Problems marked with an asterisk (*) are to be turned in. All problems are taken from Edwards and Penney, Differential Equations and Boundary Value Problems, third edition.
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Solutions to past homework, quizzes, etc.
IODE Extra Credit: due Wednesday, May 5 by 11:00 am in class.
9.5/9.6: Sixth IODE project*
You can work on this project in any of the following EWS labs: 57
Grainger, 406-B1 Engineering or 252 Everitt.
Homework 10: due Wednesday, May 5 by 11:00 am in class.
9.7: 1,2*,7,8*,9*,16*
9.6: 1,2*,6*,7*,8
Warning! Notice that the vertical boundary conditions in #8/#9 of 9.7 involve u_x rather than u. Don't forget to take this into account when setting up and solving the associated eigenvalue problem.
Hint for #16 of 9.7: the Dirichlet problem for the interior of a circular disc is solved on pages 640-641. The solution for the exterior of a disc is similar; the condition that u(r,theta) remain bounded as r tends to infinity substitutes for the condition that u(r,theta) be continuous at r=0 (see the discussion in the middle of page 641). To see how to use a boundary condition at infinity of this sort in a Dirichlet problem, take a look at Example 2 on page 639, specifically the discussion in the middle of the page at equations (18) and (19).
Homework 9: due Friday, April 23 by 4:00 pm in my office.
9.5: 1,3*,10,11*,14*,17*
9.4: 3*,4,9*,10,14,16*
For problems #3,4 in 9.4, you do not need to plot the solution.
For problem #17 in 9.5: Part (b) does not require you to solve any equations! Use part (a) together with your understanding of solutions to linear equations (superposition principle, etc.) to give a purely theoretical verification that u_tr satisfies the indicated boundary value problem. To answer part (c), find the solution to the problem for u_tr from part (b) using the procedure outlined in the section, then conclude that the solution u(x,t) to the original problem is given as the sum of u_ss and u_tr. Be sure to use the specific form for u_ss which you found in part (a).
IODE Homework 4: due Tuesday, April 27 by 4:00 pm in my office
9.1/9.2: Fifth IODE project*
You can work on this project in any of the following EWS labs: 57
Grainger, 406-B1 Engineering or 252 Everitt.
Extra Credit Problem: due any time before Wednesday, May 5.
Homework 8: due Friday, April 16 by 4:00 pm in my office.
9.3: 1,2*,3,4*,7*,9,11*,12
9.2: 1,2*,4*,5,13,17,21*,extra credit problems
What is the relationship between your answers to problems #4 and #5 in 9.2?
For problem #17 in 9.2: Leibniz's series can also be deduced from the Taylor series arctan(x)=x-x^3/3+x^5/5-x^7/7+... How?
IODE Homework 3: due Tuesday, April 13 by 4:00 pm in my office
9.1/9.2: Fourth IODE project*
You can work on this project in any of the following EWS labs: 57
Grainger, 406-B1 Engineering or 252 Everitt.
Homework 7: due Friday, April 2 by 11:00 am in class (Note change of deadline!)
9.1: 4,5,10*,12,14*,15,16*,20,25*
Hint for problem #25 in 9.1: Use a trig identity to express cos^2(omega t) in terms of cos(2 omega t). Then apply the orthogonality relations (9), (10) and (11) on p. 574.
Homework 6: due Friday, March 19 by 11:00 am in class (Note change of deadline!)
3.8: 1,2*,6,8*,13*,14*
3.6: 2,4*,8,12*,16,17*,19,24*
Hint for problem #24 in 3.6: Use a trig identity to express cos^3(omega t) in terms of cos(omega t) and cos(3 omega t).
Homework 5: due Friday, March 12 by 4:00 pm in my office
3.5: 2,4*,7,8*,21,22*,33,52,55*,56*
3.4: 3,4*,10*,16,18,22*
Hint for problem #10 in 3.4: it helps tremendously if you draw a
diagram for this question first.
Make sure that you have defined all of the relevant variables
precisely before beginning!
Homework 4: due Friday, March 5 by 4:00 pm in my office
3.3: 2,5,13*,16*,25*,41*
3.2: 3,6*,9,12*,15,17*
3.1: 1,10*,14*,19,47,48*
IODE Homework 2: due Friday, February 20 by 4:00 pm in my office
2.4/2.5: Second IODE project*
You can work on this project in any of the following EWS labs: 57
Grainger, 406-B1 Engineering or 252 Everitt.
Homework 3: due Monday, February 16 by 4:00 pm in my office
2.2: 2,4*,8*,21*,29
1.6: 3,8*,14*,21,27*
For problems #2, #4 and #8 in 2.2, find the critical points (and analyze them for stability), and sketch (by hand) the phase line and vector field with a few sample solution curves. You do not need to solve for the exact solutions, nor do you need to use the exact solution or any graphing technology to sketch the vector field.
For problem #21 in 2.2, verify the appearance of the bifurcation diagram in Figure 2.2.13.
Hint for problem #14 in 1.6: this is a homogeneous equation, so according to what we said in class it can definitely be solved by making the substitution w=y/x to convert to a separable equation. However, it turns out to be very difficult to do it this way. Try making the substitution w=x^2+y^2 instead.
IODE Homework 1: due Wednesday, February 11 by 4:00 pm in my office
1.3: First IODE project*
You can work on this project in any of the following EWS labs: 57
Grainger, 406-B1 Engineering or 252 Everitt.
I will hold office hours in the 406-B1 lab on Monday, Feb. 9 from
1:00-3:00pm.
Homework 2: due Friday, February 6 by 4:00 pm in my office
1.5: 1,3*,9,14*,16*,33,36*,additional problem*
For practice, solve #16 by two different methods and show that the answers which you get agree.
Homework 1: due Friday, January 30 by 4:00 pm in my office
1.4: 1,3,6*,7,19,20*,36*,47*
1.2: 1,6*,12,18*,25,26*
1.1: 3,8*,13,17,20*,36*