Midterm 2 (take-home)
solutions
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Homework
#1: (8/28)[solutions] |
Section
1.2: Ex 1 Section 1.3: Ex 1,2,3,5,7,8,9,10; AP 2 |
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Homework
#2: (9/6)[solutions] |
Section 2.1: Ex 1,2,3,4,6,11; AP 1 |
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Homework
#3: (9/11)[solutions] |
Section
2.2: Ex 3,4,5,9,12,14 Section 2.3: Ex 1,4; AP 1,2 |
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Homework
#4: (9/15)[solutions] |
Section 2.4: Ex 2,8,9,12,14; AP 2,3,8 |
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Homework
#5: (9/20)[solutions] |
Section
3.1: Ex 2,3,5,6 Section
3.2: Ex 2,5,10,13,15 |
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Homework
#6: (9/25)[solutions] |
Section
3.3: Ex 4; AP 2,3 Section
3.4: Ex 1,10,15; AP 1,3,4,5 |
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Homework
#7: (10/2)[solutions] |
Section
3.5: Ex 2,3; AP 1,2,3,6 Section
3.6: AP 1,2,3(i) |
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Homework
#8: (10/9)[solutions] |
Section
4.2: Ex 3; AP 2 Section
4.3: Ex 13; AP 1,2 Section
4.4: Ex 5,7; AP 1,2 |
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Homework
#9: (10/16)[solutions] |
Section
5.1: Ex 2,9; AP 2,3 Section
5.2: Ex 2,3,7,14,15 |
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Homework
#10: (10/23)[solutions] |
Section
5.3: Ex 4,5; AP 1,5 Section
5.4: Ex 1,2,3,4; AP 1,3 |
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Homework
#11: (10/30)[solutions] |
Section
6.1: Ex 2,4,13 Section
6.2: Ex 1,3,7 |
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Homework
#12: (11/3)[solutions] |
Section
7.2: Ex 1,2,8,9; AP 1,3,4,7 |
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Homework
#13: (11/6)[solutions] |
Section
7.4: AP 1,2 |
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Homework
#14: (11/13)[solutions] |
Section
9.1: Ex 1,5,10,15,16 Section
9.2: Ex 1,8,9; AP 1-5,9 Section
9.3: AP 1-5 |
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Homework
#15: (11/15)[solutions] |
1. Write a program to solve dy/dt
= f(t, y) by the 2. Use your code from Problem 1
to do AP #1 in section 9.4, and compare your results to those obtained with
the Euler and Heun methods. |
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Homework
#16: (11/29)[solutions] |
Section
9.5: Ex 6,8; AP 1-5, 11 Section
9.6: AP 4,5 11. Write a code to implement the
implicit trapezoidal rule yk+1 = yk + h/2 [f(tk, yk) + f(tk+1, yk+1)], use
it to compute approximations to the problems in 9.6 AP 4,5, and compare with
the results obtained with the Adams-Bashforth-Moulton method. |
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Homework
#17: (12/11)[solutions] |
Section
9.7: Ex 1,5; AP 1-3,6,13 Section
9.8: Ex 1(a); AP 1 Section
9.9: AP 2-7 |
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Bonus: (12/11) |
1. Write a code to compute the
eigenvalues of an n by n Matrix A. 2. Write a code to find all
roots of a degree N polynomial P(x) = aNxN + aN-1xN-1 + … + a1x + a0 By
forming the companion matrix C and using your code from 1 to find the
eigenvalues. 3. Use your code from 2 to find
all the zeros of the polynomial P(x) = x12 – 96.99x11
– 317x10 + 1519.85x9 + 7865.71x8 + 14805.3x7
+ 22484.6x6 + 17030.8x5 – 16492.3x4 –
33262.3x3 – 13543.4x2 + 3.32605x + 1.3545 |
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Solution: |
P(x)
= (x-100)(x-5)(x+3.01)(x+3)(x2+3)(x+1)3(x-.01)(x+.01)(x-1) There
is a triple root at x = -1. The other
roots are 100,
5, -3.01, -3, 1.732 i, -1.732 i, .01, -.01, 1 |