Homework Assignments for MATH 4733/5733 

Partial Differential Equations (Fall 2009)

Mon. and Wed. 2:30-3:45pm; CU 656                                                   Lynn S. Bennethum

  Key:  GL = Guenther and Lee
           ZT = Zachmanoglou and Thoe
           Problems in parenthesis:  Only graduate students must do.
 

Date Homework Due Notes
Finals Week No Homework due.  We will meet on Mon. Dec. 7th, regular time regular place (2:30-3:45pm, CU 656).

Final Exam:  Wed. Dec. 9th, 2:30-4:30pm, CU 656
Final Exam is cumulative.
Wed. Dec 2 Last Homework
Please work problems from Chapter 8:
Sections 1, 2, 3, and 4
We covered Section 1 on Monday Nov. 16th;  Sections 2, 3, and 4 will be covered on Monday, Nov. 30th.  Of course you can work ahead.
Wed. Nov. 18 EXAM  over covered material from Chapters 5, 6, and 7.

Please work problems from Chapter 7:
Section 8:  remaining problems
Section 9
Section 11,
Section 16
We are omitting Sections 10, 12, and 13.  Solutions will be provided on Monday.
Wed. Nov. 11 ZT Chapter 7, Problems from Section 7 and first 4 problems from Section 8 Next exam will be Wed. Nov. 18th over material from Chapters 5, 6, and 7.
Wed. Nov. 4 ZT Chapter 6, Problem listed from Section 5

ZT Chapter 7, Problems listed from Sections 1, 2, and 5
Problem 7.5.2 is extra credit (even for graduate students).
Wed. Oct. 28 ZT Chapter 5, Problems listed from
Sections 6,  7,  9

ZT Chapter 6, Problems listed from
Sections 1, 2, and 4.
We will omit Sections 4, 5, 8 from Chapter 5
For Chapter 6, problem 4.1b, use Liebniz' rule.

Undergraduate students do not need to do the following problems:
Chapter 5, 9.2b, 9.3
Chapter 6, 2.1
Wed. Oct. 21 ZT Chapter 5, Problems listed from
Sections 1, 2, and 3.
Read Sections 4 and 5 (no problems assigned from these sections).  
For problem 3.1:  Try to solve the IVP and find a global solution,
 i.e. a solution which works everywhere.   Show that phi(x) must
be an even function (this is the 'certain condition') in order for a
global solution to exist.    What happens if phi(x) is not an even
function?  (Where do solutions exist?).   What is the point of this problem?
Wed. Oct. 14 EXAM 1  Covers material through ZT Chapter 4

For Monday please do the problems listed from
ZT Chapter 4 (Sections 1 and 2).  These problems
will not be collected.
No homework will be turned in this week.  I will provide solutions  
to problems from ZT Chapter 4 on Monday, Oct. 12.  
A review sheet will be given out on Wed. Oct. 7.
Wed. Oct. 7 GL Section 2.1 problem 6
ZT Chapter 3, Section 5:  problems listed
       Chapter 3, Section 6:  problems listed
GL Section 2.5  problem 2
Graduate students have 12 problems assigned.
Wed.  Sept. 30 ZT
  Chapter 3, Section 3:  remaining problems.
   Chapter 3, Section 4:  problem listed.
 
GL
  Section 2.1: (2), 3, 4
We will come back and pick up ZT Chapter 3,  sections 5 and 6.
Wed. Sept. 23 ZT
Chapter 2  2.8b
Chapter 3 Problems from Section 2
Chapter 3 3.1a
Wed. Sept. 16 ZT
Section 1.4, remaining 3 problems
Section 2.1:  three problems
Section 3.1:  two problems
Problem from Section 2.2 will be due next week.
Wed. Sept. 9  ZT
Section 1.3:  remaining problems
Section 1.4:  1, 2, and 3 only.
 
Wed. Sept. 2 ZT,
Section 1.1 problems listed below
Section1.2 problems listed below
Section 1.3  problems 1, 2, and (3) only.
 
Wed. Aug. 26 Problems below from Chapter 1 of GL.
Read Ch 1 of Z and T
 


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Tentative list of Homework Problems

(those in parenthesis are required of graduate students only)

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          GL Chapter 1:  
Section 1.3:  1, (2), 4
For problem 1:  Start with equation 3-4.  Rewrite everything in 1-D.
For problem 2:  Heat flow = q dot n.  What is n?  What is q in terms of u?
Section 1.4:  1 

ZT Chapter 1:

(1.1),1.2, (1.3), 1.4

For problem 1.2:  To show 2 sets are equal (A=B), show A is contained in B and B is contained in A.

2.1, 2.4, 2.5, (2.6)

3.1, 3.2, (3.3), 3.4, 3.6 b,c

For 3.1:  reason this result geometrically only.  For 3.2:  Use 3.1

4.1, 4.2, 4.3, 4.4a, 4.5, 4.6

For 4.1 may use Leibniz Thm,.  For 4.2 use the error function.

 ZT Chapter 2:
1.5, 1.7, (1.11)
2.8b

ZT Chapter 3:

(1.1), 1.2

2.1a, (2.1c), 2.1e, 2.1g; 2.4

Problem 2.1:  Be sure to define domains carefully.  2.1a is quite involved, you may want to do this after you have done some other problems.  2.1c For 2nd integral, use a trick of adding/subtracting.  2.1e:  See Ch 2 example 2.3 – you do not have to derive u_1 or u_2, but you need to verify that the two are functionally independent first integrals.  2.1g:  See Ch 2, example 2.4 – you do not have to derive u_1 - find  u_2 and verify that the two are functionally independent first integrals.

3.1a,b,c,d,g; 

Be sure to check determinant condition to guarantee solution exists and is unique (and mentally check that coefficients and initial curve are smooth enough);  For 3.1c use results from 2.1g;

3.3, (3.4)

4.1b

what happens if you try to solve it (choose one method and try to solve it).

            ZT Chapter 3:

5.1, 5.2, 5.3, (5.4), 5.5, (5.6), (5.8 [for 5.6 only])

6.1, 6.6, 6.9

GL Chapter 2:

            Section 2.1:  

(2), 3 [graph at t=0, t=1, t=2], 4, (6 [parametrize initial curve in 2 parts])

            Section 2.5:  2

ZT Chapter 4:

(1.1), 1.2a,b ; 1.3, 1.5a

(2.1a,c); (2.2)

ZT Chapter 5:

1.1

(2.1a,c); (2.2b); 2.3

ZT Chapter 5:

3.1 [ For problem 3.1:  Try to solve the IVP and find a global solution,
 i.e. a solution which works everywhere.   Show that phi(x) must
be an even function (this is the 'certain condition') in order for a
global solution to exist.    What happens if phi(x) is not an even
function?  (Where do solutions exist?).   What is the point of this problem?]

(4.2),  4.4

6.1, 6.2a,b

7.5, 7.7

9.1, 9.2a, (9.2b), (9.3)

ZT Chapter 6:

1.1, 1.2, 1.3, 1.4

(2.1), 2.2, 2.3

(4.1a), 4.1b [for 4.1b you’ll need Liebniz’ Rule]

5.3 [This is another example of an ill-posed (not well-posed) problem.  Take a moment and note that the data does not make physical sense].

ZT Chapter 7:

1.1, 1.2a, (1.2b), 1.3 

For 1.2b:  see p. 59, number 1.1.  For 1.3:  patience.

2.3, 2.4, 2.5, 2.7 

For 2.7b, you want to integrate lambda from 0 to + infty.

(5.2) [for 5 points extra credit, do not have to do], (5.4), (5.6) 

Hint on 5.6: start with MVP, replace delta by r and integrate both sides from 0 to delta with respect to r;

(7.2), (7.3), 7.4, 7.6, 7.7a,b,c

For 7.4:  Series solution is valid only for r<a, so one must integrate first and then take limits.  For 7.7:  Take advantage of whether function is even or odd

8.1, 8.2, 8.3, 8.4, (8.5), 8.6, 8.7, 8.9, 8.10a,b,c, (8.14)

For 8.1:  patience.  For 8.4:  Do not calculate, use the fact that the integral of an odd function about an interval symmetric with respect to the origin is zero.  Do not worry about convergence

(9.3a,b), (9.4)

(10.1), (10.2), (10.3)

11.1

12.3, 12.4, 12.7

13.1, 13.3, 13.6    (depending on time, may omit this section)

16.1

ZT Chapter 8:

1.1, 1.2, 1.3, 1.4, 1.5, 1.6

2.1, 2.2, (2.3), 2.4

For this section may use ideas from Section 8.3.

(3.1), (3.3)

4.1, 4.2, (4.5), (4.7)

5.5 [don't forget c and do not assume c is 1]

6.1, 6.2, (6.5) [very important], 6.6 [extra credit], (6.7)

(7.3), 7.5

8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9

ZT Chapter 9:

1.3, 1.6, 1.7

2.1, 2.2, 2.4, 2.7, 2.9, 2.10, 2.11

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