/25 41/25
+ 0 1 0 -7/5 -17/5
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(1,:)=A(1,:)+(34/25)*A(5,:)
+{Index in position 1 exceeds array bounds (must not exceed 4).
+}
+A(1,:)=A(1,:)+(34/25)*A(4,:)
+
+A =
+
+ 1 0 0 * 3
+ 0 1 0 -7/5 -17/5
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(2,:)=A(2,:)+(7/5)*A(4,:)
+
+A =
+
+ 1 0 0 * 3
+ 0 1 0 * -2
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(3,:)=A(3,:)+(23/5)*A(4,:)
+
+A =
+
+ 1 0 0 * 3
+ 0 1 0 * -2
+ 0 0 1 92/25 192/25
+ 0 0 0 1 1
+
+A(3,:)=A(3,:)-(23/5)*A(4,:)
+
+A =
+
+ 1 0 0 * 3
+ 0 1 0 * -2
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(3,:)=A(3,:)-(23/5)*A(4,:)
+
+A =
+
+ 1 0 0 * 3
+ 0 1 0 * -2
+ 0 0 1 -138/25 -38/25
+ 0 0 0 1 1
+
+A(3,:)=A(3,:)+(23/5)*A(4,:)
+
+A =
+
+ 1 0 0 * 3
+ 0 1 0 * -2
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(3,:)=A(3,:)-(23/5)*A(4,:)
+
+A =
+
+ 1 0 0 * 3
+ 0 1 0 * -2
+ 0 0 1 -138/25 -38/25
+ 0 0 0 1 1
+
+A(3,:)=A(3,:)+(23/5)*A(4,:)
+
+A =
+
+ 1 0 0 * 3
+ 0 1 0 * -2
+ 0 0 1 -23/25 77/25
+ 0 0 0 1 1
+
+A(3,:)=A(3,:)+(23/25)*A(4,:)
+
+A =
+
+ 1 0 0 * 3
+ 0 1 0 * -2
+ 0 0 1 * 4
+ 0 0 0 1 1
+
+Aans=A
+
+Aans =
+
+ 1 0 0 * 3
+ 0 1 0 * -2
+ 0 0 1 * 4
+ 0 0 0 1 1
+
+diary off
+rref(Aog)
+
+ans =
+
+ 1 0 0 0 3
+ 0 1 0 0 -2
+ 0 0 1 0 4
+ 0 0 0 1 1
+
+diary off
+format rational
+A=[-2 1 9 1; 3 3 -4 2; 1 4 5 5]
+
+A =
+
+ Columns 1 through 3
+
+ -2 1 9
+ 3 3 -4
+ 1 4 5
+
+ Column 4
+
+ 1
+ 2
+ 5
+
+Asave=A
+
+Asave =
+
+ Columns 1 through 3
+
+ -2 1 9
+ 3 3 -4
+ 1 4 5
+
+ Column 4
+
+ 1
+ 2
+ 5
+
+a=A
+
+a =
+
+ Columns 1 through 3
+
+ -2 1 9
+ 3 3 -4
+ 1 4 5
+
+ Column 4
+
+ 1
+ 2
+ 5
+
+a([1 3],:)=a([3 1],:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 4 5
+ 3 3 -4
+ -2 1 9
+
+ Column 4
+
+ 5
+ 2
+ 1
+
+a(2,:)=a(2,:)-3+a(1,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 4 5
+ 1 4 -2
+ -2 1 9
+
+ Column 4
+
+ 5
+ 4
+ 1
+
+a(2,:)=a(2,:)+3-a(1,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 4 5
+ 3 3 -4
+ -2 1 9
+
+ Column 4
+
+ 5
+ 2
+ 1
+
+a(2,:)=a(2,:)-3*a(1,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 4 5
+ 0 -9 -19
+ -2 1 9
+
+ Column 4
+
+ 5
+ -13
+ 1
+
+a(3,:)=a(3,:)+2*a(1,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 4 5
+ 0 -9 -19
+ 0 9 19
+
+ Column 4
+
+ 5
+ -13
+ 11
+
+a(2,:)=a(2,:)/-9
+
+a =
+
+ Columns 1 through 3
+
+ 1 4 5
+ 0 1 19/9
+ 0 9 19
+
+ Column 4
+
+ 5
+ 13/9
+ 11
+
+a(3,:)=a(3,:)-9*a(2,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 4 5
+ 0 1 19/9
+ 0 0 0
+
+ Column 4
+
+ 5
+ 13/9
+ -2
+
+ref2=a
+
+ref2 =
+
+ Columns 1 through 3
+
+ 1 4 5
+ 0 1 19/9
+ 0 0 0
+
+ Column 4
+
+ 5
+ 13/9
+ -2
+
+a=[2 3 -4 1 2; 3 -1 -1 2 4; 1 -7 5 -1 6]
+
+a =
+
+ Columns 1 through 3
+
+ 2 3 -4
+ 3 -1 -1
+ 1 -7 5
+
+ Columns 4 through 5
+
+ 1 2
+ 2 4
+ -1 6
+
+a([1 3],:)=a([3 1],:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 -7 5
+ 3 -1 -1
+ 2 3 -4
+
+ Columns 4 through 5
+
+ -1 6
+ 2 4
+ 1 2
+
+a(2,:)=a(2,:)-3*a(1,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 -7 5
+ 0 20 -16
+ 2 3 -4
+
+ Columns 4 through 5
+
+ -1 6
+ 5 -14
+ 1 2
+
+a(3,:)=a(3,:)-2*a(1,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 -7 5
+ 0 20 -16
+ 0 17 -14
+
+ Columns 4 through 5
+
+ -1 6
+ 5 -14
+ 3 -10
+
+a(2,:)=a(2,:)/20
+
+a =
+
+ Columns 1 through 3
+
+ 1 -7 5
+ 0 1 -4/5
+ 0 17 -14
+
+ Columns 4 through 5
+
+ -1 6
+ 1/4 -7/10
+ 3 -10
+
+a(3,:)=a(3,:)-17*a(2,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 -7 5
+ 0 1 -4/5
+ 0 0 -2/5
+
+ Columns 4 through 5
+
+ -1 6
+ 1/4 -7/10
+ -5/4 19/10
+
+a(3,:)=a(3,:)*(-5/2)
+
+a =
+
+ Columns 1 through 3
+
+ 1 -7 5
+ 0 1 -4/5
+ 0 0 1
+
+ Columns 4 through 5
+
+ -1 6
+ 1/4 -7/10
+ 25/8 -19/4
+
+A=[2 3 -4 1 2; 3 -1 -1 2 4; 1 -7 5 -1 6]
+
+A =
+
+ Columns 1 through 3
+
+ 2 3 -4
+ 3 -1 -1
+ 1 -7 5
+
+ Columns 4 through 5
+
+ 1 2
+ 2 4
+ -1 6
+
+rref(A)
+
+ans =
+
+ Columns 1 through 3
+
+ 1 0 0
+ 0 1 0
+ 0 0 1
+
+ Columns 4 through 5
+
+ 21/8 -7/4
+ 11/4 -9/2
+ 25/8 -19/4
+
+a
+
+a =
+
+ Columns 1 through 3
+
+ 1 -7 5
+ 0 1 -4/5
+ 0 0 1
+
+ Columns 4 through 5
+
+ -1 6
+ 1/4 -7/10
+ 25/8 -19/4
+
+a(1,:)=a(1,:)+7*a(2,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 0 -3/5
+ 0 1 -4/5
+ 0 0 1
+
+ Columns 4 through 5
+
+ 3/4 11/10
+ 1/4 -7/10
+ 25/8 -19/4
+
+a(1,:)=a(1,:)+(3/5)*a(3,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 0 *
+ 0 1 -4/5
+ 0 0 1
+
+ Columns 4 through 5
+
+ 21/8 -7/4
+ 1/4 -7/10
+ 25/8 -19/4
+
+a(2,:)=a(2,:)+(4/5)*a(3,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 0 *
+ 0 1 *
+ 0 0 1
+
+ Columns 4 through 5
+
+ 21/8 -7/4
+ 11/4 -9/2
+ 25/8 -19/4
+
+rref(A)
+
+ans =
+
+ Columns 1 through 3
+
+ 1 0 0
+ 0 1 0
+ 0 0 1
+
+ Columns 4 through 5
+
+ 21/8 -7/4
+ 11/4 -9/2
+ 25/8 -19/4
+
+rref3=a
+
+rref3 =
+
+ Columns 1 through 3
+
+ 1 0 *
+ 0 1 *
+ 0 0 1
+
+ Columns 4 through 5
+
+ 21/8 -7/4
+ 11/4 -9/2
+ 25/8 -19/4
+
+rref3a=a
+
+rref3a =
+
+ Columns 1 through 3
+
+ 1 0 *
+ 0 1 *
+ 0 0 1
+
+ Columns 4 through 5
+
+ 21/8 -7/4
+ 11/4 -9/2
+ 25/8 -19/4
+
+delete rref3
+[Warning: File 'rref3' not found.]
+remove rref3
+{Undefined function 'remove' for input arguments of
+type 'char'.
+}
+a=[2 3 -4 4; 8 11 -7 8; 2 2 -4 -3]
+
+a =
+
+ Columns 1 through 3
+
+ 2 3 -4
+ 8 11 -7
+ 2 2 -4
+
+ Column 4
+
+ 4
+ 8
+ -3
+
+A=a
+
+A =
+
+ Columns 1 through 3
+
+ 2 3 -4
+ 8 11 -7
+ 2 2 -4
+
+ Column 4
+
+ 4
+ 8
+ -3
+
+rref(A)
+
+ans =
+
+ Columns 1 through 3
+
+ 1 0 0
+ 0 1 0
+ 0 0 1
+
+ Column 4
+
+ -157/18
+ 7
+ -1/9
+
+a
+
+a =
+
+ Columns 1 through 3
+
+ 2 3 -4
+ 8 11 -7
+ 2 2 -4
+
+ Column 4
+
+ 4
+ 8
+ -3
+
+a(1,:)=a(1,:)/2
+
+a =
+
+ Columns 1 through 3
+
+ 1 3/2 -2
+ 8 11 -7
+ 2 2 -4
+
+ Column 4
+
+ 2
+ 8
+ -3
+
+a(2,:)=a(2,:)-8*a(1,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 3/2 -2
+ 0 -1 9
+ 2 2 -4
+
+ Column 4
+
+ 2
+ -8
+ -3
+
+a(3,:)=a(3,:)-2*a(1,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 3/2 -2
+ 0 -1 9
+ 0 -1 0
+
+ Column 4
+
+ 2
+ -8
+ -7
+
+a(2,:)=a(2,:)/-1
+
+a =
+
+ Columns 1 through 3
+
+ 1 3/2 -2
+ 0 1 -9
+ 0 -1 0
+
+ Column 4
+
+ 2
+ 8
+ -7
+
+a(3,:)=a(3,:)+1*a(2,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 3/2 -2
+ 0 1 -9
+ 0 0 -9
+
+ Column 4
+
+ 2
+ 8
+ 1
+
+a(3,:)=a(3,:)/-9
+
+a =
+
+ Columns 1 through 3
+
+ 1 3/2 -2
+ 0 1 -9
+ 0 0 1
+
+ Column 4
+
+ 2
+ 8
+ -1/9
+
+a(1,:)=a(1,:)-(3/2)*a(2,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 0 23/2
+ 0 1 -9
+ 0 0 1
+
+ Column 4
+
+ -10
+ 8
+ -1/9
+
+a(2,:)=a(2,:)+9*a(3,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 0 23/2
+ 0 1 0
+ 0 0 1
+
+ Column 4
+
+ -10
+ 7
+ -1/9
+
+a(1,:)=a(1,:)-(23/2)*a(3,:)
+
+a =
+
+ Columns 1 through 3
+
+ 1 0 0
+ 0 1 0
+ 0 0 1
+
+ Column 4
+
+ -157/18
+ 7
+ -1/9
+
+rref3b=a
+
+rref3b =
+
+ Columns 1 through 3
+
+ 1 0 0
+ 0 1 0
+ 0 0 1
+
+ Column 4
+
+ -157/18
+ 7
+ -1/9
+
+diary off
diff --git a/math2373/lab3.txt b/math2373/lab3.txt
new file mode 100644
index 0000000..5ddc15a
--- /dev/null
+++ b/math2373/lab3.txt
@@ -0,0 +1,12 @@
+ezplot(y=t^3-9*t, [-4,4,-30,30])
+ ezplot(y=t^3-9*t, [-4,4,-30,30])
+ ↑
+{Error: Incorrect use of '=' operator. To assign a value to a variable,
+use '='. To compare values for equality, use '=='.
+}
+ezplot('y=t^3-9*t', [-4,4,-30,30])
+hold on
+ezplot('y=t^3-(49/4)*t', [-4,4,-30,30])
+ezplot('y=t^3-16*t', [-4,4,-30,30])
+hold off
+ezplot('y=1+cos(t)', [0,10,-2,4])
diff --git a/math2373/lab4.txt b/math2373/lab4.txt
new file mode 100644
index 0000000..6360716
--- /dev/null
+++ b/math2373/lab4.txt
@@ -0,0 +1,173 @@
+v.*w
+
+ans =
+
+ 10 36 32 -12 42
+
+v*w
+{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('mtimes')" style="font-weight:bold"> * </a>
+Incorrect dimensions for matrix multiplication. Check that the number of columns in the first
+matrix matches the number of rows in the second matrix. To perform elementwise
+multiplication, use '.*'.
+}
+v.^3
+
+ans =
+
+ 8 27 64 -8 216
+
+v./w
+
+ans =
+
+ 0.4000 0.2500 0.5000 -0.3333 0.8571
+
+a = [0,1,2,3,4,5]
+
+a =
+
+ 0 1 2 3 4 5
+
+b=a.^3-9*a.^2+18*a
+
+b =
+
+ 0 10 8 0 -8 -10
+
+plot(a,b)
+c=(0:0.1:5);
+d=c.^3-9*c.^2+18*c;
+plot(c,d);
+c,d
+
+c =
+
+ Columns 1 through 9
+
+ 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000
+
+ Columns 10 through 18
+
+ 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000
+
+ Columns 19 through 27
+
+ 1.8000 1.9000 2.0000 2.1000 2.2000 2.3000 2.4000 2.5000 2.6000
+
+ Columns 28 through 36
+
+ 2.7000 2.8000 2.9000 3.0000 3.1000 3.2000 3.3000 3.4000 3.5000
+
+ Columns 37 through 45
+
+ 3.6000 3.7000 3.8000 3.9000 4.0000 4.1000 4.2000 4.3000 4.4000
+
+ Columns 46 through 51
+
+ 4.5000 4.6000 4.7000 4.8000 4.9000 5.0000
+
+
+d =
+
+ Columns 1 through 9
+
+ 0 1.7110 3.2480 4.6170 5.8240 6.8750 7.7760 8.5330 9.1520
+
+ Columns 10 through 18
+
+ 9.6390 10.0000 10.2410 10.3680 10.3870 10.3040 10.1250 9.8560 9.5030
+
+ Columns 19 through 27
+
+ 9.0720 8.5690 8.0000 7.3710 6.6880 5.9570 5.1840 4.3750 3.5360
+
+ Columns 28 through 36
+
+ 2.6730 1.7920 0.8990 0 -0.8990 -1.7920 -2.6730 -3.5360 -4.3750
+
+ Columns 37 through 45
+
+ -5.1840 -5.9570 -6.6880 -7.3710 -8.0000 -8.5690 -9.0720 -9.5030 -9.8560
+
+ Columns 46 through 51
+
+ -10.1250 -10.3040 -10.3870 -10.3680 -10.2410 -10.0000
+
+e =(-2:0.2:6);
+g = e.^3-5*e.^2-4*e+20
+
+g =
+
+ Columns 1 through 9
+
+ 0 5.1680 9.5040 13.0560 15.8720 18.0000 19.4880 20.3840 20.7360
+
+ Columns 10 through 18
+
+ 20.5920 20.0000 19.0080 17.6640 16.0160 14.1120 12.0000 9.7280 7.3440
+
+ Columns 19 through 27
+
+ 4.8960 2.4320 0 -2.3520 -4.5760 -6.6240 -8.4480 -10.0000 -11.2320
+
+ Columns 28 through 36
+
+ -12.0960 -12.5440 -12.5280 -12.0000 -10.9120 -9.2160 -6.8640 -3.8080 0
+
+ Columns 37 through 41
+
+ 4.6080 10.0640 16.4160 23.7120 32.0000
+
+plot(e,g)
+d = (0, 2, 4, 5, 6, 8)
+ d = (0, 2, 4, 5, 6, 8)
+ ↑
+{Error: Invalid expression. When calling a function or indexing a variable, use parentheses.
+Otherwise, check for mismatched delimiters.
+}
+d = [0, 2, 4, 5, 6, 8]
+
+d =
+
+ 0 2 4 5 6 8
+
+f = [0, 20, 30, 50, 70, 100];
+plot(d,f,’r:p’);
+ plot(d,f,’r:p’);
+ ↑
+{Error: Invalid text character. Check for unsupported symbol, invisible character, or
+pasting of non-ASCII characters.
+}
+plot(d,f,'r:p');
+plot(d,f,'b:s');
+plot(d,f,’b:p’);
+ plot(d,f,’b:p’);
+ ↑
+{Error: Invalid text character. Check for unsupported symbol,
+invisible character, or pasting of non-ASCII characters.
+}
+xlabel('Dog years');
+ylabel('Human years');
+title('The passage of time')
+plot(d,f,'b:p');
+q = [0,2,4,5,6,8]
+
+q =
+
+ 0 2 4 5 6 8
+
+q = [0,2,4,5,6,8];
+r = [0,20,30,30,50,100];
+plot(d,f,'r:p');
+hold on
+lsline
+hold off
+plot(q,r,'r:p');
+lsline;
+man
+{Undefined function or variable 'man'.
+}
+xlabel('Decades of Life')
+ylabel('Likliness of Death');
+title('Funny Graph Title');
+diary off
diff --git a/math2373/lab4/graph2lab5.png b/math2373/lab4/graph2lab5.png
new file mode 100644
index 0000000..7900a8a
--- /dev/null
+++ b/math2373/lab4/graph2lab5.png
Binary files differ
diff --git a/math2373/lab4/graph3lab5.png b/math2373/lab4/graph3lab5.png
new file mode 100644
index 0000000..3d36211
--- /dev/null
+++ b/math2373/lab4/graph3lab5.png
Binary files differ
diff --git a/math2373/lab4/graph4lab5.png b/math2373/lab4/graph4lab5.png
new file mode 100644
index 0000000..98ab9d8
--- /dev/null
+++ b/math2373/lab4/graph4lab5.png
Binary files differ
diff --git a/math2373/lab4/graph5lab5.png b/math2373/lab4/graph5lab5.png
new file mode 100644
index 0000000..60f8dcc
--- /dev/null
+++ b/math2373/lab4/graph5lab5.png
Binary files differ
diff --git a/math2373/lab4/graph6lab5.png b/math2373/lab4/graph6lab5.png
new file mode 100644
index 0000000..21b765e
--- /dev/null
+++ b/math2373/lab4/graph6lab5.png
Binary files differ
diff --git a/math2373/lab4/testt.png b/math2373/lab4/testt.png
new file mode 100644
index 0000000..278d4dc
--- /dev/null
+++ b/math2373/lab4/testt.png
Binary files differ
diff --git a/math2373/lab5/lab4.txt b/math2373/lab5/lab4.txt
new file mode 100644
index 0000000..b45f0f3
--- /dev/null
+++ b/math2373/lab5/lab4.txt
@@ -0,0 +1,59 @@
+N=10; sum_of_fourths; y
+
+y =
+
+ Columns 1 through 5
+
+ 0 1 17 98 354
+
+ Columns 6 through 10
+
+ 979 2275 4676 8772 15333
+
+ Column 11
+
+ 25333
+
+N=10; sum_of_nn; y
+
+y =
+
+ 1.2913
+
+N=10; sum_of_nn; y
+
+y =
+
+ 1.2913
+
+N=10; multseries; y
+
+y =
+
+ 3.0677
+
+N=100; multseries; y
+
+y =
+
+ 3.1338
+
+N=1000; multseries; y
+
+y =
+
+ 3.1408
+
+N=10000; multseries; y
+
+y =
+
+ 3.1415
+
+N=100000; multseries; y
+
+y =
+
+ 3.1416
+
+diary off
diff --git a/math2373/lab5/multseries.m b/math2373/lab5/multseries.m
new file mode 100644
index 0000000..d4b06d6
--- /dev/null
+++ b/math2373/lab5/multseries.m
@@ -0,0 +1,4 @@
+y=2;
+for n=1:N
+ y=y*((2*n)*(2*n))/((2*n-1)*(2*n+1));
+end \ No newline at end of file
diff --git a/math2373/lab5/sum_of_fourths.m b/math2373/lab5/sum_of_fourths.m
new file mode 100644
index 0000000..80c535f
--- /dev/null
+++ b/math2373/lab5/sum_of_fourths.m
@@ -0,0 +1,4 @@
+y(1)=0;
+for n=1:N
+ y(n+1)=y(n)+n^4;
+end \ No newline at end of file
diff --git a/math2373/lab5/sum_of_nn.m b/math2373/lab5/sum_of_nn.m
new file mode 100644
index 0000000..dd191b7
--- /dev/null
+++ b/math2373/lab5/sum_of_nn.m
@@ -0,0 +1,4 @@
+y=0;
+for n=1:N
+ y=y+1/(n^n);
+end \ No newline at end of file
diff --git a/math2373/lab6/alltogethernow.png b/math2373/lab6/alltogethernow.png
new file mode 100644
index 0000000..acd239f
--- /dev/null
+++ b/math2373/lab6/alltogethernow.png
Binary files differ
diff --git a/math2373/lab6/approx.m b/math2373/lab6/approx.m
new file mode 100644
index 0000000..8fb87f2
--- /dev/null
+++ b/math2373/lab6/approx.m
@@ -0,0 +1,6 @@
+z=8-2*2-7*exp(-2/2);%exact solution at t=2
+for k=1:5
+ N=5*2^(k-1);eulerN;
+ %difference between Euler approximation and exact solution at t=2.
+ error(k)=y(N+1)-z;
+end \ No newline at end of file
diff --git a/math2373/lab6/badEstimate.png b/math2373/lab6/badEstimate.png
new file mode 100644
index 0000000..cba0f75
--- /dev/null
+++ b/math2373/lab6/badEstimate.png
Binary files differ
diff --git a/math2373/lab6/euler5.m b/math2373/lab6/euler5.m
new file mode 100644
index 0000000..2de61e3
--- /dev/null
+++ b/math2373/lab6/euler5.m
@@ -0,0 +1,5 @@
+h=2/5; t(1)=0; y(1)=1;
+for n=1:5
+ t(n+1)=t(n)+h;
+ y(n+1)=y(n)+(-y(n)+t(n))*h;
+end \ No newline at end of file
diff --git a/math2373/lab6/eulerN.m b/math2373/lab6/eulerN.m
new file mode 100644
index 0000000..13a7cbc
--- /dev/null
+++ b/math2373/lab6/eulerN.m
@@ -0,0 +1,5 @@
+h=2/N; t(1)=0; y(1)=1;
+for n=1:N
+ t(n+1)=t(n)+h;
+ y(n+1)=y(n)+(-0.5*y(n)-t(n)+2)*h;
+end \ No newline at end of file
diff --git a/math2373/lab6/fullEuler.png b/math2373/lab6/fullEuler.png
new file mode 100644
index 0000000..6e70356
--- /dev/null
+++ b/math2373/lab6/fullEuler.png
Binary files differ
diff --git a/math2373/lab6/lab6.txt b/math2373/lab6/lab6.txt
new file mode 100644
index 0000000..e11acb6
--- /dev/null
+++ b/math2373/lab6/lab6.txt
@@ -0,0 +1,3337 @@
+N=10; eulerN; plot(t,y);
+hold on
+N=5; eulerN; plot(t,y);
+clear
+N=5; eulerN; plot(t,y);
+hold on
+N=10; eulerN; plot(t,y);
+N=20; eulerN; plot(t,y);
+N=40; eulerN; plot(t,y);
+N=80; eulerN; plot(t,y);
+x=0:0.001:2
+
+x =
+
+ Columns 1 through 6
+
+ 0 0.0010 0.0020 0.0030 0.0040 0.0050
+
+ Columns 7 through 12
+
+ 0.0060 0.0070 0.0080 0.0090 0.0100 0.0110
+
+ Columns 13 through 18
+
+ 0.0120 0.0130 0.0140 0.0150 0.0160 0.0170
+
+ Columns 19 through 24
+
+ 0.0180 0.0190 0.0200 0.0210 0.0220 0.0230
+
+ Columns 25 through 30
+
+ 0.0240 0.0250 0.0260 0.0270 0.0280 0.0290
+
+ Columns 31 through 36
+
+ 0.0300 0.0310 0.0320 0.0330 0.0340 0.0350
+
+ Columns 37 through 42
+
+ 0.0360 0.0370 0.0380 0.0390 0.0400 0.0410
+
+ Columns 43 through 48
+
+ 0.0420 0.0430 0.0440 0.0450 0.0460 0.0470
+
+ Columns 49 through 54
+
+ 0.0480 0.0490 0.0500 0.0510 0.0520 0.0530
+
+ Columns 55 through 60
+
+ 0.0540 0.0550 0.0560 0.0570 0.0580 0.0590
+
+ Columns 61 through 66
+
+ 0.0600 0.0610 0.0620 0.0630 0.0640 0.0650
+
+ Columns 67 through 72
+
+ 0.0660 0.0670 0.0680 0.0690 0.0700 0.0710
+
+ Columns 73 through 78
+
+ 0.0720 0.0730 0.0740 0.0750 0.0760 0.0770
+
+ Columns 79 through 84
+
+ 0.0780 0.0790 0.0800 0.0810 0.0820 0.0830
+
+ Columns 85 through 90
+
+ 0.0840 0.0850 0.0860 0.0870 0.0880 0.0890
+
+ Columns 91 through 96
+
+ 0.0900 0.0910 0.0920 0.0930 0.0940 0.0950
+
+ Columns 97 through 102
+
+ 0.0960 0.0970 0.0980 0.0990 0.1000 0.1010
+
+ Columns 103 through 108
+
+ 0.1020 0.1030 0.1040 0.1050 0.1060 0.1070
+
+ Columns 109 through 114
+
+ 0.1080 0.1090 0.1100 0.1110 0.1120 0.1130
+
+ Columns 115 through 120
+
+ 0.1140 0.1150 0.1160 0.1170 0.1180 0.1190
+
+ Columns 121 through 126
+
+ 0.1200 0.1210 0.1220 0.1230 0.1240 0.1250
+
+ Columns 127 through 132
+
+ 0.1260 0.1270 0.1280 0.1290 0.1300 0.1310
+
+ Columns 133 through 138
+
+ 0.1320 0.1330 0.1340 0.1350 0.1360 0.1370
+
+ Columns 139 through 144
+
+ 0.1380 0.1390 0.1400 0.1410 0.1420 0.1430
+
+ Columns 145 through 150
+
+ 0.1440 0.1450 0.1460 0.1470 0.1480 0.1490
+
+ Columns 151 through 156
+
+ 0.1500 0.1510 0.1520 0.1530 0.1540 0.1550
+
+ Columns 157 through 162
+
+ 0.1560 0.1570 0.1580 0.1590 0.1600 0.1610
+
+ Columns 163 through 168
+
+ 0.1620 0.1630 0.1640 0.1650 0.1660 0.1670
+
+ Columns 169 through 174
+
+ 0.1680 0.1690 0.1700 0.1710 0.1720 0.1730
+
+ Columns 175 through 180
+
+ 0.1740 0.1750 0.1760 0.1770 0.1780 0.1790
+
+ Columns 181 through 186
+
+ 0.1800 0.1810 0.1820 0.1830 0.1840 0.1850
+
+ Columns 187 through 192
+
+ 0.1860 0.1870 0.1880 0.1890 0.1900 0.1910
+
+ Columns 193 through 198
+
+ 0.1920 0.1930 0.1940 0.1950 0.1960 0.1970
+
+ Columns 199 through 204
+
+ 0.1980 0.1990 0.2000 0.2010 0.2020 0.2030
+
+ Columns 205 through 210
+
+ 0.2040 0.2050 0.2060 0.2070 0.2080 0.2090
+
+ Columns 211 through 216
+
+ 0.2100 0.2110 0.2120 0.2130 0.2140 0.2150
+
+ Columns 217 through 222
+
+ 0.2160 0.2170 0.2180 0.2190 0.2200 0.2210
+
+ Columns 223 through 228
+
+ 0.2220 0.2230 0.2240 0.2250 0.2260 0.2270
+
+ Columns 229 through 234
+
+ 0.2280 0.2290 0.2300 0.2310 0.2320 0.2330
+
+ Columns 235 through 240
+
+ 0.2340 0.2350 0.2360 0.2370 0.2380 0.2390
+
+ Columns 241 through 246
+
+ 0.2400 0.2410 0.2420 0.2430 0.2440 0.2450
+
+ Columns 247 through 252
+
+ 0.2460 0.2470 0.2480 0.2490 0.2500 0.2510
+
+ Columns 253 through 258
+
+ 0.2520 0.2530 0.2540 0.2550 0.2560 0.2570
+
+ Columns 259 through 264
+
+ 0.2580 0.2590 0.2600 0.2610 0.2620 0.2630
+
+ Columns 265 through 270
+
+ 0.2640 0.2650 0.2660 0.2670 0.2680 0.2690
+
+ Columns 271 through 276
+
+ 0.2700 0.2710 0.2720 0.2730 0.2740 0.2750
+
+ Columns 277 through 282
+
+ 0.2760 0.2770 0.2780 0.2790 0.2800 0.2810
+
+ Columns 283 through 288
+
+ 0.2820 0.2830 0.2840 0.2850 0.2860 0.2870
+
+ Columns 289 through 294
+
+ 0.2880 0.2890 0.2900 0.2910 0.2920 0.2930
+
+ Columns 295 through 300
+
+ 0.2940 0.2950 0.2960 0.2970 0.2980 0.2990
+
+ Columns 301 through 306
+
+ 0.3000 0.3010 0.3020 0.3030 0.3040 0.3050
+
+ Columns 307 through 312
+
+ 0.3060 0.3070 0.3080 0.3090 0.3100 0.3110
+
+ Columns 313 through 318
+
+ 0.3120 0.3130 0.3140 0.3150 0.3160 0.3170
+
+ Columns 319 through 324
+
+ 0.3180 0.3190 0.3200 0.3210 0.3220 0.3230
+
+ Columns 325 through 330
+
+ 0.3240 0.3250 0.3260 0.3270 0.3280 0.3290
+
+ Columns 331 through 336
+
+ 0.3300 0.3310 0.3320 0.3330 0.3340 0.3350
+
+ Columns 337 through 342
+
+ 0.3360 0.3370 0.3380 0.3390 0.3400 0.3410
+
+ Columns 343 through 348
+
+ 0.3420 0.3430 0.3440 0.3450 0.3460 0.3470
+
+ Columns 349 through 354
+
+ 0.3480 0.3490 0.3500 0.3510 0.3520 0.3530
+
+ Columns 355 through 360
+
+ 0.3540 0.3550 0.3560 0.3570 0.3580 0.3590
+
+ Columns 361 through 366
+
+ 0.3600 0.3610 0.3620 0.3630 0.3640 0.3650
+
+ Columns 367 through 372
+
+ 0.3660 0.3670 0.3680 0.3690 0.3700 0.3710
+
+ Columns 373 through 378
+
+ 0.3720 0.3730 0.3740 0.3750 0.3760 0.3770
+
+ Columns 379 through 384
+
+ 0.3780 0.3790 0.3800 0.3810 0.3820 0.3830
+
+ Columns 385 through 390
+
+ 0.3840 0.3850 0.3860 0.3870 0.3880 0.3890
+
+ Columns 391 through 396
+
+ 0.3900 0.3910 0.3920 0.3930 0.3940 0.3950
+
+ Columns 397 through 402
+
+ 0.3960 0.3970 0.3980 0.3990 0.4000 0.4010
+
+ Columns 403 through 408
+
+ 0.4020 0.4030 0.4040 0.4050 0.4060 0.4070
+
+ Columns 409 through 414
+
+ 0.4080 0.4090 0.4100 0.4110 0.4120 0.4130
+
+ Columns 415 through 420
+
+ 0.4140 0.4150 0.4160 0.4170 0.4180 0.4190
+
+ Columns 421 through 426
+
+ 0.4200 0.4210 0.4220 0.4230 0.4240 0.4250
+
+ Columns 427 through 432
+
+ 0.4260 0.4270 0.4280 0.4290 0.4300 0.4310
+
+ Columns 433 through 438
+
+ 0.4320 0.4330 0.4340 0.4350 0.4360 0.4370
+
+ Columns 439 through 444
+
+ 0.4380 0.4390 0.4400 0.4410 0.4420 0.4430
+
+ Columns 445 through 450
+
+ 0.4440 0.4450 0.4460 0.4470 0.4480 0.4490
+
+ Columns 451 through 456
+
+ 0.4500 0.4510 0.4520 0.4530 0.4540 0.4550
+
+ Columns 457 through 462
+
+ 0.4560 0.4570 0.4580 0.4590 0.4600 0.4610
+
+ Columns 463 through 468
+
+ 0.4620 0.4630 0.4640 0.4650 0.4660 0.4670
+
+ Columns 469 through 474
+
+ 0.4680 0.4690 0.4700 0.4710 0.4720 0.4730
+
+ Columns 475 through 480
+
+ 0.4740 0.4750 0.4760 0.4770 0.4780 0.4790
+
+ Columns 481 through 486
+
+ 0.4800 0.4810 0.4820 0.4830 0.4840 0.4850
+
+ Columns 487 through 492
+
+ 0.4860 0.4870 0.4880 0.4890 0.4900 0.4910
+
+ Columns 493 through 498
+
+ 0.4920 0.4930 0.4940 0.4950 0.4960 0.4970
+
+ Columns 499 through 504
+
+ 0.4980 0.4990 0.5000 0.5010 0.5020 0.5030
+
+ Columns 505 through 510
+
+ 0.5040 0.5050 0.5060 0.5070 0.5080 0.5090
+
+ Columns 511 through 516
+
+ 0.5100 0.5110 0.5120 0.5130 0.5140 0.5150
+
+ Columns 517 through 522
+
+ 0.5160 0.5170 0.5180 0.5190 0.5200 0.5210
+
+ Columns 523 through 528
+
+ 0.5220 0.5230 0.5240 0.5250 0.5260 0.5270
+
+ Columns 529 through 534
+
+ 0.5280 0.5290 0.5300 0.5310 0.5320 0.5330
+
+ Columns 535 through 540
+
+ 0.5340 0.5350 0.5360 0.5370 0.5380 0.5390
+
+ Columns 541 through 546
+
+ 0.5400 0.5410 0.5420 0.5430 0.5440 0.5450
+
+ Columns 547 through 552
+
+ 0.5460 0.5470 0.5480 0.5490 0.5500 0.5510
+
+ Columns 553 through 558
+
+ 0.5520 0.5530 0.5540 0.5550 0.5560 0.5570
+
+ Columns 559 through 564
+
+ 0.5580 0.5590 0.5600 0.5610 0.5620 0.5630
+
+ Columns 565 through 570
+
+ 0.5640 0.5650 0.5660 0.5670 0.5680 0.5690
+
+ Columns 571 through 576
+
+ 0.5700 0.5710 0.5720 0.5730 0.5740 0.5750
+
+ Columns 577 through 582
+
+ 0.5760 0.5770 0.5780 0.5790 0.5800 0.5810
+
+ Columns 583 through 588
+
+ 0.5820 0.5830 0.5840 0.5850 0.5860 0.5870
+
+ Columns 589 through 594
+
+ 0.5880 0.5890 0.5900 0.5910 0.5920 0.5930
+
+ Columns 595 through 600
+
+ 0.5940 0.5950 0.5960 0.5970 0.5980 0.5990
+
+ Columns 601 through 606
+
+ 0.6000 0.6010 0.6020 0.6030 0.6040 0.6050
+
+ Columns 607 through 612
+
+ 0.6060 0.6070 0.6080 0.6090 0.6100 0.6110
+
+ Columns 613 through 618
+
+ 0.6120 0.6130 0.6140 0.6150 0.6160 0.6170
+
+ Columns 619 through 624
+
+ 0.6180 0.6190 0.6200 0.6210 0.6220 0.6230
+
+ Columns 625 through 630
+
+ 0.6240 0.6250 0.6260 0.6270 0.6280 0.6290
+
+ Columns 631 through 636
+
+ 0.6300 0.6310 0.6320 0.6330 0.6340 0.6350
+
+ Columns 637 through 642
+
+ 0.6360 0.6370 0.6380 0.6390 0.6400 0.6410
+
+ Columns 643 through 648
+
+ 0.6420 0.6430 0.6440 0.6450 0.6460 0.6470
+
+ Columns 649 through 654
+
+ 0.6480 0.6490 0.6500 0.6510 0.6520 0.6530
+
+ Columns 655 through 660
+
+ 0.6540 0.6550 0.6560 0.6570 0.6580 0.6590
+
+ Columns 661 through 666
+
+ 0.6600 0.6610 0.6620 0.6630 0.6640 0.6650
+
+ Columns 667 through 672
+
+ 0.6660 0.6670 0.6680 0.6690 0.6700 0.6710
+
+ Columns 673 through 678
+
+ 0.6720 0.6730 0.6740 0.6750 0.6760 0.6770
+
+ Columns 679 through 684
+
+ 0.6780 0.6790 0.6800 0.6810 0.6820 0.6830
+
+ Columns 685 through 690
+
+ 0.6840 0.6850 0.6860 0.6870 0.6880 0.6890
+
+ Columns 691 through 696
+
+ 0.6900 0.6910 0.6920 0.6930 0.6940 0.6950
+
+ Columns 697 through 702
+
+ 0.6960 0.6970 0.6980 0.6990 0.7000 0.7010
+
+ Columns 703 through 708
+
+ 0.7020 0.7030 0.7040 0.7050 0.7060 0.7070
+
+ Columns 709 through 714
+
+ 0.7080 0.7090 0.7100 0.7110 0.7120 0.7130
+
+ Columns 715 through 720
+
+ 0.7140 0.7150 0.7160 0.7170 0.7180 0.7190
+
+ Columns 721 through 726
+
+ 0.7200 0.7210 0.7220 0.7230 0.7240 0.7250
+
+ Columns 727 through 732
+
+ 0.7260 0.7270 0.7280 0.7290 0.7300 0.7310
+
+ Columns 733 through 738
+
+ 0.7320 0.7330 0.7340 0.7350 0.7360 0.7370
+
+ Columns 739 through 744
+
+ 0.7380 0.7390 0.7400 0.7410 0.7420 0.7430
+
+ Columns 745 through 750
+
+ 0.7440 0.7450 0.7460 0.7470 0.7480 0.7490
+
+ Columns 751 through 756
+
+ 0.7500 0.7510 0.7520 0.7530 0.7540 0.7550
+
+ Columns 757 through 762
+
+ 0.7560 0.7570 0.7580 0.7590 0.7600 0.7610
+
+ Columns 763 through 768
+
+ 0.7620 0.7630 0.7640 0.7650 0.7660 0.7670
+
+ Columns 769 through 774
+
+ 0.7680 0.7690 0.7700 0.7710 0.7720 0.7730
+
+ Columns 775 through 780
+
+ 0.7740 0.7750 0.7760 0.7770 0.7780 0.7790
+
+ Columns 781 through 786
+
+ 0.7800 0.7810 0.7820 0.7830 0.7840 0.7850
+
+ Columns 787 through 792
+
+ 0.7860 0.7870 0.7880 0.7890 0.7900 0.7910
+
+ Columns 793 through 798
+
+ 0.7920 0.7930 0.7940 0.7950 0.7960 0.7970
+
+ Columns 799 through 804
+
+ 0.7980 0.7990 0.8000 0.8010 0.8020 0.8030
+
+ Columns 805 through 810
+
+ 0.8040 0.8050 0.8060 0.8070 0.8080 0.8090
+
+ Columns 811 through 816
+
+ 0.8100 0.8110 0.8120 0.8130 0.8140 0.8150
+
+ Columns 817 through 822
+
+ 0.8160 0.8170 0.8180 0.8190 0.8200 0.8210
+
+ Columns 823 through 828
+
+ 0.8220 0.8230 0.8240 0.8250 0.8260 0.8270
+
+ Columns 829 through 834
+
+ 0.8280 0.8290 0.8300 0.8310 0.8320 0.8330
+
+ Columns 835 through 840
+
+ 0.8340 0.8350 0.8360 0.8370 0.8380 0.8390
+
+ Columns 841 through 846
+
+ 0.8400 0.8410 0.8420 0.8430 0.8440 0.8450
+
+ Columns 847 through 852
+
+ 0.8460 0.8470 0.8480 0.8490 0.8500 0.8510
+
+ Columns 853 through 858
+
+ 0.8520 0.8530 0.8540 0.8550 0.8560 0.8570
+
+ Columns 859 through 864
+
+ 0.8580 0.8590 0.8600 0.8610 0.8620 0.8630
+
+ Columns 865 through 870
+
+ 0.8640 0.8650 0.8660 0.8670 0.8680 0.8690
+
+ Columns 871 through 876
+
+ 0.8700 0.8710 0.8720 0.8730 0.8740 0.8750
+
+ Columns 877 through 882
+
+ 0.8760 0.8770 0.8780 0.8790 0.8800 0.8810
+
+ Columns 883 through 888
+
+ 0.8820 0.8830 0.8840 0.8850 0.8860 0.8870
+
+ Columns 889 through 894
+
+ 0.8880 0.8890 0.8900 0.8910 0.8920 0.8930
+
+ Columns 895 through 900
+
+ 0.8940 0.8950 0.8960 0.8970 0.8980 0.8990
+
+ Columns 901 through 906
+
+ 0.9000 0.9010 0.9020 0.9030 0.9040 0.9050
+
+ Columns 907 through 912
+
+ 0.9060 0.9070 0.9080 0.9090 0.9100 0.9110
+
+ Columns 913 through 918
+
+ 0.9120 0.9130 0.9140 0.9150 0.9160 0.9170
+
+ Columns 919 through 924
+
+ 0.9180 0.9190 0.9200 0.9210 0.9220 0.9230
+
+ Columns 925 through 930
+
+ 0.9240 0.9250 0.9260 0.9270 0.9280 0.9290
+
+ Columns 931 through 936
+
+ 0.9300 0.9310 0.9320 0.9330 0.9340 0.9350
+
+ Columns 937 through 942
+
+ 0.9360 0.9370 0.9380 0.9390 0.9400 0.9410
+
+ Columns 943 through 948
+
+ 0.9420 0.9430 0.9440 0.9450 0.9460 0.9470
+
+ Columns 949 through 954
+
+ 0.9480 0.9490 0.9500 0.9510 0.9520 0.9530
+
+ Columns 955 through 960
+
+ 0.9540 0.9550 0.9560 0.9570 0.9580 0.9590
+
+ Columns 961 through 966
+
+ 0.9600 0.9610 0.9620 0.9630 0.9640 0.9650
+
+ Columns 967 through 972
+
+ 0.9660 0.9670 0.9680 0.9690 0.9700 0.9710
+
+ Columns 973 through 978
+
+ 0.9720 0.9730 0.9740 0.9750 0.9760 0.9770
+
+ Columns 979 through 984
+
+ 0.9780 0.9790 0.9800 0.9810 0.9820 0.9830
+
+ Columns 985 through 990
+
+ 0.9840 0.9850 0.9860 0.9870 0.9880 0.9890
+
+ Columns 991 through 996
+
+ 0.9900 0.9910 0.9920 0.9930 0.9940 0.9950
+
+ Columns 997 through 1002
+
+ 0.9960 0.9970 0.9980 0.9990 1.0000 1.0010
+
+ Columns 1003 through 1008
+
+ 1.0020 1.0030 1.0040 1.0050 1.0060 1.0070
+
+ Columns 1009 through 1014
+
+ 1.0080 1.0090 1.0100 1.0110 1.0120 1.0130
+
+ Columns 1015 through 1020
+
+ 1.0140 1.0150 1.0160 1.0170 1.0180 1.0190
+
+ Columns 1021 through 1026
+
+ 1.0200 1.0210 1.0220 1.0230 1.0240 1.0250
+
+ Columns 1027 through 1032
+
+ 1.0260 1.0270 1.0280 1.0290 1.0300 1.0310
+
+ Columns 1033 through 1038
+
+ 1.0320 1.0330 1.0340 1.0350 1.0360 1.0370
+
+ Columns 1039 through 1044
+
+ 1.0380 1.0390 1.0400 1.0410 1.0420 1.0430
+
+ Columns 1045 through 1050
+
+ 1.0440 1.0450 1.0460 1.0470 1.0480 1.0490
+
+ Columns 1051 through 1056
+
+ 1.0500 1.0510 1.0520 1.0530 1.0540 1.0550
+
+ Columns 1057 through 1062
+
+ 1.0560 1.0570 1.0580 1.0590 1.0600 1.0610
+
+ Columns 1063 through 1068
+
+ 1.0620 1.0630 1.0640 1.0650 1.0660 1.0670
+
+ Columns 1069 through 1074
+
+ 1.0680 1.0690 1.0700 1.0710 1.0720 1.0730
+
+ Columns 1075 through 1080
+
+ 1.0740 1.0750 1.0760 1.0770 1.0780 1.0790
+
+ Columns 1081 through 1086
+
+ 1.0800 1.0810 1.0820 1.0830 1.0840 1.0850
+
+ Columns 1087 through 1092
+
+ 1.0860 1.0870 1.0880 1.0890 1.0900 1.0910
+
+ Columns 1093 through 1098
+
+ 1.0920 1.0930 1.0940 1.0950 1.0960 1.0970
+
+ Columns 1099 through 1104
+
+ 1.0980 1.0990 1.1000 1.1010 1.1020 1.1030
+
+ Columns 1105 through 1110
+
+ 1.1040 1.1050 1.1060 1.1070 1.1080 1.1090
+
+ Columns 1111 through 1116
+
+ 1.1100 1.1110 1.1120 1.1130 1.1140 1.1150
+
+ Columns 1117 through 1122
+
+ 1.1160 1.1170 1.1180 1.1190 1.1200 1.1210
+
+ Columns 1123 through 1128
+
+ 1.1220 1.1230 1.1240 1.1250 1.1260 1.1270
+
+ Columns 1129 through 1134
+
+ 1.1280 1.1290 1.1300 1.1310 1.1320 1.1330
+
+ Columns 1135 through 1140
+
+ 1.1340 1.1350 1.1360 1.1370 1.1380 1.1390
+
+ Columns 1141 through 1146
+
+ 1.1400 1.1410 1.1420 1.1430 1.1440 1.1450
+
+ Columns 1147 through 1152
+
+ 1.1460 1.1470 1.1480 1.1490 1.1500 1.1510
+
+ Columns 1153 through 1158
+
+ 1.1520 1.1530 1.1540 1.1550 1.1560 1.1570
+
+ Columns 1159 through 1164
+
+ 1.1580 1.1590 1.1600 1.1610 1.1620 1.1630
+
+ Columns 1165 through 1170
+
+ 1.1640 1.1650 1.1660 1.1670 1.1680 1.1690
+
+ Columns 1171 through 1176
+
+ 1.1700 1.1710 1.1720 1.1730 1.1740 1.1750
+
+ Columns 1177 through 1182
+
+ 1.1760 1.1770 1.1780 1.1790 1.1800 1.1810
+
+ Columns 1183 through 1188
+
+ 1.1820 1.1830 1.1840 1.1850 1.1860 1.1870
+
+ Columns 1189 through 1194
+
+ 1.1880 1.1890 1.1900 1.1910 1.1920 1.1930
+
+ Columns 1195 through 1200
+
+ 1.1940 1.1950 1.1960 1.1970 1.1980 1.1990
+
+ Columns 1201 through 1206
+
+ 1.2000 1.2010 1.2020 1.2030 1.2040 1.2050
+
+ Columns 1207 through 1212
+
+ 1.2060 1.2070 1.2080 1.2090 1.2100 1.2110
+
+ Columns 1213 through 1218
+
+ 1.2120 1.2130 1.2140 1.2150 1.2160 1.2170
+
+ Columns 1219 through 1224
+
+ 1.2180 1.2190 1.2200 1.2210 1.2220 1.2230
+
+ Columns 1225 through 1230
+
+ 1.2240 1.2250 1.2260 1.2270 1.2280 1.2290
+
+ Columns 1231 through 1236
+
+ 1.2300 1.2310 1.2320 1.2330 1.2340 1.2350
+
+ Columns 1237 through 1242
+
+ 1.2360 1.2370 1.2380 1.2390 1.2400 1.2410
+
+ Columns 1243 through 1248
+
+ 1.2420 1.2430 1.2440 1.2450 1.2460 1.2470
+
+ Columns 1249 through 1254
+
+ 1.2480 1.2490 1.2500 1.2510 1.2520 1.2530
+
+ Columns 1255 through 1260
+
+ 1.2540 1.2550 1.2560 1.2570 1.2580 1.2590
+
+ Columns 1261 through 1266
+
+ 1.2600 1.2610 1.2620 1.2630 1.2640 1.2650
+
+ Columns 1267 through 1272
+
+ 1.2660 1.2670 1.2680 1.2690 1.2700 1.2710
+
+ Columns 1273 through 1278
+
+ 1.2720 1.2730 1.2740 1.2750 1.2760 1.2770
+
+ Columns 1279 through 1284
+
+ 1.2780 1.2790 1.2800 1.2810 1.2820 1.2830
+
+ Columns 1285 through 1290
+
+ 1.2840 1.2850 1.2860 1.2870 1.2880 1.2890
+
+ Columns 1291 through 1296
+
+ 1.2900 1.2910 1.2920 1.2930 1.2940 1.2950
+
+ Columns 1297 through 1302
+
+ 1.2960 1.2970 1.2980 1.2990 1.3000 1.3010
+
+ Columns 1303 through 1308
+
+ 1.3020 1.3030 1.3040 1.3050 1.3060 1.3070
+
+ Columns 1309 through 1314
+
+ 1.3080 1.3090 1.3100 1.3110 1.3120 1.3130
+
+ Columns 1315 through 1320
+
+ 1.3140 1.3150 1.3160 1.3170 1.3180 1.3190
+
+ Columns 1321 through 1326
+
+ 1.3200 1.3210 1.3220 1.3230 1.3240 1.3250
+
+ Columns 1327 through 1332
+
+ 1.3260 1.3270 1.3280 1.3290 1.3300 1.3310
+
+ Columns 1333 through 1338
+
+ 1.3320 1.3330 1.3340 1.3350 1.3360 1.3370
+
+ Columns 1339 through 1344
+
+ 1.3380 1.3390 1.3400 1.3410 1.3420 1.3430
+
+ Columns 1345 through 1350
+
+ 1.3440 1.3450 1.3460 1.3470 1.3480 1.3490
+
+ Columns 1351 through 1356
+
+ 1.3500 1.3510 1.3520 1.3530 1.3540 1.3550
+
+ Columns 1357 through 1362
+
+ 1.3560 1.3570 1.3580 1.3590 1.3600 1.3610
+
+ Columns 1363 through 1368
+
+ 1.3620 1.3630 1.3640 1.3650 1.3660 1.3670
+
+ Columns 1369 through 1374
+
+ 1.3680 1.3690 1.3700 1.3710 1.3720 1.3730
+
+ Columns 1375 through 1380
+
+ 1.3740 1.3750 1.3760 1.3770 1.3780 1.3790
+
+ Columns 1381 through 1386
+
+ 1.3800 1.3810 1.3820 1.3830 1.3840 1.3850
+
+ Columns 1387 through 1392
+
+ 1.3860 1.3870 1.3880 1.3890 1.3900 1.3910
+
+ Columns 1393 through 1398
+
+ 1.3920 1.3930 1.3940 1.3950 1.3960 1.3970
+
+ Columns 1399 through 1404
+
+ 1.3980 1.3990 1.4000 1.4010 1.4020 1.4030
+
+ Columns 1405 through 1410
+
+ 1.4040 1.4050 1.4060 1.4070 1.4080 1.4090
+
+ Columns 1411 through 1416
+
+ 1.4100 1.4110 1.4120 1.4130 1.4140 1.4150
+
+ Columns 1417 through 1422
+
+ 1.4160 1.4170 1.4180 1.4190 1.4200 1.4210
+
+ Columns 1423 through 1428
+
+ 1.4220 1.4230 1.4240 1.4250 1.4260 1.4270
+
+ Columns 1429 through 1434
+
+ 1.4280 1.4290 1.4300 1.4310 1.4320 1.4330
+
+ Columns 1435 through 1440
+
+ 1.4340 1.4350 1.4360 1.4370 1.4380 1.4390
+
+ Columns 1441 through 1446
+
+ 1.4400 1.4410 1.4420 1.4430 1.4440 1.4450
+
+ Columns 1447 through 1452
+
+ 1.4460 1.4470 1.4480 1.4490 1.4500 1.4510
+
+ Columns 1453 through 1458
+
+ 1.4520 1.4530 1.4540 1.4550 1.4560 1.4570
+
+ Columns 1459 through 1464
+
+ 1.4580 1.4590 1.4600 1.4610 1.4620 1.4630
+
+ Columns 1465 through 1470
+
+ 1.4640 1.4650 1.4660 1.4670 1.4680 1.4690
+
+ Columns 1471 through 1476
+
+ 1.4700 1.4710 1.4720 1.4730 1.4740 1.4750
+
+ Columns 1477 through 1482
+
+ 1.4760 1.4770 1.4780 1.4790 1.4800 1.4810
+
+ Columns 1483 through 1488
+
+ 1.4820 1.4830 1.4840 1.4850 1.4860 1.4870
+
+ Columns 1489 through 1494
+
+ 1.4880 1.4890 1.4900 1.4910 1.4920 1.4930
+
+ Columns 1495 through 1500
+
+ 1.4940 1.4950 1.4960 1.4970 1.4980 1.4990
+
+ Columns 1501 through 1506
+
+ 1.5000 1.5010 1.5020 1.5030 1.5040 1.5050
+
+ Columns 1507 through 1512
+
+ 1.5060 1.5070 1.5080 1.5090 1.5100 1.5110
+
+ Columns 1513 through 1518
+
+ 1.5120 1.5130 1.5140 1.5150 1.5160 1.5170
+
+ Columns 1519 through 1524
+
+ 1.5180 1.5190 1.5200 1.5210 1.5220 1.5230
+
+ Columns 1525 through 1530
+
+ 1.5240 1.5250 1.5260 1.5270 1.5280 1.5290
+
+ Columns 1531 through 1536
+
+ 1.5300 1.5310 1.5320 1.5330 1.5340 1.5350
+
+ Columns 1537 through 1542
+
+ 1.5360 1.5370 1.5380 1.5390 1.5400 1.5410
+
+ Columns 1543 through 1548
+
+ 1.5420 1.5430 1.5440 1.5450 1.5460 1.5470
+
+ Columns 1549 through 1554
+
+ 1.5480 1.5490 1.5500 1.5510 1.5520 1.5530
+
+ Columns 1555 through 1560
+
+ 1.5540 1.5550 1.5560 1.5570 1.5580 1.5590
+
+ Columns 1561 through 1566
+
+ 1.5600 1.5610 1.5620 1.5630 1.5640 1.5650
+
+ Columns 1567 through 1572
+
+ 1.5660 1.5670 1.5680 1.5690 1.5700 1.5710
+
+ Columns 1573 through 1578
+
+ 1.5720 1.5730 1.5740 1.5750 1.5760 1.5770
+
+ Columns 1579 through 1584
+
+ 1.5780 1.5790 1.5800 1.5810 1.5820 1.5830
+
+ Columns 1585 through 1590
+
+ 1.5840 1.5850 1.5860 1.5870 1.5880 1.5890
+
+ Columns 1591 through 1596
+
+ 1.5900 1.5910 1.5920 1.5930 1.5940 1.5950
+
+ Columns 1597 through 1602
+
+ 1.5960 1.5970 1.5980 1.5990 1.6000 1.6010
+
+ Columns 1603 through 1608
+
+ 1.6020 1.6030 1.6040 1.6050 1.6060 1.6070
+
+ Columns 1609 through 1614
+
+ 1.6080 1.6090 1.6100 1.6110 1.6120 1.6130
+
+ Columns 1615 through 1620
+
+ 1.6140 1.6150 1.6160 1.6170 1.6180 1.6190
+
+ Columns 1621 through 1626
+
+ 1.6200 1.6210 1.6220 1.6230 1.6240 1.6250
+
+ Columns 1627 through 1632
+
+ 1.6260 1.6270 1.6280 1.6290 1.6300 1.6310
+
+ Columns 1633 through 1638
+
+ 1.6320 1.6330 1.6340 1.6350 1.6360 1.6370
+
+ Columns 1639 through 1644
+
+ 1.6380 1.6390 1.6400 1.6410 1.6420 1.6430
+
+ Columns 1645 through 1650
+
+ 1.6440 1.6450 1.6460 1.6470 1.6480 1.6490
+
+ Columns 1651 through 1656
+
+ 1.6500 1.6510 1.6520 1.6530 1.6540 1.6550
+
+ Columns 1657 through 1662
+
+ 1.6560 1.6570 1.6580 1.6590 1.6600 1.6610
+
+ Columns 1663 through 1668
+
+ 1.6620 1.6630 1.6640 1.6650 1.6660 1.6670
+
+ Columns 1669 through 1674
+
+ 1.6680 1.6690 1.6700 1.6710 1.6720 1.6730
+
+ Columns 1675 through 1680
+
+ 1.6740 1.6750 1.6760 1.6770 1.6780 1.6790
+
+ Columns 1681 through 1686
+
+ 1.6800 1.6810 1.6820 1.6830 1.6840 1.6850
+
+ Columns 1687 through 1692
+
+ 1.6860 1.6870 1.6880 1.6890 1.6900 1.6910
+
+ Columns 1693 through 1698
+
+ 1.6920 1.6930 1.6940 1.6950 1.6960 1.6970
+
+ Columns 1699 through 1704
+
+ 1.6980 1.6990 1.7000 1.7010 1.7020 1.7030
+
+ Columns 1705 through 1710
+
+ 1.7040 1.7050 1.7060 1.7070 1.7080 1.7090
+
+ Columns 1711 through 1716
+
+ 1.7100 1.7110 1.7120 1.7130 1.7140 1.7150
+
+ Columns 1717 through 1722
+
+ 1.7160 1.7170 1.7180 1.7190 1.7200 1.7210
+
+ Columns 1723 through 1728
+
+ 1.7220 1.7230 1.7240 1.7250 1.7260 1.7270
+
+ Columns 1729 through 1734
+
+ 1.7280 1.7290 1.7300 1.7310 1.7320 1.7330
+
+ Columns 1735 through 1740
+
+ 1.7340 1.7350 1.7360 1.7370 1.7380 1.7390
+
+ Columns 1741 through 1746
+
+ 1.7400 1.7410 1.7420 1.7430 1.7440 1.7450
+
+ Columns 1747 through 1752
+
+ 1.7460 1.7470 1.7480 1.7490 1.7500 1.7510
+
+ Columns 1753 through 1758
+
+ 1.7520 1.7530 1.7540 1.7550 1.7560 1.7570
+
+ Columns 1759 through 1764
+
+ 1.7580 1.7590 1.7600 1.7610 1.7620 1.7630
+
+ Columns 1765 through 1770
+
+ 1.7640 1.7650 1.7660 1.7670 1.7680 1.7690
+
+ Columns 1771 through 1776
+
+ 1.7700 1.7710 1.7720 1.7730 1.7740 1.7750
+
+ Columns 1777 through 1782
+
+ 1.7760 1.7770 1.7780 1.7790 1.7800 1.7810
+
+ Columns 1783 through 1788
+
+ 1.7820 1.7830 1.7840 1.7850 1.7860 1.7870
+
+ Columns 1789 through 1794
+
+ 1.7880 1.7890 1.7900 1.7910 1.7920 1.7930
+
+ Columns 1795 through 1800
+
+ 1.7940 1.7950 1.7960 1.7970 1.7980 1.7990
+
+ Columns 1801 through 1806
+
+ 1.8000 1.8010 1.8020 1.8030 1.8040 1.8050
+
+ Columns 1807 through 1812
+
+ 1.8060 1.8070 1.8080 1.8090 1.8100 1.8110
+
+ Columns 1813 through 1818
+
+ 1.8120 1.8130 1.8140 1.8150 1.8160 1.8170
+
+ Columns 1819 through 1824
+
+ 1.8180 1.8190 1.8200 1.8210 1.8220 1.8230
+
+ Columns 1825 through 1830
+
+ 1.8240 1.8250 1.8260 1.8270 1.8280 1.8290
+
+ Columns 1831 through 1836
+
+ 1.8300 1.8310 1.8320 1.8330 1.8340 1.8350
+
+ Columns 1837 through 1842
+
+ 1.8360 1.8370 1.8380 1.8390 1.8400 1.8410
+
+ Columns 1843 through 1848
+
+ 1.8420 1.8430 1.8440 1.8450 1.8460 1.8470
+
+ Columns 1849 through 1854
+
+ 1.8480 1.8490 1.8500 1.8510 1.8520 1.8530
+
+ Columns 1855 through 1860
+
+ 1.8540 1.8550 1.8560 1.8570 1.8580 1.8590
+
+ Columns 1861 through 1866
+
+ 1.8600 1.8610 1.8620 1.8630 1.8640 1.8650
+
+ Columns 1867 through 1872
+
+ 1.8660 1.8670 1.8680 1.8690 1.8700 1.8710
+
+ Columns 1873 through 1878
+
+ 1.8720 1.8730 1.8740 1.8750 1.8760 1.8770
+
+ Columns 1879 through 1884
+
+ 1.8780 1.8790 1.8800 1.8810 1.8820 1.8830
+
+ Columns 1885 through 1890
+
+ 1.8840 1.8850 1.8860 1.8870 1.8880 1.8890
+
+ Columns 1891 through 1896
+
+ 1.8900 1.8910 1.8920 1.8930 1.8940 1.8950
+
+ Columns 1897 through 1902
+
+ 1.8960 1.8970 1.8980 1.8990 1.9000 1.9010
+
+ Columns 1903 through 1908
+
+ 1.9020 1.9030 1.9040 1.9050 1.9060 1.9070
+
+ Columns 1909 through 1914
+
+ 1.9080 1.9090 1.9100 1.9110 1.9120 1.9130
+
+ Columns 1915 through 1920
+
+ 1.9140 1.9150 1.9160 1.9170 1.9180 1.9190
+
+ Columns 1921 through 1926
+
+ 1.9200 1.9210 1.9220 1.9230 1.9240 1.9250
+
+ Columns 1927 through 1932
+
+ 1.9260 1.9270 1.9280 1.9290 1.9300 1.9310
+
+ Columns 1933 through 1938
+
+ 1.9320 1.9330 1.9340 1.9350 1.9360 1.9370
+
+ Columns 1939 through 1944
+
+ 1.9380 1.9390 1.9400 1.9410 1.9420 1.9430
+
+ Columns 1945 through 1950
+
+ 1.9440 1.9450 1.9460 1.9470 1.9480 1.9490
+
+ Columns 1951 through 1956
+
+ 1.9500 1.9510 1.9520 1.9530 1.9540 1.9550
+
+ Columns 1957 through 1962
+
+ 1.9560 1.9570 1.9580 1.9590 1.9600 1.9610
+
+ Columns 1963 through 1968
+
+ 1.9620 1.9630 1.9640 1.9650 1.9660 1.9670
+
+ Columns 1969 through 1974
+
+ 1.9680 1.9690 1.9700 1.9710 1.9720 1.9730
+
+ Columns 1975 through 1980
+
+ 1.9740 1.9750 1.9760 1.9770 1.9780 1.9790
+
+ Columns 1981 through 1986
+
+ 1.9800 1.9810 1.9820 1.9830 1.9840 1.9850
+
+ Columns 1987 through 1992
+
+ 1.9860 1.9870 1.9880 1.9890 1.9900 1.9910
+
+ Columns 1993 through 1998
+
+ 1.9920 1.9930 1.9940 1.9950 1.9960 1.9970
+
+ Columns 1999 through 2001
+
+ 1.9980 1.9990 2.0000
+
+x=0:0.001:2;
+y=8-2*x-7*exp(-x/2); graph(x,y);
+{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('matlab.internal.graph.MLGraph')" style="font-weight:bold">matlab.internal.graph.MLGraph</a>
+Source must be a dense double array of positive integer node
+indices.
+
+Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('matlab.internal.graph.constructFromEdgeList', '/soft/MATLAB/R2018a/toolbox/matlab/graphfun/+matlab/+internal/+graph/constructFromEdgeList.m', 136)" style="font-weight:bold">matlab.internal.graph.constructFromEdgeList</a> (<a href="matlab: opentoline('/soft/MATLAB/R2018a/toolbox/matlab/graphfun/+matlab/+internal/+graph/constructFromEdgeList.m',136,0)">line 136</a>)
+ G = underlyingCtor(s, t, totalNodes);
+
+Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('graph', '/soft/MATLAB/R2018a/toolbox/matlab/graphfun/@graph/graph.m', 298)" style="font-weight:bold">graph</a> (<a href="matlab: opentoline('/soft/MATLAB/R2018a/toolbox/matlab/graphfun/@graph/graph.m',298,0)">line 298</a>)
+ matlab.internal.graph.constructFromEdgeList(...
+}
+clear x,y
+
+y =
+
+ Columns 1 through 6
+
+ 1.0000 1.0015 1.0030 1.0045 1.0060 1.0075
+
+ Columns 7 through 12
+
+ 1.0090 1.0105 1.0119 1.0134 1.0149 1.0164
+
+ Columns 13 through 18
+
+ 1.0179 1.0194 1.0208 1.0223 1.0238 1.0252
+
+ Columns 19 through 24
+
+ 1.0267 1.0282 1.0297 1.0311 1.0326 1.0340
+
+ Columns 25 through 30
+
+ 1.0355 1.0370 1.0384 1.0399 1.0413 1.0428
+
+ Columns 31 through 36
+
+ 1.0442 1.0457 1.0471 1.0486 1.0500 1.0514
+
+ Columns 37 through 42
+
+ 1.0529 1.0543 1.0557 1.0572 1.0586 1.0600
+
+ Columns 43 through 48
+
+ 1.0615 1.0629 1.0643 1.0657 1.0672 1.0686
+
+ Columns 49 through 54
+
+ 1.0700 1.0714 1.0728 1.0742 1.0757 1.0771
+
+ Columns 55 through 60
+
+ 1.0785 1.0799 1.0813 1.0827 1.0841 1.0855
+
+ Columns 61 through 66
+
+ 1.0869 1.0883 1.0897 1.0911 1.0925 1.0938
+
+ Columns 67 through 72
+
+ 1.0952 1.0966 1.0980 1.0994 1.1008 1.1021
+
+ Columns 73 through 78
+
+ 1.1035 1.1049 1.1063 1.1076 1.1090 1.1104
+
+ Columns 79 through 84
+
+ 1.1117 1.1131 1.1145 1.1158 1.1172 1.1186
+
+ Columns 85 through 90
+
+ 1.1199 1.1213 1.1226 1.1240 1.1253 1.1267
+
+ Columns 91 through 96
+
+ 1.1280 1.1294 1.1307 1.1320 1.1334 1.1347
+
+ Columns 97 through 102
+
+ 1.1361 1.1374 1.1387 1.1401 1.1414 1.1427
+
+ Columns 103 through 108
+
+ 1.1440 1.1454 1.1467 1.1480 1.1493 1.1507
+
+ Columns 109 through 114
+
+ 1.1520 1.1533 1.1546 1.1559 1.1572 1.1585
+
+ Columns 115 through 120
+
+ 1.1598 1.1611 1.1625 1.1638 1.1651 1.1664
+
+ Columns 121 through 126
+
+ 1.1676 1.1689 1.1702 1.1715 1.1728 1.1741
+
+ Columns 127 through 132
+
+ 1.1754 1.1767 1.1780 1.1792 1.1805 1.1818
+
+ Columns 133 through 138
+
+ 1.1831 1.1844 1.1856 1.1869 1.1882 1.1894
+
+ Columns 139 through 144
+
+ 1.1907 1.1920 1.1932 1.1945 1.1958 1.1970
+
+ Columns 145 through 150
+
+ 1.1983 1.1995 1.2008 1.2020 1.2033 1.2045
+
+ Columns 151 through 156
+
+ 1.2058 1.2070 1.2083 1.2095 1.2108 1.2120
+
+ Columns 157 through 162
+
+ 1.2132 1.2145 1.2157 1.2170 1.2182 1.2194
+
+ Columns 163 through 168
+
+ 1.2206 1.2219 1.2231 1.2243 1.2255 1.2268
+
+ Columns 169 through 174
+
+ 1.2280 1.2292 1.2304 1.2316 1.2328 1.2341
+
+ Columns 175 through 180
+
+ 1.2353 1.2365 1.2377 1.2389 1.2401 1.2413
+
+ Columns 181 through 186
+
+ 1.2425 1.2437 1.2449 1.2461 1.2473 1.2485
+
+ Columns 187 through 192
+
+ 1.2496 1.2508 1.2520 1.2532 1.2544 1.2556
+
+ Columns 193 through 198
+
+ 1.2568 1.2579 1.2591 1.2603 1.2615 1.2626
+
+ Columns 199 through 204
+
+ 1.2638 1.2650 1.2661 1.2673 1.2685 1.2696
+
+ Columns 205 through 210
+
+ 1.2708 1.2720 1.2731 1.2743 1.2754 1.2766
+
+ Columns 211 through 216
+
+ 1.2777 1.2789 1.2800 1.2812 1.2823 1.2835
+
+ Columns 217 through 222
+
+ 1.2846 1.2857 1.2869 1.2880 1.2892 1.2903
+
+ Columns 223 through 228
+
+ 1.2914 1.2926 1.2937 1.2948 1.2959 1.2971
+
+ Columns 229 through 234
+
+ 1.2982 1.2993 1.3004 1.3016 1.3027 1.3038
+
+ Columns 235 through 240
+
+ 1.3049 1.3060 1.3071 1.3082 1.3093 1.3105
+
+ Columns 241 through 246
+
+ 1.3116 1.3127 1.3138 1.3149 1.3160 1.3171
+
+ Columns 247 through 252
+
+ 1.3182 1.3192 1.3203 1.3214 1.3225 1.3236
+
+ Columns 253 through 258
+
+ 1.3247 1.3258 1.3269 1.3279 1.3290 1.3301
+
+ Columns 259 through 264
+
+ 1.3312 1.3323 1.3333 1.3344 1.3355 1.3365
+
+ Columns 265 through 270
+
+ 1.3376 1.3387 1.3397 1.3408 1.3419 1.3429
+
+ Columns 271 through 276
+
+ 1.3440 1.3450 1.3461 1.3472 1.3482 1.3493
+
+ Columns 277 through 282
+
+ 1.3503 1.3514 1.3524 1.3534 1.3545 1.3555
+
+ Columns 283 through 288
+
+ 1.3566 1.3576 1.3587 1.3597 1.3607 1.3618
+
+ Columns 289 through 294
+
+ 1.3628 1.3638 1.3648 1.3659 1.3669 1.3679
+
+ Columns 295 through 300
+
+ 1.3689 1.3700 1.3710 1.3720 1.3730 1.3740
+
+ Columns 301 through 306
+
+ 1.3750 1.3761 1.3771 1.3781 1.3791 1.3801
+
+ Columns 307 through 312
+
+ 1.3811 1.3821 1.3831 1.3841 1.3851 1.3861
+
+ Columns 313 through 318
+
+ 1.3871 1.3881 1.3891 1.3901 1.3911 1.3920
+
+ Columns 319 through 324
+
+ 1.3930 1.3940 1.3950 1.3960 1.3970 1.3979
+
+ Columns 325 through 330
+
+ 1.3989 1.3999 1.4009 1.4018 1.4028 1.4038
+
+ Columns 331 through 336
+
+ 1.4047 1.4057 1.4067 1.4076 1.4086 1.4096
+
+ Columns 337 through 342
+
+ 1.4105 1.4115 1.4124 1.4134 1.4143 1.4153
+
+ Columns 343 through 348
+
+ 1.4162 1.4172 1.4181 1.4191 1.4200 1.4210
+
+ Columns 349 through 354
+
+ 1.4219 1.4229 1.4238 1.4247 1.4257 1.4266
+
+ Columns 355 through 360
+
+ 1.4275 1.4285 1.4294 1.4303 1.4313 1.4322
+
+ Columns 361 through 366
+
+ 1.4331 1.4340 1.4350 1.4359 1.4368 1.4377
+
+ Columns 367 through 372
+
+ 1.4386 1.4395 1.4404 1.4414 1.4423 1.4432
+
+ Columns 373 through 378
+
+ 1.4441 1.4450 1.4459 1.4468 1.4477 1.4486
+
+ Columns 379 through 384
+
+ 1.4495 1.4504 1.4513 1.4522 1.4531 1.4540
+
+ Columns 385 through 390
+
+ 1.4549 1.4557 1.4566 1.4575 1.4584 1.4593
+
+ Columns 391 through 396
+
+ 1.4602 1.4610 1.4619 1.4628 1.4637 1.4645
+
+ Columns 397 through 402
+
+ 1.4654 1.4663 1.4672 1.4680 1.4689 1.4697
+
+ Columns 403 through 408
+
+ 1.4706 1.4715 1.4723 1.4732 1.4741 1.4749
+
+ Columns 409 through 414
+
+ 1.4758 1.4766 1.4775 1.4783 1.4792 1.4800
+
+ Columns 415 through 420
+
+ 1.4809 1.4817 1.4826 1.4834 1.4842 1.4851
+
+ Columns 421 through 426
+
+ 1.4859 1.4867 1.4876 1.4884 1.4892 1.4901
+
+ Columns 427 through 432
+
+ 1.4909 1.4917 1.4926 1.4934 1.4942 1.4950
+
+ Columns 433 through 438
+
+ 1.4959 1.4967 1.4975 1.4983 1.4991 1.4999
+
+ Columns 439 through 444
+
+ 1.5007 1.5016 1.5024 1.5032 1.5040 1.5048
+
+ Columns 445 through 450
+
+ 1.5056 1.5064 1.5072 1.5080 1.5088 1.5096
+
+ Columns 451 through 456
+
+ 1.5104 1.5112 1.5120 1.5128 1.5136 1.5143
+
+ Columns 457 through 462
+
+ 1.5151 1.5159 1.5167 1.5175 1.5183 1.5190
+
+ Columns 463 through 468
+
+ 1.5198 1.5206 1.5214 1.5222 1.5229 1.5237
+
+ Columns 469 through 474
+
+ 1.5245 1.5252 1.5260 1.5268 1.5275 1.5283
+
+ Columns 475 through 480
+
+ 1.5291 1.5298 1.5306 1.5313 1.5321 1.5329
+
+ Columns 481 through 486
+
+ 1.5336 1.5344 1.5351 1.5359 1.5366 1.5374
+
+ Columns 487 through 492
+
+ 1.5381 1.5388 1.5396 1.5403 1.5411 1.5418
+
+ Columns 493 through 498
+
+ 1.5425 1.5433 1.5440 1.5447 1.5455 1.5462
+
+ Columns 499 through 504
+
+ 1.5469 1.5477 1.5484 1.5491 1.5498 1.5506
+
+ Columns 505 through 510
+
+ 1.5513 1.5520 1.5527 1.5534 1.5542 1.5549
+
+ Columns 511 through 516
+
+ 1.5556 1.5563 1.5570 1.5577 1.5584 1.5591
+
+ Columns 517 through 522
+
+ 1.5598 1.5605 1.5612 1.5619 1.5626 1.5633
+
+ Columns 523 through 528
+
+ 1.5640 1.5647 1.5654 1.5661 1.5668 1.5675
+
+ Columns 529 through 534
+
+ 1.5682 1.5689 1.5696 1.5702 1.5709 1.5716
+
+ Columns 535 through 540
+
+ 1.5723 1.5730 1.5736 1.5743 1.5750 1.5757
+
+ Columns 541 through 546
+
+ 1.5763 1.5770 1.5777 1.5784 1.5790 1.5797
+
+ Columns 547 through 552
+
+ 1.5804 1.5810 1.5817 1.5823 1.5830 1.5837
+
+ Columns 553 through 558
+
+ 1.5843 1.5850 1.5856 1.5863 1.5869 1.5876
+
+ Columns 559 through 564
+
+ 1.5882 1.5889 1.5895 1.5902 1.5908 1.5914
+
+ Columns 565 through 570
+
+ 1.5921 1.5927 1.5934 1.5940 1.5946 1.5953
+
+ Columns 571 through 576
+
+ 1.5959 1.5965 1.5972 1.5978 1.5984 1.5990
+
+ Columns 577 through 582
+
+ 1.5997 1.6003 1.6009 1.6015 1.6022 1.6028
+
+ Columns 583 through 588
+
+ 1.6034 1.6040 1.6046 1.6052 1.6058 1.6065
+
+ Columns 589 through 594
+
+ 1.6071 1.6077 1.6083 1.6089 1.6095 1.6101
+
+ Columns 595 through 600
+
+ 1.6107 1.6113 1.6119 1.6125 1.6131 1.6137
+
+ Columns 601 through 606
+
+ 1.6143 1.6149 1.6155 1.6160 1.6166 1.6172
+
+ Columns 607 through 612
+
+ 1.6178 1.6184 1.6190 1.6196 1.6201 1.6207
+
+ Columns 613 through 618
+
+ 1.6213 1.6219 1.6224 1.6230 1.6236 1.6242
+
+ Columns 619 through 624
+
+ 1.6247 1.6253 1.6259 1.6264 1.6270 1.6276
+
+ Columns 625 through 630
+
+ 1.6281 1.6287 1.6293 1.6298 1.6304 1.6309
+
+ Columns 631 through 636
+
+ 1.6315 1.6320 1.6326 1.6331 1.6337 1.6342
+
+ Columns 637 through 642
+
+ 1.6348 1.6353 1.6359 1.6364 1.6370 1.6375
+
+ Columns 643 through 648
+
+ 1.6380 1.6386 1.6391 1.6396 1.6402 1.6407
+
+ Columns 649 through 654
+
+ 1.6412 1.6418 1.6423 1.6428 1.6434 1.6439
+
+ Columns 655 through 660
+
+ 1.6444 1.6449 1.6455 1.6460 1.6465 1.6470
+
+ Columns 661 through 666
+
+ 1.6475 1.6480 1.6486 1.6491 1.6496 1.6501
+
+ Columns 667 through 672
+
+ 1.6506 1.6511 1.6516 1.6521 1.6526 1.6531
+
+ Columns 673 through 678
+
+ 1.6536 1.6541 1.6546 1.6551 1.6556 1.6561
+
+ Columns 679 through 684
+
+ 1.6566 1.6571 1.6576 1.6581 1.6586 1.6591
+
+ Columns 685 through 690
+
+ 1.6596 1.6600 1.6605 1.6610 1.6615 1.6620
+
+ Columns 691 through 696
+
+ 1.6625 1.6629 1.6634 1.6639 1.6644 1.6648
+
+ Columns 697 through 702
+
+ 1.6653 1.6658 1.6662 1.6667 1.6672 1.6676
+
+ Columns 703 through 708
+
+ 1.6681 1.6686 1.6690 1.6695 1.6700 1.6704
+
+ Columns 709 through 714
+
+ 1.6709 1.6713 1.6718 1.6722 1.6727 1.6731
+
+ Columns 715 through 720
+
+ 1.6736 1.6740 1.6745 1.6749 1.6754 1.6758
+
+ Columns 721 through 726
+
+ 1.6763 1.6767 1.6771 1.6776 1.6780 1.6785
+
+ Columns 727 through 732
+
+ 1.6789 1.6793 1.6798 1.6802 1.6806 1.6811
+
+ Columns 733 through 738
+
+ 1.6815 1.6819 1.6823 1.6828 1.6832 1.6836
+
+ Columns 739 through 744
+
+ 1.6840 1.6844 1.6849 1.6853 1.6857 1.6861
+
+ Columns 745 through 750
+
+ 1.6865 1.6869 1.6873 1.6878 1.6882 1.6886
+
+ Columns 751 through 756
+
+ 1.6890 1.6894 1.6898 1.6902 1.6906 1.6910
+
+ Columns 757 through 762
+
+ 1.6914 1.6918 1.6922 1.6926 1.6930 1.6934
+
+ Columns 763 through 768
+
+ 1.6938 1.6941 1.6945 1.6949 1.6953 1.6957
+
+ Columns 769 through 774
+
+ 1.6961 1.6965 1.6968 1.6972 1.6976 1.6980
+
+ Columns 775 through 780
+
+ 1.6984 1.6987 1.6991 1.6995 1.6999 1.7002
+
+ Columns 781 through 786
+
+ 1.7006 1.7010 1.7013 1.7017 1.7021 1.7024
+
+ Columns 787 through 792
+
+ 1.7028 1.7032 1.7035 1.7039 1.7042 1.7046
+
+ Columns 793 through 798
+
+ 1.7050 1.7053 1.7057 1.7060 1.7064 1.7067
+
+ Columns 799 through 804
+
+ 1.7071 1.7074 1.7078 1.7081 1.7084 1.7088
+
+ Columns 805 through 810
+
+ 1.7091 1.7095 1.7098 1.7102 1.7105 1.7108
+
+ Columns 811 through 816
+
+ 1.7112 1.7115 1.7118 1.7122 1.7125 1.7128
+
+ Columns 817 through 822
+
+ 1.7131 1.7135 1.7138 1.7141 1.7144 1.7148
+
+ Columns 823 through 828
+
+ 1.7151 1.7154 1.7157 1.7160 1.7164 1.7167
+
+ Columns 829 through 834
+
+ 1.7170 1.7173 1.7176 1.7179 1.7182 1.7185
+
+ Columns 835 through 840
+
+ 1.7189 1.7192 1.7195 1.7198 1.7201 1.7204
+
+ Columns 841 through 846
+
+ 1.7207 1.7210 1.7213 1.7216 1.7219 1.7222
+
+ Columns 847 through 852
+
+ 1.7224 1.7227 1.7230 1.7233 1.7236 1.7239
+
+ Columns 853 through 858
+
+ 1.7242 1.7245 1.7248 1.7250 1.7253 1.7256
+
+ Columns 859 through 864
+
+ 1.7259 1.7262 1.7264 1.7267 1.7270 1.7273
+
+ Columns 865 through 870
+
+ 1.7275 1.7278 1.7281 1.7283 1.7286 1.7289
+
+ Columns 871 through 876
+
+ 1.7291 1.7294 1.7297 1.7299 1.7302 1.7305
+
+ Columns 877 through 882
+
+ 1.7307 1.7310 1.7312 1.7315 1.7317 1.7320
+
+ Columns 883 through 888
+
+ 1.7323 1.7325 1.7328 1.7330 1.7332 1.7335
+
+ Columns 889 through 894
+
+ 1.7337 1.7340 1.7342 1.7345 1.7347 1.7350
+
+ Columns 895 through 900
+
+ 1.7352 1.7354 1.7357 1.7359 1.7361 1.7364
+
+ Columns 901 through 906
+
+ 1.7366 1.7368 1.7371 1.7373 1.7375 1.7377
+
+ Columns 907 through 912
+
+ 1.7380 1.7382 1.7384 1.7386 1.7389 1.7391
+
+ Columns 913 through 918
+
+ 1.7393 1.7395 1.7397 1.7400 1.7402 1.7404
+
+ Columns 919 through 924
+
+ 1.7406 1.7408 1.7410 1.7412 1.7414 1.7416
+
+ Columns 925 through 930
+
+ 1.7418 1.7420 1.7423 1.7425 1.7427 1.7429
+
+ Columns 931 through 936
+
+ 1.7431 1.7433 1.7434 1.7436 1.7438 1.7440
+
+ Columns 937 through 942
+
+ 1.7442 1.7444 1.7446 1.7448 1.7450 1.7452
+
+ Columns 943 through 948
+
+ 1.7454 1.7455 1.7457 1.7459 1.7461 1.7463
+
+ Columns 949 through 954
+
+ 1.7464 1.7466 1.7468 1.7470 1.7472 1.7473
+
+ Columns 955 through 960
+
+ 1.7475 1.7477 1.7478 1.7480 1.7482 1.7483
+
+ Columns 961 through 966
+
+ 1.7485 1.7487 1.7488 1.7490 1.7492 1.7493
+
+ Columns 967 through 972
+
+ 1.7495 1.7496 1.7498 1.7500 1.7501 1.7503
+
+ Columns 973 through 978
+
+ 1.7504 1.7506 1.7507 1.7509 1.7510 1.7512
+
+ Columns 979 through 984
+
+ 1.7513 1.7515 1.7516 1.7518 1.7519 1.7520
+
+ Columns 985 through 990
+
+ 1.7522 1.7523 1.7525 1.7526 1.7527 1.7529
+
+ Columns 991 through 996
+
+ 1.7530 1.7531 1.7533 1.7534 1.7535 1.7537
+
+ Columns 997 through 1002
+
+ 1.7538 1.7539 1.7540 1.7542 1.7543 1.7544
+
+ Columns 1003 through 1008
+
+ 1.7545 1.7546 1.7548 1.7549 1.7550 1.7551
+
+ Columns 1009 through 1014
+
+ 1.7552 1.7553 1.7555 1.7556 1.7557 1.7558
+
+ Columns 1015 through 1020
+
+ 1.7559 1.7560 1.7561 1.7562 1.7563 1.7564
+
+ Columns 1021 through 1026
+
+ 1.7565 1.7566 1.7567 1.7568 1.7569 1.7570
+
+ Columns 1027 through 1032
+
+ 1.7571 1.7572 1.7573 1.7574 1.7575 1.7576
+
+ Columns 1033 through 1038
+
+ 1.7577 1.7578 1.7579 1.7579 1.7580 1.7581
+
+ Columns 1039 through 1044
+
+ 1.7582 1.7583 1.7584 1.7584 1.7585 1.7586
+
+ Columns 1045 through 1050
+
+ 1.7587 1.7587 1.7588 1.7589 1.7590 1.7590
+
+ Columns 1051 through 1056
+
+ 1.7591 1.7592 1.7593 1.7593 1.7594 1.7595
+
+ Columns 1057 through 1062
+
+ 1.7595 1.7596 1.7596 1.7597 1.7598 1.7598
+
+ Columns 1063 through 1068
+
+ 1.7599 1.7599 1.7600 1.7601 1.7601 1.7602
+
+ Columns 1069 through 1074
+
+ 1.7602 1.7603 1.7603 1.7604 1.7604 1.7605
+
+ Columns 1075 through 1080
+
+ 1.7605 1.7606 1.7606 1.7606 1.7607 1.7607
+
+ Columns 1081 through 1086
+
+ 1.7608 1.7608 1.7608 1.7609 1.7609 1.7609
+
+ Columns 1087 through 1092
+
+ 1.7610 1.7610 1.7610 1.7611 1.7611 1.7611
+
+ Columns 1093 through 1098
+
+ 1.7612 1.7612 1.7612 1.7612 1.7613 1.7613
+
+ Columns 1099 through 1104
+
+ 1.7613 1.7613 1.7614 1.7614 1.7614 1.7614
+
+ Columns 1105 through 1110
+
+ 1.7614 1.7614 1.7614 1.7615 1.7615 1.7615
+
+ Columns 1111 through 1116
+
+ 1.7615 1.7615 1.7615 1.7615 1.7615 1.7615
+
+ Columns 1117 through 1122
+
+ 1.7615 1.7615 1.7615 1.7615 1.7615 1.7615
+
+ Columns 1123 through 1128
+
+ 1.7615 1.7615 1.7615 1.7615 1.7615 1.7615
+
+ Columns 1129 through 1134
+
+ 1.7615 1.7615 1.7615 1.7615 1.7615 1.7614
+
+ Columns 1135 through 1140
+
+ 1.7614 1.7614 1.7614 1.7614 1.7614 1.7613
+
+ Columns 1141 through 1146
+
+ 1.7613 1.7613 1.7613 1.7613 1.7612 1.7612
+
+ Columns 1147 through 1152
+
+ 1.7612 1.7612 1.7611 1.7611 1.7611 1.7610
+
+ Columns 1153 through 1158
+
+ 1.7610 1.7610 1.7609 1.7609 1.7609 1.7608
+
+ Columns 1159 through 1164
+
+ 1.7608 1.7608 1.7607 1.7607 1.7606 1.7606
+
+ Columns 1165 through 1170
+
+ 1.7605 1.7605 1.7605 1.7604 1.7604 1.7603
+
+ Columns 1171 through 1176
+
+ 1.7603 1.7602 1.7602 1.7601 1.7601 1.7600
+
+ Columns 1177 through 1182
+
+ 1.7599 1.7599 1.7598 1.7598 1.7597 1.7596
+
+ Columns 1183 through 1188
+
+ 1.7596 1.7595 1.7595 1.7594 1.7593 1.7593
+
+ Columns 1189 through 1194
+
+ 1.7592 1.7591 1.7591 1.7590 1.7589 1.7588
+
+ Columns 1195 through 1200
+
+ 1.7588 1.7587 1.7586 1.7586 1.7585 1.7584
+
+ Columns 1201 through 1206
+
+ 1.7583 1.7582 1.7582 1.7581 1.7580 1.7579
+
+ Columns 1207 through 1212
+
+ 1.7578 1.7577 1.7577 1.7576 1.7575 1.7574
+
+ Columns 1213 through 1218
+
+ 1.7573 1.7572 1.7571 1.7570 1.7569 1.7568
+
+ Columns 1219 through 1224
+
+ 1.7567 1.7566 1.7565 1.7564 1.7563 1.7562
+
+ Columns 1225 through 1230
+
+ 1.7561 1.7560 1.7559 1.7558 1.7557 1.7556
+
+ Columns 1231 through 1236
+
+ 1.7555 1.7554 1.7553 1.7552 1.7551 1.7550
+
+ Columns 1237 through 1242
+
+ 1.7549 1.7547 1.7546 1.7545 1.7544 1.7543
+
+ Columns 1243 through 1248
+
+ 1.7542 1.7540 1.7539 1.7538 1.7537 1.7535
+
+ Columns 1249 through 1254
+
+ 1.7534 1.7533 1.7532 1.7530 1.7529 1.7528
+
+ Columns 1255 through 1260
+
+ 1.7527 1.7525 1.7524 1.7523 1.7521 1.7520
+
+ Columns 1261 through 1266
+
+ 1.7519 1.7517 1.7516 1.7514 1.7513 1.7512
+
+ Columns 1267 through 1272
+
+ 1.7510 1.7509 1.7507 1.7506 1.7505 1.7503
+
+ Columns 1273 through 1278
+
+ 1.7502 1.7500 1.7499 1.7497 1.7496 1.7494
+
+ Columns 1279 through 1284
+
+ 1.7493 1.7491 1.7490 1.7488 1.7486 1.7485
+
+ Columns 1285 through 1290
+
+ 1.7483 1.7482 1.7480 1.7478 1.7477 1.7475
+
+ Columns 1291 through 1296
+
+ 1.7474 1.7472 1.7470 1.7469 1.7467 1.7465
+
+ Columns 1297 through 1302
+
+ 1.7464 1.7462 1.7460 1.7459 1.7457 1.7455
+
+ Columns 1303 through 1308
+
+ 1.7453 1.7452 1.7450 1.7448 1.7446 1.7444
+
+ Columns 1309 through 1314
+
+ 1.7443 1.7441 1.7439 1.7437 1.7435 1.7434
+
+ Columns 1315 through 1320
+
+ 1.7432 1.7430 1.7428 1.7426 1.7424 1.7422
+
+ Columns 1321 through 1326
+
+ 1.7420 1.7418 1.7417 1.7415 1.7413 1.7411
+
+ Columns 1327 through 1332
+
+ 1.7409 1.7407 1.7405 1.7403 1.7401 1.7399
+
+ Columns 1333 through 1338
+
+ 1.7397 1.7395 1.7393 1.7391 1.7389 1.7387
+
+ Columns 1339 through 1344
+
+ 1.7385 1.7382 1.7380 1.7378 1.7376 1.7374
+
+ Columns 1345 through 1350
+
+ 1.7372 1.7370 1.7368 1.7366 1.7363 1.7361
+
+ Columns 1351 through 1356
+
+ 1.7359 1.7357 1.7355 1.7352 1.7350 1.7348
+
+ Columns 1357 through 1362
+
+ 1.7346 1.7344 1.7341 1.7339 1.7337 1.7335
+
+ Columns 1363 through 1368
+
+ 1.7332 1.7330 1.7328 1.7325 1.7323 1.7321
+
+ Columns 1369 through 1374
+
+ 1.7318 1.7316 1.7314 1.7311 1.7309 1.7307
+
+ Columns 1375 through 1380
+
+ 1.7304 1.7302 1.7299 1.7297 1.7295 1.7292
+
+ Columns 1381 through 1386
+
+ 1.7290 1.7287 1.7285 1.7282 1.7280 1.7277
+
+ Columns 1387 through 1392
+
+ 1.7275 1.7272 1.7270 1.7267 1.7265 1.7262
+
+ Columns 1393 through 1398
+
+ 1.7260 1.7257 1.7255 1.7252 1.7249 1.7247
+
+ Columns 1399 through 1404
+
+ 1.7244 1.7242 1.7239 1.7236 1.7234 1.7231
+
+ Columns 1405 through 1410
+
+ 1.7228 1.7226 1.7223 1.7220 1.7218 1.7215
+
+ Columns 1411 through 1416
+
+ 1.7212 1.7210 1.7207 1.7204 1.7202 1.7199
+
+ Columns 1417 through 1422
+
+ 1.7196 1.7193 1.7190 1.7188 1.7185 1.7182
+
+ Columns 1423 through 1428
+
+ 1.7179 1.7176 1.7174 1.7171 1.7168 1.7165
+
+ Columns 1429 through 1434
+
+ 1.7162 1.7159 1.7157 1.7154 1.7151 1.7148
+
+ Columns 1435 through 1440
+
+ 1.7145 1.7142 1.7139 1.7136 1.7133 1.7130
+
+ Columns 1441 through 1446
+
+ 1.7127 1.7124 1.7121 1.7118 1.7115 1.7112
+
+ Columns 1447 through 1452
+
+ 1.7109 1.7106 1.7103 1.7100 1.7097 1.7094
+
+ Columns 1453 through 1458
+
+ 1.7091 1.7088 1.7085 1.7082 1.7079 1.7076
+
+ Columns 1459 through 1464
+
+ 1.7073 1.7069 1.7066 1.7063 1.7060 1.7057
+
+ Columns 1465 through 1470
+
+ 1.7054 1.7051 1.7047 1.7044 1.7041 1.7038
+
+ Columns 1471 through 1476
+
+ 1.7035 1.7031 1.7028 1.7025 1.7022 1.7018
+
+ Columns 1477 through 1482
+
+ 1.7015 1.7012 1.7009 1.7005 1.7002 1.6999
+
+ Columns 1483 through 1488
+
+ 1.6995 1.6992 1.6989 1.6985 1.6982 1.6979
+
+ Columns 1489 through 1494
+
+ 1.6975 1.6972 1.6969 1.6965 1.6962 1.6958
+
+ Columns 1495 through 1500
+
+ 1.6955 1.6952 1.6948 1.6945 1.6941 1.6938
+
+ Columns 1501 through 1506
+
+ 1.6934 1.6931 1.6927 1.6924 1.6920 1.6917
+
+ Columns 1507 through 1512
+
+ 1.6913 1.6910 1.6906 1.6903 1.6899 1.6896
+
+ Columns 1513 through 1518
+
+ 1.6892 1.6889 1.6885 1.6881 1.6878 1.6874
+
+ Columns 1519 through 1524
+
+ 1.6871 1.6867 1.6863 1.6860 1.6856 1.6852
+
+ Columns 1525 through 1530
+
+ 1.6849 1.6845 1.6841 1.6838 1.6834 1.6830
+
+ Columns 1531 through 1536
+
+ 1.6827 1.6823 1.6819 1.6815 1.6812 1.6808
+
+ Columns 1537 through 1542
+
+ 1.6804 1.6800 1.6797 1.6793 1.6789 1.6785
+
+ Columns 1543 through 1548
+
+ 1.6781 1.6778 1.6774 1.6770 1.6766 1.6762
+
+ Columns 1549 through 1554
+
+ 1.6758 1.6755 1.6751 1.6747 1.6743 1.6739
+
+ Columns 1555 through 1560
+
+ 1.6735 1.6731 1.6727 1.6723 1.6719 1.6716
+
+ Columns 1561 through 1566
+
+ 1.6712 1.6708 1.6704 1.6700 1.6696 1.6692
+
+ Columns 1567 through 1572
+
+ 1.6688 1.6684 1.6680 1.6676 1.6672 1.6668
+
+ Columns 1573 through 1578
+
+ 1.6664 1.6659 1.6655 1.6651 1.6647 1.6643
+
+ Columns 1579 through 1584
+
+ 1.6639 1.6635 1.6631 1.6627 1.6623 1.6618
+
+ Columns 1585 through 1590
+
+ 1.6614 1.6610 1.6606 1.6602 1.6598 1.6594
+
+ Columns 1591 through 1596
+
+ 1.6589 1.6585 1.6581 1.6577 1.6572 1.6568
+
+ Columns 1597 through 1602
+
+ 1.6564 1.6560 1.6556 1.6551 1.6547 1.6543
+
+ Columns 1603 through 1608
+
+ 1.6538 1.6534 1.6530 1.6526 1.6521 1.6517
+
+ Columns 1609 through 1614
+
+ 1.6513 1.6508 1.6504 1.6499 1.6495 1.6491
+
+ Columns 1615 through 1620
+
+ 1.6486 1.6482 1.6478 1.6473 1.6469 1.6464
+
+ Columns 1621 through 1626
+
+ 1.6460 1.6456 1.6451 1.6447 1.6442 1.6438
+
+ Columns 1627 through 1632
+
+ 1.6433 1.6429 1.6424 1.6420 1.6415 1.6411
+
+ Columns 1633 through 1638
+
+ 1.6406 1.6402 1.6397 1.6393 1.6388 1.6384
+
+ Columns 1639 through 1644
+
+ 1.6379 1.6374 1.6370 1.6365 1.6361 1.6356
+
+ Columns 1645 through 1650
+
+ 1.6351 1.6347 1.6342 1.6338 1.6333 1.6328
+
+ Columns 1651 through 1656
+
+ 1.6324 1.6319 1.6314 1.6310 1.6305 1.6300
+
+ Columns 1657 through 1662
+
+ 1.6295 1.6291 1.6286 1.6281 1.6277 1.6272
+
+ Columns 1663 through 1668
+
+ 1.6267 1.6262 1.6258 1.6253 1.6248 1.6243
+
+ Columns 1669 through 1674
+
+ 1.6238 1.6234 1.6229 1.6224 1.6219 1.6214
+
+ Columns 1675 through 1680
+
+ 1.6209 1.6205 1.6200 1.6195 1.6190 1.6185
+
+ Columns 1681 through 1686
+
+ 1.6180 1.6175 1.6170 1.6166 1.6161 1.6156
+
+ Columns 1687 through 1692
+
+ 1.6151 1.6146 1.6141 1.6136 1.6131 1.6126
+
+ Columns 1693 through 1698
+
+ 1.6121 1.6116 1.6111 1.6106 1.6101 1.6096
+
+ Columns 1699 through 1704
+
+ 1.6091 1.6086 1.6081 1.6076 1.6071 1.6066
+
+ Columns 1705 through 1710
+
+ 1.6061 1.6056 1.6051 1.6045 1.6040 1.6035
+
+ Columns 1711 through 1716
+
+ 1.6030 1.6025 1.6020 1.6015 1.6010 1.6005
+
+ Columns 1717 through 1722
+
+ 1.5999 1.5994 1.5989 1.5984 1.5979 1.5973
+
+ Columns 1723 through 1728
+
+ 1.5968 1.5963 1.5958 1.5953 1.5947 1.5942
+
+ Columns 1729 through 1734
+
+ 1.5937 1.5932 1.5926 1.5921 1.5916 1.5911
+
+ Columns 1735 through 1740
+
+ 1.5905 1.5900 1.5895 1.5889 1.5884 1.5879
+
+ Columns 1741 through 1746
+
+ 1.5873 1.5868 1.5863 1.5857 1.5852 1.5847
+
+ Columns 1747 through 1752
+
+ 1.5841 1.5836 1.5830 1.5825 1.5820 1.5814
+
+ Columns 1753 through 1758
+
+ 1.5809 1.5803 1.5798 1.5793 1.5787 1.5782
+
+ Columns 1759 through 1764
+
+ 1.5776 1.5771 1.5765 1.5760 1.5754 1.5749
+
+ Columns 1765 through 1770
+
+ 1.5743 1.5738 1.5732 1.5727 1.5721 1.5716
+
+ Columns 1771 through 1776
+
+ 1.5710 1.5704 1.5699 1.5693 1.5688 1.5682
+
+ Columns 1777 through 1782
+
+ 1.5677 1.5671 1.5665 1.5660 1.5654 1.5648
+
+ Columns 1783 through 1788
+
+ 1.5643 1.5637 1.5632 1.5626 1.5620 1.5615
+
+ Columns 1789 through 1794
+
+ 1.5609 1.5603 1.5597 1.5592 1.5586 1.5580
+
+ Columns 1795 through 1800
+
+ 1.5575 1.5569 1.5563 1.5557 1.5552 1.5546
+
+ Columns 1801 through 1806
+
+ 1.5540 1.5534 1.5529 1.5523 1.5517 1.5511
+
+ Columns 1807 through 1812
+
+ 1.5505 1.5500 1.5494 1.5488 1.5482 1.5476
+
+ Columns 1813 through 1818
+
+ 1.5470 1.5465 1.5459 1.5453 1.5447 1.5441
+
+ Columns 1819 through 1824
+
+ 1.5435 1.5429 1.5423 1.5417 1.5411 1.5406
+
+ Columns 1825 through 1830
+
+ 1.5400 1.5394 1.5388 1.5382 1.5376 1.5370
+
+ Columns 1831 through 1836
+
+ 1.5364 1.5358 1.5352 1.5346 1.5340 1.5334
+
+ Columns 1837 through 1842
+
+ 1.5328 1.5322 1.5316 1.5310 1.5304 1.5298
+
+ Columns 1843 through 1848
+
+ 1.5292 1.5285 1.5279 1.5273 1.5267 1.5261
+
+ Columns 1849 through 1854
+
+ 1.5255 1.5249 1.5243 1.5237 1.5231 1.5224
+
+ Columns 1855 through 1860
+
+ 1.5218 1.5212 1.5206 1.5200 1.5194 1.5187
+
+ Columns 1861 through 1866
+
+ 1.5181 1.5175 1.5169 1.5163 1.5156 1.5150
+
+ Columns 1867 through 1872
+
+ 1.5144 1.5138 1.5131 1.5125 1.5119 1.5113
+
+ Columns 1873 through 1878
+
+ 1.5106 1.5100 1.5094 1.5088 1.5081 1.5075
+
+ Columns 1879 through 1884
+
+ 1.5069 1.5062 1.5056 1.5050 1.5043 1.5037
+
+ Columns 1885 through 1890
+
+ 1.5031 1.5024 1.5018 1.5012 1.5005 1.4999
+
+ Columns 1891 through 1896
+
+ 1.4992 1.4986 1.4980 1.4973 1.4967 1.4960
+
+ Columns 1897 through 1902
+
+ 1.4954 1.4947 1.4941 1.4935 1.4928 1.4922
+
+ Columns 1903 through 1908
+
+ 1.4915 1.4909 1.4902 1.4896 1.4889 1.4883
+
+ Columns 1909 through 1914
+
+ 1.4876 1.4870 1.4863 1.4857 1.4850 1.4844
+
+ Columns 1915 through 1920
+
+ 1.4837 1.4830 1.4824 1.4817 1.4811 1.4804
+
+ Columns 1921 through 1926
+
+ 1.4797 1.4791 1.4784 1.4778 1.4771 1.4764
+
+ Columns 1927 through 1932
+
+ 1.4758 1.4751 1.4744 1.4738 1.4731 1.4725
+
+ Columns 1933 through 1938
+
+ 1.4718 1.4711 1.4704 1.4698 1.4691 1.4684
+
+ Columns 1939 through 1944
+
+ 1.4678 1.4671 1.4664 1.4657 1.4651 1.4644
+
+ Columns 1945 through 1950
+
+ 1.4637 1.4630 1.4624 1.4617 1.4610 1.4603
+
+ Columns 1951 through 1956
+
+ 1.4597 1.4590 1.4583 1.4576 1.4569 1.4562
+
+ Columns 1957 through 1962
+
+ 1.4556 1.4549 1.4542 1.4535 1.4528 1.4521
+
+ Columns 1963 through 1968
+
+ 1.4514 1.4508 1.4501 1.4494 1.4487 1.4480
+
+ Columns 1969 through 1974
+
+ 1.4473 1.4466 1.4459 1.4452 1.4445 1.4438
+
+ Columns 1975 through 1980
+
+ 1.4431 1.4425 1.4418 1.4411 1.4404 1.4397
+
+ Columns 1981 through 1986
+
+ 1.4390 1.4383 1.4376 1.4369 1.4362 1.4355
+
+ Columns 1987 through 1992
+
+ 1.4348 1.4341 1.4333 1.4326 1.4319 1.4312
+
+ Columns 1993 through 1998
+
+ 1.4305 1.4298 1.4291 1.4284 1.4277 1.4270
+
+ Columns 1999 through 2001
+
+ 1.4263 1.4256 1.4248
+
+clear y
+x=0:0.01:2
+
+x =
+
+ Columns 1 through 6
+
+ 0 0.0100 0.0200 0.0300 0.0400 0.0500
+
+ Columns 7 through 12
+
+ 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100
+
+ Columns 13 through 18
+
+ 0.1200 0.1300 0.1400 0.1500 0.1600 0.1700
+
+ Columns 19 through 24
+
+ 0.1800 0.1900 0.2000 0.2100 0.2200 0.2300
+
+ Columns 25 through 30
+
+ 0.2400 0.2500 0.2600 0.2700 0.2800 0.2900
+
+ Columns 31 through 36
+
+ 0.3000 0.3100 0.3200 0.3300 0.3400 0.3500
+
+ Columns 37 through 42
+
+ 0.3600 0.3700 0.3800 0.3900 0.4000 0.4100
+
+ Columns 43 through 48
+
+ 0.4200 0.4300 0.4400 0.4500 0.4600 0.4700
+
+ Columns 49 through 54
+
+ 0.4800 0.4900 0.5000 0.5100 0.5200 0.5300
+
+ Columns 55 through 60
+
+ 0.5400 0.5500 0.5600 0.5700 0.5800 0.5900
+
+ Columns 61 through 66
+
+ 0.6000 0.6100 0.6200 0.6300 0.6400 0.6500
+
+ Columns 67 through 72
+
+ 0.6600 0.6700 0.6800 0.6900 0.7000 0.7100
+
+ Columns 73 through 78
+
+ 0.7200 0.7300 0.7400 0.7500 0.7600 0.7700
+
+ Columns 79 through 84
+
+ 0.7800 0.7900 0.8000 0.8100 0.8200 0.8300
+
+ Columns 85 through 90
+
+ 0.8400 0.8500 0.8600 0.8700 0.8800 0.8900
+
+ Columns 91 through 96
+
+ 0.9000 0.9100 0.9200 0.9300 0.9400 0.9500
+
+ Columns 97 through 102
+
+ 0.9600 0.9700 0.9800 0.9900 1.0000 1.0100
+
+ Columns 103 through 108
+
+ 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700
+
+ Columns 109 through 114
+
+ 1.0800 1.0900 1.1000 1.1100 1.1200 1.1300
+
+ Columns 115 through 120
+
+ 1.1400 1.1500 1.1600 1.1700 1.1800 1.1900
+
+ Columns 121 through 126
+
+ 1.2000 1.2100 1.2200 1.2300 1.2400 1.2500
+
+ Columns 127 through 132
+
+ 1.2600 1.2700 1.2800 1.2900 1.3000 1.3100
+
+ Columns 133 through 138
+
+ 1.3200 1.3300 1.3400 1.3500 1.3600 1.3700
+
+ Columns 139 through 144
+
+ 1.3800 1.3900 1.4000 1.4100 1.4200 1.4300
+
+ Columns 145 through 150
+
+ 1.4400 1.4500 1.4600 1.4700 1.4800 1.4900
+
+ Columns 151 through 156
+
+ 1.5000 1.5100 1.5200 1.5300 1.5400 1.5500
+
+ Columns 157 through 162
+
+ 1.5600 1.5700 1.5800 1.5900 1.6000 1.6100
+
+ Columns 163 through 168
+
+ 1.6200 1.6300 1.6400 1.6500 1.6600 1.6700
+
+ Columns 169 through 174
+
+ 1.6800 1.6900 1.7000 1.7100 1.7200 1.7300
+
+ Columns 175 through 180
+
+ 1.7400 1.7500 1.7600 1.7700 1.7800 1.7900
+
+ Columns 181 through 186
+
+ 1.8000 1.8100 1.8200 1.8300 1.8400 1.8500
+
+ Columns 187 through 192
+
+ 1.8600 1.8700 1.8800 1.8900 1.9000 1.9100
+
+ Columns 193 through 198
+
+ 1.9200 1.9300 1.9400 1.9500 1.9600 1.9700
+
+ Columns 199 through 201
+
+ 1.9800 1.9900 2.0000
+
+y=8-2*x-7*exp(-x/2); graph(x,y);
+{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('matlab.internal.graph.MLGraph')" style="font-weight:bold">matlab.internal.graph.MLGraph</a>
+Source must be a dense double array of positive integer node
+indices.
+
+Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('matlab.internal.graph.constructFromEdgeList', '/soft/MATLAB/R2018a/toolbox/matlab/graphfun/+matlab/+internal/+graph/constructFromEdgeList.m', 136)" style="font-weight:bold">matlab.internal.graph.constructFromEdgeList</a> (<a href="matlab: opentoline('/soft/MATLAB/R2018a/toolbox/matlab/graphfun/+matlab/+internal/+graph/constructFromEdgeList.m',136,0)">line 136</a>)
+ G = underlyingCtor(s, t, totalNodes);
+
+Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('graph', '/soft/MATLAB/R2018a/toolbox/matlab/graphfun/@graph/graph.m', 298)" style="font-weight:bold">graph</a> (<a href="matlab: opentoline('/soft/MATLAB/R2018a/toolbox/matlab/graphfun/@graph/graph.m',298,0)">line 298</a>)
+ matlab.internal.graph.constructFromEdgeList(...
+}
+y=8-2*x-7*exp(-x/2);
+graph(x,y)
+{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('matlab.internal.graph.MLGraph')" style="font-weight:bold">matlab.internal.graph.MLGraph</a>
+Source must be a dense double array of positive integer node
+indices.
+
+Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('matlab.internal.graph.constructFromEdgeList', '/soft/MATLAB/R2018a/toolbox/matlab/graphfun/+matlab/+internal/+graph/constructFromEdgeList.m', 136)" style="font-weight:bold">matlab.internal.graph.constructFromEdgeList</a> (<a href="matlab: opentoline('/soft/MATLAB/R2018a/toolbox/matlab/graphfun/+matlab/+internal/+graph/constructFromEdgeList.m',136,0)">line 136</a>)
+ G = underlyingCtor(s, t, totalNodes);
+
+Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('graph', '/soft/MATLAB/R2018a/toolbox/matlab/graphfun/@graph/graph.m', 298)" style="font-weight:bold">graph</a> (<a href="matlab: opentoline('/soft/MATLAB/R2018a/toolbox/matlab/graphfun/@graph/graph.m',298,0)">line 298</a>)
+ matlab.internal.graph.constructFromEdgeList(...
+}
+plot(x,y);
+hold off
+clear
+N=5; eulerN; plot(t,y);
+hold on
+N=10; eulerN; plot(t,y);
+N=20; eulerN; plot(t,y);
+N=40; eulerN; plot(t,y);
+N=80; eulerN; plot(t,y);
+x=0:0.01:2
+
+x =
+
+ Columns 1 through 6
+
+ 0 0.0100 0.0200 0.0300 0.0400 0.0500
+
+ Columns 7 through 12
+
+ 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100
+
+ Columns 13 through 18
+
+ 0.1200 0.1300 0.1400 0.1500 0.1600 0.1700
+
+ Columns 19 through 24
+
+ 0.1800 0.1900 0.2000 0.2100 0.2200 0.2300
+
+ Columns 25 through 30
+
+ 0.2400 0.2500 0.2600 0.2700 0.2800 0.2900
+
+ Columns 31 through 36
+
+ 0.3000 0.3100 0.3200 0.3300 0.3400 0.3500
+
+ Columns 37 through 42
+
+ 0.3600 0.3700 0.3800 0.3900 0.4000 0.4100
+
+ Columns 43 through 48
+
+ 0.4200 0.4300 0.4400 0.4500 0.4600 0.4700
+
+ Columns 49 through 54
+
+ 0.4800 0.4900 0.5000 0.5100 0.5200 0.5300
+
+ Columns 55 through 60
+
+ 0.5400 0.5500 0.5600 0.5700 0.5800 0.5900
+
+ Columns 61 through 66
+
+ 0.6000 0.6100 0.6200 0.6300 0.6400 0.6500
+
+ Columns 67 through 72
+
+ 0.6600 0.6700 0.6800 0.6900 0.7000 0.7100
+
+ Columns 73 through 78
+
+ 0.7200 0.7300 0.7400 0.7500 0.7600 0.7700
+
+ Columns 79 through 84
+
+ 0.7800 0.7900 0.8000 0.8100 0.8200 0.8300
+
+ Columns 85 through 90
+
+ 0.8400 0.8500 0.8600 0.8700 0.8800 0.8900
+
+ Columns 91 through 96
+
+ 0.9000 0.9100 0.9200 0.9300 0.9400 0.9500
+
+ Columns 97 through 102
+
+ 0.9600 0.9700 0.9800 0.9900 1.0000 1.0100
+
+ Columns 103 through 108
+
+ 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700
+
+ Columns 109 through 114
+
+ 1.0800 1.0900 1.1000 1.1100 1.1200 1.1300
+
+ Columns 115 through 120
+
+ 1.1400 1.1500 1.1600 1.1700 1.1800 1.1900
+
+ Columns 121 through 126
+
+ 1.2000 1.2100 1.2200 1.2300 1.2400 1.2500
+
+ Columns 127 through 132
+
+ 1.2600 1.2700 1.2800 1.2900 1.3000 1.3100
+
+ Columns 133 through 138
+
+ 1.3200 1.3300 1.3400 1.3500 1.3600 1.3700
+
+ Columns 139 through 144
+
+ 1.3800 1.3900 1.4000 1.4100 1.4200 1.4300
+
+ Columns 145 through 150
+
+ 1.4400 1.4500 1.4600 1.4700 1.4800 1.4900
+
+ Columns 151 through 156
+
+ 1.5000 1.5100 1.5200 1.5300 1.5400 1.5500
+
+ Columns 157 through 162
+
+ 1.5600 1.5700 1.5800 1.5900 1.6000 1.6100
+
+ Columns 163 through 168
+
+ 1.6200 1.6300 1.6400 1.6500 1.6600 1.6700
+
+ Columns 169 through 174
+
+ 1.6800 1.6900 1.7000 1.7100 1.7200 1.7300
+
+ Columns 175 through 180
+
+ 1.7400 1.7500 1.7600 1.7700 1.7800 1.7900
+
+ Columns 181 through 186
+
+ 1.8000 1.8100 1.8200 1.8300 1.8400 1.8500
+
+ Columns 187 through 192
+
+ 1.8600 1.8700 1.8800 1.8900 1.9000 1.9100
+
+ Columns 193 through 198
+
+ 1.9200 1.9300 1.9400 1.9500 1.9600 1.9700
+
+ Columns 199 through 201
+
+ 1.9800 1.9900 2.0000
+
+z=8-2*x-7*exp(-x/2); plot(x,z);
+z=8-2*x-7*exp(-x/2)
+
+z =
+
+ Columns 1 through 6
+
+ 1.0000 1.0149 1.0297 1.0442 1.0586 1.0728
+
+ Columns 7 through 12
+
+ 1.0869 1.1008 1.1145 1.1280 1.1414 1.1546
+
+ Columns 13 through 18
+
+ 1.1676 1.1805 1.1932 1.2058 1.2182 1.2304
+
+ Columns 19 through 24
+
+ 1.2425 1.2544 1.2661 1.2777 1.2892 1.3004
+
+ Columns 25 through 30
+
+ 1.3116 1.3225 1.3333 1.3440 1.3545 1.3648
+
+ Columns 31 through 36
+
+ 1.3750 1.3851 1.3950 1.4047 1.4143 1.4238
+
+ Columns 37 through 42
+
+ 1.4331 1.4423 1.4513 1.4602 1.4689 1.4775
+
+ Columns 43 through 48
+
+ 1.4859 1.4942 1.5024 1.5104 1.5183 1.5260
+
+ Columns 49 through 54
+
+ 1.5336 1.5411 1.5484 1.5556 1.5626 1.5696
+
+ Columns 55 through 60
+
+ 1.5763 1.5830 1.5895 1.5959 1.6022 1.6083
+
+ Columns 61 through 66
+
+ 1.6143 1.6201 1.6259 1.6315 1.6370 1.6423
+
+ Columns 67 through 72
+
+ 1.6475 1.6526 1.6576 1.6625 1.6672 1.6718
+
+ Columns 73 through 78
+
+ 1.6763 1.6806 1.6849 1.6890 1.6930 1.6968
+
+ Columns 79 through 84
+
+ 1.7006 1.7042 1.7078 1.7112 1.7144 1.7176
+
+ Columns 85 through 90
+
+ 1.7207 1.7236 1.7264 1.7291 1.7317 1.7342
+
+ Columns 91 through 96
+
+ 1.7366 1.7389 1.7410 1.7431 1.7450 1.7468
+
+ Columns 97 through 102
+
+ 1.7485 1.7501 1.7516 1.7530 1.7543 1.7555
+
+ Columns 103 through 108
+
+ 1.7565 1.7575 1.7584 1.7591 1.7598 1.7603
+
+ Columns 109 through 114
+
+ 1.7608 1.7611 1.7614 1.7615 1.7615 1.7615
+
+ Columns 115 through 120
+
+ 1.7613 1.7611 1.7607 1.7603 1.7597 1.7591
+
+ Columns 121 through 126
+
+ 1.7583 1.7575 1.7565 1.7555 1.7544 1.7532
+
+ Columns 127 through 132
+
+ 1.7519 1.7505 1.7490 1.7474 1.7457 1.7439
+
+ Columns 133 through 138
+
+ 1.7420 1.7401 1.7380 1.7359 1.7337 1.7314
+
+ Columns 139 through 144
+
+ 1.7290 1.7265 1.7239 1.7212 1.7185 1.7157
+
+ Columns 145 through 150
+
+ 1.7127 1.7097 1.7066 1.7035 1.7002 1.6969
+
+ Columns 151 through 156
+
+ 1.6934 1.6899 1.6863 1.6827 1.6789 1.6751
+
+ Columns 157 through 162
+
+ 1.6712 1.6672 1.6631 1.6589 1.6547 1.6504
+
+ Columns 163 through 168
+
+ 1.6460 1.6415 1.6370 1.6324 1.6277 1.6229
+
+ Columns 169 through 174
+
+ 1.6180 1.6131 1.6081 1.6030 1.5979 1.5926
+
+ Columns 175 through 180
+
+ 1.5873 1.5820 1.5765 1.5710 1.5654 1.5597
+
+ Columns 181 through 186
+
+ 1.5540 1.5482 1.5423 1.5364 1.5304 1.5243
+
+ Columns 187 through 192
+
+ 1.5181 1.5119 1.5056 1.4992 1.4928 1.4863
+
+ Columns 193 through 198
+
+ 1.4797 1.4731 1.4664 1.4597 1.4528 1.4459
+
+ Columns 199 through 201
+
+ 1.4390 1.4319 1.4248
+
+z=8-2*x-7*exp(-x/2);
+plot(x,z)
+N=5; eulerN; plot(t,y);
+clear
+N=5; eulerN; plot(t,y);
+clear
+N=5; eulerN; plot(t,y);
+N=10; eulerN; plot(t,y);
+clear
+N=10; eulerN; plot(t,y);
+N=5; eulerN; plot(t,y);
+hold on
+N=10; eulerN; plot(t,y);
+clear
+N=5; eulerN; plot(t,y);
+hold on
+clear; N=10; eulerN; plot(t,y);
+clear; N=20; eulerN; plot(t,y);
+clear; N=40; eulerN; plot(t,y);
+clear; N=80; eulerN; plot(t,y);
+z=8-2*x-7*exp(-x/2); plot(x,z);
+{Undefined function or variable 'x'.
+}
+x=0:0.01:2
+
+x =
+
+ Columns 1 through 6
+
+ 0 0.0100 0.0200 0.0300 0.0400 0.0500
+
+ Columns 7 through 12
+
+ 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100
+
+ Columns 13 through 18
+
+ 0.1200 0.1300 0.1400 0.1500 0.1600 0.1700
+
+ Columns 19 through 24
+
+ 0.1800 0.1900 0.2000 0.2100 0.2200 0.2300
+
+ Columns 25 through 30
+
+ 0.2400 0.2500 0.2600 0.2700 0.2800 0.2900
+
+ Columns 31 through 36
+
+ 0.3000 0.3100 0.3200 0.3300 0.3400 0.3500
+
+ Columns 37 through 42
+
+ 0.3600 0.3700 0.3800 0.3900 0.4000 0.4100
+
+ Columns 43 through 48
+
+ 0.4200 0.4300 0.4400 0.4500 0.4600 0.4700
+
+ Columns 49 through 54
+
+ 0.4800 0.4900 0.5000 0.5100 0.5200 0.5300
+
+ Columns 55 through 60
+
+ 0.5400 0.5500 0.5600 0.5700 0.5800 0.5900
+
+ Columns 61 through 66
+
+ 0.6000 0.6100 0.6200 0.6300 0.6400 0.6500
+
+ Columns 67 through 72
+
+ 0.6600 0.6700 0.6800 0.6900 0.7000 0.7100
+
+ Columns 73 through 78
+
+ 0.7200 0.7300 0.7400 0.7500 0.7600 0.7700
+
+ Columns 79 through 84
+
+ 0.7800 0.7900 0.8000 0.8100 0.8200 0.8300
+
+ Columns 85 through 90
+
+ 0.8400 0.8500 0.8600 0.8700 0.8800 0.8900
+
+ Columns 91 through 96
+
+ 0.9000 0.9100 0.9200 0.9300 0.9400 0.9500
+
+ Columns 97 through 102
+
+ 0.9600 0.9700 0.9800 0.9900 1.0000 1.0100
+
+ Columns 103 through 108
+
+ 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700
+
+ Columns 109 through 114
+
+ 1.0800 1.0900 1.1000 1.1100 1.1200 1.1300
+
+ Columns 115 through 120
+
+ 1.1400 1.1500 1.1600 1.1700 1.1800 1.1900
+
+ Columns 121 through 126
+
+ 1.2000 1.2100 1.2200 1.2300 1.2400 1.2500
+
+ Columns 127 through 132
+
+ 1.2600 1.2700 1.2800 1.2900 1.3000 1.3100
+
+ Columns 133 through 138
+
+ 1.3200 1.3300 1.3400 1.3500 1.3600 1.3700
+
+ Columns 139 through 144
+
+ 1.3800 1.3900 1.4000 1.4100 1.4200 1.4300
+
+ Columns 145 through 150
+
+ 1.4400 1.4500 1.4600 1.4700 1.4800 1.4900
+
+ Columns 151 through 156
+
+ 1.5000 1.5100 1.5200 1.5300 1.5400 1.5500
+
+ Columns 157 through 162
+
+ 1.5600 1.5700 1.5800 1.5900 1.6000 1.6100
+
+ Columns 163 through 168
+
+ 1.6200 1.6300 1.6400 1.6500 1.6600 1.6700
+
+ Columns 169 through 174
+
+ 1.6800 1.6900 1.7000 1.7100 1.7200 1.7300
+
+ Columns 175 through 180
+
+ 1.7400 1.7500 1.7600 1.7700 1.7800 1.7900
+
+ Columns 181 through 186
+
+ 1.8000 1.8100 1.8200 1.8300 1.8400 1.8500
+
+ Columns 187 through 192
+
+ 1.8600 1.8700 1.8800 1.8900 1.9000 1.9100
+
+ Columns 193 through 198
+
+ 1.9200 1.9300 1.9400 1.9500 1.9600 1.9700
+
+ Columns 199 through 201
+
+ 1.9800 1.9900 2.0000
+
+z=8-2*x-7*exp(-x/2); plot(x,z);
+z=8-2*2-7*exp(-2/2);%exact solution at t=2for k=1:5N=5*2^(k-1);eulerN;%difference between Euler approximation and exact solution at t=2.error(k)=y(N+1)-z;end
+clear
+approx;
+error
+
+error =
+
+ 0.2814 0.1344 0.0658 0.0325 0.0162
+
+error(2)/2
+
+ans =
+
+ 0.0672
+
+clear
+diary off]
diff --git a/math2373/lab6/partialEuler.png b/math2373/lab6/partialEuler.png
new file mode 100644
index 0000000..fe054d6
--- /dev/null
+++ b/math2373/lab6/partialEuler.png
Binary files differ
diff --git a/math2373/lab7/lab7.txt b/math2373/lab7/lab7.txt
new file mode 100644
index 0000000..446d49a
--- /dev/null
+++ b/math2373/lab7/lab7.txt
@@ -0,0 +1,135 @@
+p100OG; p2
+
+p2 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+d=200; p100OG; p2
+
+p2 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+d=500; p100OG; p2
+
+p2 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+d=100; p100OG; p3
+
+p3 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+d=100; p100OG; p4
+
+p4 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+d=100; p100OG; p5
+
+p5 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+p100OG; p5
+
+p5 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+clear p5
+p100OG; p5
+
+p5 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+p100OG; p5
+
+p5 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+p100OG; p5
+
+p5 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+p100OG; p5
+
+p5 =
+
+ 0.2264
+ 0.1132
+ 0.0377
+ 0.3396
+ 0.2830
+
+diary off
+I=eye(5);R=rref(AI);
+{Undefined function or variable 'AI'.
+}
+I=eye(5);R=rref(A-I);
+{Matrix dimensions must agree.
+}
+I=eye(6);R=rref(A-I);
+v=-R(:,5);
+v=-R(:,6);
+v=-R(:,6); v(6)=1;
+p=v/sum(v);
+p
+
+p =
+
+ 0.0851
+ 0.1702
+ 0.1064
+ 0.1560
+ 0.2695
+ 0.2128
+
+diary off
diff --git a/math2373/lab7/p100.m b/math2373/lab7/p100.m
new file mode 100644
index 0000000..3559149
--- /dev/null
+++ b/math2373/lab7/p100.m
@@ -0,0 +1,20 @@
+A=[ 0 1/2 0 0 0 0;
+ 0 0 1/3 0 1/2 0;
+ 1/4 1/2 0 0 0 0;
+ 1/4 0 0 0 1/2 0;
+ 1/4 0 1/3 0 0 1;
+ 1/4 0 1/3 1 0 0; ];
+%Matrix A from lab
+p1=[1;0;0;0;0;0];
+p2=[0;1;0;0;0;0];
+p3=[0;0;1;0;0;0];
+p4=[0;0;0;1;0;0];
+p5=[0;0;0;0;1;0];
+p6=[0;0;0;0;0;1];
+for n=1:100
+ p1=A*p1;
+ p2=A*p2;
+ p3=A*p3;
+ p4=A*p4;
+ p5=A*p5;
+end
diff --git a/math2373/lab7/p100OG.m b/math2373/lab7/p100OG.m
new file mode 100644
index 0000000..87fcc0f
--- /dev/null
+++ b/math2373/lab7/p100OG.m
@@ -0,0 +1,19 @@
+A=[0 1/3 1/2 1/2 0;
+ 1/2 0 0 0 0;
+ 0 1/3 0 0 0;
+ 0 1/3 1/2 0 1;
+ 1/2 0 0 1/2 0];
+%Matrix A from lab
+p1=[1;0;0;0;0];
+p2=[0;1;0;0;0];
+p3=[0;0;1;0;0];
+p4=[0;0;0;1;0];
+p5=[0;0;0;0;1];
+for n=1:600
+ p1=A*p1;
+ p2=A*p2;
+ p3=A*p3;
+ p4=A*p4;
+ p5=A*p5;
+end
+
diff --git a/math2373/lab8.txt b/math2373/lab8.txt
new file mode 100644
index 0000000..baa88c9
--- /dev/null
+++ b/math2373/lab8.txt
@@ -0,0 +1,148 @@
+diary off
+diary off
+A=[4 -3; -7 8]
+
+A =
+
+ 4 -3
+ -7 8
+
+[P,D]=eig(A)
+
+P =
+
+ -0.7071 0.3939
+ -0.7071 -0.9191
+
+
+D =
+
+ 1 0
+ 0 11
+
+c=inv(P)*[10;-5]
+
+c =
+
+ -7.7782
+ 11.4237
+
+R=[c(1) 0 0; 0 c(2) 0], E=P*R
+
+R =
+
+ -7.7782 0 0
+ 0 11.4237 0
+
+
+E =
+
+ 5.5000 4.5000 0
+ 5.5000 -10.5000 0
+
+R=[c(1) 0; 0 c(2)], E=P*R
+
+R =
+
+ -7.7782 0
+ 0 11.4237
+
+
+E =
+
+ 5.5000 4.5000
+ 5.5000 -10.5000
+
+A=[12 -7 4;6 -1 1;-12 12 -7];
+[P,D]=eig(A)
+
+P =
+
+ 0.2024 0.7071 0.2617
+ -0.1215 0.7071 0.7328
+ -0.9717 0.0000 0.6281
+
+
+D =
+
+ -3.0000 0 0
+ 0 5.0000 0
+ 0 0 2.0000
+
+c= inv(P)*[10;20;25]
+
+c =
+
+ -21.6109
+ 17.9723
+ 6.3683
+
+c= inv(P)*[-10;20;25]
+
+c =
+
+ 27.7855
+ -52.7384
+ 82.7882
+
+R=[c(1) 0 0; 0 c(2) 0; 0 0 c(3)], E=P*R
+
+R =
+
+ 27.7855 0 0
+ 0 -52.7384 0
+ 0 0 82.7882
+
+
+E =
+
+ 5.6250 -37.2917 21.6667
+ -3.3750 -37.2917 60.6667
+ -27.0000 -0.0000 52.0000
+
+clear
+A=[0 0 1 0; 0 0 0 1; 25 18 0 0; 12 40 0 0];
+[P,D]=eig(A)
+
+P =
+
+ 0.0849 0.2169 0.0849 0.2169
+ 0.1131 -0.1085 0.1131 -0.1085
+ 0.5940 0.8677 -0.5940 -0.8677
+ 0.7920 -0.4339 -0.7920 0.4339
+
+
+D =
+
+ 7.0000 0 0 0
+ 0 4.0000 0 0
+ 0 0 -7.0000 0
+ 0 0 0 -4.0000
+
+c= inv(P)*[23;16;69;0]
+
+c =
+
+ 104.2294
+ 47.3549
+ 72.5473
+ -10.4768
+
+R=[c(1) 0 0 0; 0 c(2) 0 0; 0 0 c(3) 0; 0 0 0 c(4)], E=P*R
+
+R =
+
+ 104.2294 0 0 0
+ 0 47.3549 0 0
+ 0 0 72.5473 0
+ 0 0 0 -10.4768
+
+
+E =
+
+ 8.8442 10.2727 6.1558 -2.2727
+ 11.7922 -5.1364 8.2078 1.1364
+ 61.9091 41.0909 -43.0909 9.0909
+ 82.5455 -20.5455 -57.4545 -4.5455
+
+diary of
diff --git a/math2373/lab9.txt b/math2373/lab9.txt
new file mode 100644
index 0000000..5079803
--- /dev/null
+++ b/math2373/lab9.txt
@@ -0,0 +1,323 @@
+t=[0:2:100]
+
+t =
+
+ Columns 1 through 11
+
+ 0 2 4 6 8 10 12 14 16 18 20
+
+ Columns 12 through 22
+
+ 22 24 26 28 30 32 34 36 38 40 42
+
+ Columns 23 through 33
+
+ 44 46 48 50 52 54 56 58 60 62 64
+
+ Columns 34 through 44
+
+ 66 68 70 72 74 76 78 80 82 84 86
+
+ Columns 45 through 51
+
+ 88 90 92 94 96 98 100
+
+clear
+t=[0:2:100];
+x=10+exp(-0.2618*t)
+
+x =
+
+ Columns 1 through 6
+
+ 11.0000 10.5924 10.3509 10.2079 10.1231 10.0729
+
+ Columns 7 through 12
+
+ 10.0432 10.0256 10.0152 10.0090 10.0053 10.0032
+
+ Columns 13 through 18
+
+ 10.0019 10.0011 10.0007 10.0004 10.0002 10.0001
+
+ Columns 19 through 24
+
+ 10.0001 10.0000 10.0000 10.0000 10.0000 10.0000
+
+ Columns 25 through 30
+
+ 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
+
+ Columns 31 through 36
+
+ 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
+
+ Columns 37 through 42
+
+ 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
+
+ Columns 43 through 48
+
+ 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
+
+ Columns 49 through 51
+
+ 10.0000 10.0000 10.0000
+
+clear
+t=[0:2:100];
+x=10+exp(-0.2618*t);
+Q=[-14.4721 10 -5.5279; 8.9443 -10 -8.9443; -5.5279 10 -14.4721];
+x=10+Q*exp(-0.2618*t);
+{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('mtimes')" style="font-weight:bold"> * </a>
+Incorrect dimensions for matrix multiplication. Check that the
+number of columns in the first matrix matches the number of rows in
+the second matrix. To perform elementwise multiplication, use '.*'.
+}
+x=10+Q.*exp(-0.2618*t);
+{Matrix dimensions must agree.
+}
+x=10+Q[1:].*exp(-0.2618*t);
+ x=10+Q[1:].*exp(-0.2618*t);
+ ↑
+{Error: Invalid expression. When calling a function or indexing a
+variable, use parentheses. Otherwise, check for mismatched
+delimiters.
+}
+x=10+Q[:1].*exp(-0.2618*t);
+ x=10+Q[:1].*exp(-0.2618*t);
+ ↑
+{Error: Invalid expression. When calling a function or indexing a
+variable, use parentheses. Otherwise, check for mismatched
+delimiters.
+}
+x=10+Q.*exp(-0.2618*t);
+{Matrix dimensions must agree.
+}
+x=10+Q(:,1).*exp(-0.2618*t);
+plot(t,x)
+x=10+Q(1,:).*exp(-0.2618*t);
+{Matrix dimensions must agree.
+}
+x=10+Q(:,1).*exp(-0.2618*t);
+plot(t,x)
+clear x
+x=10+Q(:,1).*exp(-0.2618*t);
+clear x
+Q(:,1)
+
+ans =
+
+ -14.4721
+ 8.9443
+ -5.5279
+
+x=10+Q(:,1)*exp(-0.2618*t);
+x=10+Q(1,:)*exp(-0.2618*t);
+{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('mtimes')" style="font-weight:bold"> * </a>
+Incorrect dimensions for matrix multiplication. Check that the
+number of columns in the first matrix matches the number of rows
+in the second matrix. To perform elementwise multiplication, use
+'.*'.
+}
+x=10+Q(:,1)*exp(-0.2618*t);
+plot(t,x)
+x=10+Q(1)*exp(-0.2618*t);
+Q(1)
+
+ans =
+
+ -14.4721
+
+x=10+Q(1)*exp(-0.2618*t)+Q(2)*exp(-0.2618*t)+Q(3)*exp(-0.2618*t);
+plot(t,x)
+F=-.2618; x=10+Q(1)*exp(F*t)+Q(2)*exp(F*t)+Q(3)*exp(F*t);
+plot(t,x);
+hold on;
+F=-.2618, y=3; y=10+Q(y+1)*exp(F*t)+Q(y+2)*exp(F*t)+Q(y+3)*exp(F*t);
+
+F =
+
+ -0.2618
+
+F=-.2618; y=3; y=10+Q(y+1)*exp(F*t)+Q(y+2)*exp(F*t)+Q(y+3)*exp(F*t);
+plot(t,y)
+F=-0.2; y=3; y=10+Q(y+1)*exp(F*t)+Q(y+2)*exp(F*t)+Q(y+3)*exp(F*t);
+plot(t,y)
+hold off
+plot(t,x)
+Q(4)
+
+ans =
+
+ 10
+
+Q(3
+ Q(3
+ ↑
+{Error: Invalid expression. When calling a function or indexing a
+variable, use parentheses. Otherwise, check for mismatched
+delimiters.
+}
+Q(3)
+
+ans =
+
+ -5.5279
+
+Q(0)
+{Array indices must be positive integers or logical values.
+}
+Q(4)
+
+ans =
+
+ 10
+
+Q(5)
+
+ans =
+
+ -10
+
+Q(6)
+
+ans =
+
+ 10
+
+Q(7)
+
+ans =
+
+ -5.5279
+
+Q(8)
+
+ans =
+
+ -8.9443
+
+Q(9)
+
+ans =
+
+ -14.4721
+
+Q(10)
+{Index exceeds array bounds.
+}
+Q(5)
+
+ans =
+
+ -10
+
+Q(6)
+
+ans =
+
+ 10
+
+F=-0.2; y=3; y=10+Q(y,1)*exp(F*t)+Q(y,2)*exp(F*t)+Q(y,3)*exp(F*t);
+F=-0.2; y=0; x=10+Q(y,1)*exp(F*t)+Q(y,2)*exp(F*t)+Q(y,3)*exp(F*t);
+{Index in position 1 is invalid. Array indices must be positive
+integers or logical values.
+}
+F=-0.2; y=1; x=10+Q(y,1)*exp(F*t)+Q(y,2)*exp(F*t)+Q(y,3)*exp(F*t);
+F=-0.2618; y=1; x=10+Q(y,1)*exp(F*t)+Q(y,2)*exp(F*t)+Q(y,3)*exp(F*t);
+plot(t,x)
+hold on;
+F=-0.2; y=2; x=10+Q(y,1)*exp(F*t)+Q(y,2)*exp(F*t)+Q(y,3)*exp(F*t);
+plot(t,y)
+F=-0.2618; y=1; x=10+Q(y,1)*exp(F*t)+Q(y,2)*exp(F*t)+Q(y,3)*exp(F*t);
+F=-0.2; y=2; y=10+Q(y,1)*exp(F*t)+Q(y,2)*exp(F*t)+Q(y,3)*exp(F*t);
+plot(t,y)
+clear plot
+F=-0.2618; y=1; x=10+Q(y,1)*exp(F*t)+Q(y,2)*exp(F*t)+Q(y,3)*exp(F*t);
+F=-0.2618; z=2; y=10+Q(z,1)*exp(F*t)+Q(z,2)*exp(F*t)+Q(z,3)*exp(F*t);
+F=-0.2; z=2; y=10+Q(z,1)*exp(F*t)+Q(z,2)*exp(F*t)+Q(z,3)*exp(F*t);
+plot(t,y)
+plot(t,x)
+hold onl
+{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('hold', '/soft/MATLAB/R2018a/toolbox/matlab/graphics/hold.m', 83)" style="font-weight:bold">hold</a> (<a href="matlab: opentoline('/soft/MATLAB/R2018a/toolbox/matlab/graphics/hold.m',83,0)">line 83</a>)
+Unknown command option.
+}
+hold on
+plot(t,y)
+F=-0.2; z=2; y=10+Q(z,1)*exp(F*t)+Q(z,2)*exp(F*t)+Q(z,3)*exp(F*t);
+Q(2,1)
+
+ans =
+
+ 8.9443
+
+F=-0.2; z=2; y=10+Q(z,1)*exp(F*t)+Q(z,2)*exp(F*t)+Q(z,3)*exp(F*t);
+F=-0.2; a=2; z=10+Q(a,1)*exp(F*t)+Q(a,2)*exp(F*t)+Q(a,3)*exp(F*t);
+F=-0.0382; a=3; z=10+Q(a,1)*exp(F*t)+Q(a,2)*exp(F*t)+Q(a,3)*exp(F*t);
+plot (t,z)
+clear plot;
+plot (t,x)
+plot (t,z)
+plot (t,x)
+hold on
+plot (t,z)
+F=-0.2; z=2; y=10+Q(z,1)*exp(F*t)+Q(z,2)*exp(F*t)+Q(z,3)*exp(F*t);
+plot(t,y)
+plot(t,x); plot(t,y) plot(t,z)
+ plot(t,x); plot(t,y) plot(t,z)
+ ↑
+{Error: Invalid expression. Check for missing multiplication
+operator, missing or unbalanced delimiters, or other syntax
+error. To construct matrices, use brackets instead of
+parentheses.
+}
+plot(t,x); plot(t,y); plot(t,z)
+clear plot
+plot(t,x); hold on; plot(t,y); plot(t,z)
+plot(t,x); plot(t,y); plot(t,z)
+hold on
+plot(t,x); plot(t,y); plot(t,z)
+F=-0.2; z=2; y=10+Q(z,1)*exp(F*t)+Q(z,2)*exp(F*t)+Q(z,3)*exp(F*t);
+plot(t,x); plot(t,y); plot(t,z)
+F=-0.0382; a=3; z=10+Q(a,1)*exp(F*t)+Q(a,2)*exp(F*t)+Q(a,3)*exp(F*t);
+plot(t,x); plot(t,y); plot(t,z)
+hold on;
+plot(t,x); plot(t,y); plot(t,z)
+F=-0.0382; z=10+Q(a,1)*exp(-.2618*t)+Q(a,2)*exp(-.2*t)+Q(a,3)*exp(-.0382*t);
+a=1; z=10+Q(a,1)*exp(-.2618*t)+Q(a,2)*exp(-.2*t)+Q(a,3)*exp(-.0382*t);
+a=1; x=10+Q(a,1)*exp(-.2618*t)+Q(a,2)*exp(-.2*t)+Q(a,3)*exp(-.0382*t);
+a=2; y=10+Q(a,1)*exp(-.2618*t)+Q(a,2)*exp(-.2*t)+Q(a,3)*exp(-.0382*t);
+a=3; z=10+Q(a,1)*exp(-.2618*t)+Q(a,2)*exp(-.2*t)+Q(a,3)*exp(-.0382*t);
+hold on;
+plot(t,x); plot(t,y); plot(t,z)
+plot(t,x,'b:s'); plot(t,y,'r:p'); plot(t,z,'g,t')
+{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('plot')" style="font-weight:bold">plot</a>
+Error in color/linetype argument.
+}
+plot(t,x,'b:s'); plot(t,y,'r:p'); plot(t,z,'g,o')
+{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('plot')" style="font-weight:bold">plot</a>
+Error in color/linetype argument.
+}
+plot(t,x,'b:s'); plot(t,y,'r:p'); plot(t,z,'-o')
+t.label("time")
+{Dot indexing is not supported for variables of this type.
+}
+t.label('time')
+{Dot indexing is not supported for variables of this type.
+}
+x.label('time')
+{Dot indexing is not supported for variables of this type.
+}
+xlabel('time')
+xlabel('Time')
+ylabel('Amount of salt')
+xlabel('Time (seconds)')
+xlabel('Time (min)')
+plot(t,x,'b:s'); plot(t,y,'r:p'); plot(t,z,'-o')
+xlabel('Time (min)')
+ylabel('Amount of salt')
+hold on;
+plot(t,x,'b:s'); plot(t,y,'r:p'); plot(t,z,'-o')
+xlabel('Time (min)')
+ylabel('Amount of salt')
generated by cgit v1.2.3 (git 2.46.0) at 2024-11-21 16:56:11 +0000