Reading:
• ZT, Chapter 8
• Review the Lecture of 5 December
• Review the Lecture of 7 December
• Review the Class of 9 December
• Don't forget the Bank of Old Tests

Practice Problems:
(not to be handed in)

1. P. 283, #4.1-4.8
2. P. 290, #5.3-5.5
3. P. 298, #6.1-6.8
4. Keep checking for more.

Past homework assignments

Reading:
• Review as necessary, the calculus-related materials of ZT, Chapter 1
• Look at the derivation of the heat equation.

Reading:
• Review as necessary, the calculus-related materials of ZT, Chapter 1, especially section 4
• Look at the derivation of the heat equation.
• Familiarize yourself with the notation and terminology in ZT, pp. 57-59 and 112-114.
• Review the Lecture of 22 August
• Review the Lecture of 24 August
• Review the Lecture of 26 August

Exercises:
1. Identify the orders of the following differential equations

   

2. Which of those equations are linear? Which are autonomous?
3. ZT, p. 21, #4.1, 4.4
4. ZT, p. 33, #1.4

Reading:
• ZT, Chapter 3, sections 1-3
• Review the Lecture of 29 August
• Review the Lecture of 31 August

Exercises:
1. ZT, p. 33, #1.6
2. ZT, p. 41, #2.2, 2.7

Reading:
• ZT, Chapter 3, sections 3-6
• Review the Lecture of 7 September
• Review the Lecture of 9 September

Exercises:
1. ZT, p. 41, #2.8
2. ZT, p. 43, #3.1 (b), (d); #3.2 (a), (b)
3. ZT, p. 51, #4.1 (a),(c), #4.2 (a)

Reading:
• ZT, Chapter 3 (exc. section 7)
• Review the Lecture of 12 September
• Review the Lecture of 14 September
• Review the Lecture of 16 September
• For other helpful reaing and more practice problems, we recommend Schaum's Outline, Partial Differential Equations, by Duchateau and Zachmann (no relation to Zachmanoglou).

Practice Problems:
(not to be handed in)
1. P. 43, all.
2. P. 51, all.
3. Actually, you could do all the problems in Chapters 1-3 of Z-T
4. Some sample solutions for the second homework assignment
5. Some sample solutions for the third homework assignment
6. There is also a test from last year here

Reading:
• ZT, Chapter 4
• Review the Lecture of 21 September
• Review the Lecture of 23 September
• Review the Test Solutions

Exercises:
1. Solve the two PDEs as requested on the last page of last Monday's text.
2. ZT, p. 107, #2,1 (a), (c); 2.2, 2.3, 2.6

Reading:
• ZT, Section 8.2 (beginning on p. 271)
• ZT, Chapter 5, Sections 1-5.
• The section of HH entitled Traveling waves
• Review the Lecture of 26 September
• Review the Lecture of 28 September
• Review the Lecture of 30 September
• Review the Solutions to the extra credit/test problems

Exercises:
1. ZT, p. 107, #2,9
2. HH, Exercise VII.1
3. ZT, p. 117, #1.1

Reading:
• ZT, Section 8.2 (beginning on p. 271)
• ZT, Chapter 5, all.
• Review the Lecture of 3 October
• Review the Lecture of 5 October
• Review the Lecture of 7 October

Exercises:
1. ZT, p. 273, #2.1-2.4 (a).
2. ZT, p. 123, #2.1, 2.2.
3. ZT, p. 131, #4.3 (a).
4. ZT, p. 143, #7.7 (a).
5. classify the following PDEs and reduce them to canonical form

   

Reading:
• We will have covered chapters 1-5 of ZT
• Review the Lecture of 10 October
• Review the Lecture of 12 October
• Review the Lecture of 14 October
• Look at the relevant parts of last year's Tests #2 and 3. (Material was covered in a different order last year.)
• Look at some selected recent homework solutions.
• Additional reading may be posted later.

Practice Problems:
(not to be handed in)
• ZT, all problems in Chapter V.

Reading:
• ZT, Chapter 6
• ZT, Chapter 7, Sections 1-2.
• Review the Lecture of 26 October
• Review the Lecture of 28 October
• Look at the solutions of the second test.

Exercises:

• ZT, p. 156, #1.3, 1.4.
• ZT, p. 196, #5.4, 5.5 (You may use either the approach in Friday's class or the material from Section 5 for these problems)
• Suppose that u_1,2 satisfy u = f on a smooth domain , and u = g on the boundary of , where f and g are continuous functions. Show that u₁ = u₂.
• Suppose that u satisfies u = f on a smooth domain , and that f(x) > 0 on . How does f(x) compare with the average of f(y) over a small sphere centered at x? (The sphere is small enough to be contained in .)

Reading:
• ZT, Chapter 9, Sections 1-2.
• ZT, Chapter 7, Section 2.
• (Optional, for background) The section of HH entitled The Geometry of Functions
• (Optional, for background) The section of HH entitled Fourier Series
• The section of HH entitled The Mathematics of Hot Rods
• Review the Lecture of 31 October
• Review the Lecture of 2 November
• Review the Lecture of 4 November

Exercises:

1. ZT p. 173, #1.2,1.3
2. ZT p. 335, #1.3,1.6
3. ZT p. 342, #2.3,2.7
4. HH, Exercises VIII 1, 2.

Reading:
• ZT, Chapter 7, Sections 1-8; However, the parts with the representation theorem and Poisson's integral will not be on the test..
• (Optional, for background) The section of HH entitled The Geometry of Functions
• The section of HH entitled Fourier Series
• The section of HH entitled The Mathematics of Hot Rods
• The section of HH entitled PDEs on a Disk
• Here are solutions to two troublesome homework problems from ZT:
  • P. 156, #1.3
  • P. 156, #1.4
• And here are some solutions for the latest problem set; here is yet another one, following up on Friday's class.
• Review the Lecture of 7 November
• Review the Lecture of 9 November
• Review the Lecture of 11/11/11

Practice problems:

1. Any of the Exercises in ZT or HH in the sections we have read so far would be useful for test preparation.
2. Don't forget the Tests from past 4347 classes.

Reading:
• ZT, Chapter 9, sections 3-4
• ZT, Chapter 7, section 5, this time paying attention to the representation theorem; section 9.
• Review the Test Solutions
• Review the Lecture of 16 November
• Review the Lecture of 18 November

Exercises:

1. ZT, p. 347, #3.8,3.9
2. ZT, p. 351, #4.2,4.3,
3. ZT, p. 342, #2.9
4. ZT, p. 226, #9.2,9.4

Reading:
• Review the solution to Exercise 2b from last week.
• ZT, Chapter 8, section 1
• Review the Lecture of 21 November
• Review the Lecture of 23 November

Exercises:

1. ZT, p. 244, #13.3, 13.6
2. Find a Green function such that if f is continuous, then the equation u = Gf provides a solution for L(u) = f, u(0) = u'(0) = 0, where L is as defined below. Here Gf is operational notation for an integral of G(x,y) f(y) dy
   1. L(u) = u''
   2. L(u) = 2u'' + u' - u
3. Suppose that u solves the 3-dimensional wave equation u_tt = u, but is spherically symmetric. (I.e., u is independent of the angular variables in the spherical system.) At t=0, u(r,0) = 0, whereas u_t(r,0) = 1, for 0 < r < 2, and 0 for 0 > 2. Solve for u(r,t), t > 0.

Reading:
• Review the solution to Exercise 2b from last week.
• ZT, Chapter 8
• Review the Lecture of 28 November
• Review the Lecture of 30 November
• Review the Lecture of 2 December

Practice Problems:
(not to be handed in)

1. P. 235, #11.1-11.3
2. P. 270, #1.1-1.5
3. P. 279, #3.1, 3.3, 3.4

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