1Math 442 Intro to PDE
Homework
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Due |
Section | Pages | Exercises | Comment |
|---|---|---|---|---|---|
| HW 1 | Aug 31 |
1.1 | |
2abc, 3bcef, 10, 12 | |
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1.2 | |
1, 3, 6, 7 | |
| HW 2 | Sep 7 |
1.3 | p18-19 | 2, 4, 6 | #2: take a naive
approach; ditermine T and re-use the wave equation #4: "homogeneity in the horizontal directions" means that u=u(z,t) is independent of x and y #6: we are assuming that kappa , c and rho are all constant and we write k=kappa/(c rho): also, you can use formula (5) on p151 |
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1.4 | p24-25 | 1, 3, 5 | #3: note that D is a
region in 3 dimensions |
| HW 3 | Sep 14 |
2.1 | p36-37 |
1, 3, 5, 8, 9 | |
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2.2 | p40 |
1, 2, 3, 5 | |
| HW 4 | Sep 21 |
2.3 | p44-45 |
3, 5(a), 6 | In 3(a), show u(x,t)
>= 0 instead of u(x,t) > 0. |
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1.5 | p27 |
2 | |
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2.4 | p50-51 |
1, 4 | |
| HW 5 | Sep 28 | 2.4, 2.5 | Download the homework | Answer Key: p1, p2, p3, p4 | |
| No HW | Oct 5 | 3.3, 3.4 | You may solve #2 in the section 3.4. (Don't turn this in.) | ||
| HW 6 | Oct 12 |
4.1 | p87 |
2, 4 | In 2, Strauss means
Dirichlet BCs. In 4, explain where the assumption 0 < r < 2 pi c/l is used. |
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4.2 | p90 |
2, 3 | In 2(a), it is better
to wirte the eigenfunctions as cos (n pi x/2l) for odd n. In 3, make sure you consider all cases: lambda > 0, = 0, < 0. |
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4.3 | p97 |
1 | Consider only when a < -1/l. |
| HW 7 | Oct 19 |
5.1 | p108 |
8 | |
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5.2 | p113 |
9, 11, 17 | |
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5.3 | p118-119 |
3, 6 | In 3, change the BCs,
using instead that u_x(0,t)=0 and u(l,t)=0. Use the given ICs. You may
want to use the result from Exercise 4.2.2 in your previous homework. |
| HW 8 | Oct 26 |
5.3 | p120 |
15 | |
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5.4 | p129-131 |
5, 8(a)(b), 9, 13, 18 | In 13, use l=pi. |
| HW 9 | Nov 2 |
5.4 | p131 |
13 | Use l=pi. Even if you
aleady handed in this problem for HW 8, turn this in again. |
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5.5 | p139-140 |
5, 12 | In 5, put the absolute
value signs outside of the series on left first,and then show it. In 12, you may use #5.4.9. |
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5.6 | p144-145 |
5, 8, 9, 13(a)(b) | In 5, you are NOT
allowed to use the formula (12) immediately. Assume c=1. In 5, also, note that sin 5x and sin3x are already in the form of Fourier sine series on (0, pi). In 9, assume h=1 and k=3. In 13, you can refer #4.1.4. But here, r is just positive. |
| No HW | Nov 9 | |
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| HW 10 | Nov 16 |
6.1 | p154 |
2, 5, 9 | |
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6.2 | p158-159 |
3, 6, 7(a) | In 6, assume g(x,y)=
cos(2 pi x) - 2cos(3 pi x)cos(4 pi y). In 7, use exponential functions instead of cosh and sinh. |
| HW 11 | Nov 30 | 6.1, 6.3, 2.4, 9.4 | Download the homework | |
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| HW12 | Dec 7 |
OPTIONAL |
If you hand this HW in,
I will drop two lowest HWs including the result of this. No late HW will be accepted (4:50 pm). Don't drop in my mailbox. Bring yours to the class or to my office. Even you don't hand this HW in, I strongly recommend you solve these problems before the final exam. |
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10.3 | p263-264 |
6, 8, 10 | In 6, use (11) on p270
or hint in #6.1.2. In 8(a), see #4.3.1. In 10, see Example 2 on p262. |
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10.6 | p278 |
6 | See Example 2 and the table on p262. |
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12.3 | p329-330 |
1(5)(6)(7), 2(iii)-(vi), 9 | |
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12.4 | p333 |
1 |
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