Section Homework problems
1.1 #1-11,13,15
1.2 #1,3,5,7,21
1.3 #1,3,5,7,9,11,15
2.2 #1,5,7,13,21,25
2.3 #1,3,9,15,25
3.1 #3,5,9,11,13,19
3.3 #4,5,7
4.1.1 #1,3,7,9,11(a,b)
4.1.2 #15,17,19,23,27
4.1.3 #31,33,35
4.2 #1,3,5,17
4.3 #1,7,11,17,31,37
4.4 #5,7,15,19,21,23,29,35
4.6 #1,23,25
4.7 #1,5,17,19,23,27(but don't do the graphing utility part)
4.8 #1,3,5,9
5.1.1, 5.1.2 #1,3,9,17,21,23(b)
5.1.3, 5.1.4 #29,31,45,47
8.1 #1,5,7,11,15,17,23
8.2.1 #1,9,13
8.2.2 #19,23
8.2.3 #33,41
8.3 #1,5,9,11,13
8.4 #1,3,5,9,14
Here are some practice problems to prepare you for the exam on 3/31/11
1.1 # 1-10,12,15,17
1.2 # 2,4,7,13,15,23,24
1.3 # 4,6,8,10,14
2.2 # 2-18(odd),24
2.3 # 6,8,10,12,30
3.1 # 1,6,8,12,15,19,23,25
3.3 # 6,12
4.1 # 2,5,10,16,18,20,21,24,25,26,32,34
4.2 # 2,6,19
4.3 # 4-14(odd),15,16,18,19,27,31,33
4.4 # 4,8,10,12,14,16
Here are some practice problems to prepare you for the final exam
4.5 # 2,19,26
4.7 # 3,9,15,21
4.8 # 4,6,8
5.1 # 2,5,6,22,30,33,46,48
8.1 # 2,8,12,19,24
8.2 # 3,11,14,20,23,27,35,43
8.3 # 13,19
8.4 # 4,7,10,13
Mathematica code for numerical and analytical solutions of ordinary differential equations:
(*Euler's Method*)
Clear[x, y, f, h]
f[x_, y_] = 2*x - 3*y + 1
y = 5;
h = .1;
For[x = 1, x < 1.3, x = x + h, y = y + h*f[x, y]; Print[x + h]; Print[y]]
(*Improved Euler's Method*)
Clear[x, y, y1, f, h]
f[x_, y_] = 2*x - 3*y + 1
y = 5;
h = .1;
For[x = 1, x < 1.3, x = x + h, y1 = y + h*f[x, y];
y = y + h*(f[x, y] + f[x + h, y1])/2; Print[x + h]; Print[y]]
(*Runge--Kutta Method, RK-4*)
Clear[x, y, f, h, k1, k2, k3, k4]
f[x_, y_] = 2*x - 3*y + 1
y = 5;
h = .1;
For[x = 1, x < 1.3, x = x + h, k1=f(x,y); k2=f(x+h/2,y+h*k1/2); k3=f(x+h/2,y+h*k2/2); k4=f(x+h,y+h*k3); y = y + h*(k1+2*k2+2*k3+k4)/6; Print[x + h]; Print[y]]
(*DSolve Command*)
Clear[x, y, f]
f[x_, y_] = 2*x - 3*y + 1
DSolve[y'[x] == f[x, y[x]], y[x], x]
(*DSolve Command with initial conditions*)
Clear[x, y, f]
f[x_, y_] = 2*x - 3*y + 1
DSolve[{y'[x] == f[x, y[x]], y[1] == 5}, y[x], x]
(*NDSolve Command*)
Clear[x, y, f, g, sol]
f[x_, y_] = 2*x - 3*y + 1
sol = NDSolve[{y'[x] == f[x, y[x]], y[1] == 5}, y[x], {x, 1, 2}]
g[x_] = y[x] /. sol{{1}}
Plot[g[x], {x, 1, 2}]
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