Homework Assignments for MATH 5733 Partial Differential Equations (Fall 2005)

Mon. and Wed. 5:30-6:45pm; CU 626                                                   Lynn S. Bennethum

Final Exam:  Take home.  To be available on Friday, Dec. 9th.  Due on Friday Dec. 16th, noon.

Extra Class:  Monday Dec. 12th, 5:30-6:45pm.  Attendance will be worth 30 homework points.

Test 2, Monday Dec. 5th.  Through Chapter 7.  

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 11  Due  Wed. Nov. 30           

Problems from ZT Chapter 7: Sections 8 and 9   For problem 8.2, change to ‘derive equation (8.5)’
                             Start problems from Section 10

                              Test 2 will be on Mon. Dec. 5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 10  Due  Wed. Nov. 16           

Problems from ZT Chapter 7: Sections 5 and 7
                             Read Section 6

                             Start problems from Section 8

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 9  Due  Wed. Nov. 9           

Problems from ZT Chapter 7: Sections 1 and 2
                             Read Sections 3 and 4

                             Start problems from Section 5
                             

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 8  Due  Wed. Nov. 2           

Problems from ZT Chapter 5: Section 9
                             Chapter 6: Sections 1, 2, 4 and 5 
                             

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 7  Due  Wed. Oct. 26           

Problems from ZT Chapter 5: Sections 2, 3, 4, 6, and 7

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
TEST 1   Wed. Oct. 19              

The test will cover material in this class through ZT Chapter 4.  No notes or technology will be allowed.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 6   Due Wed. Oct. 12               

Problems from ZT Chapter 3: Section 6
                             Chapter 4: Sections 1 and 2
                              Chapter 5: Section 1

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 5   Due Wed. Oct. 5             

                        Problems for ZT Chapter 3:  Sections 1, 2, 4, and 5  (huge homework set…)   

 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 4   Due Wed. Sept. 21              

                        Problems for GL Chapter 2   

 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 3   Due Wed. Sept. 14               

                        ZT   Ch 1.  Problems from Section 3 and 4.

 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 2   Due Wed. Sept. 7
                 ZT    Ch 1. Problems from below, 1.2 – 2.6   Start problems from Section 3.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HW 1   Due Wed. Aug. 31  (to be assigned on Wed. Aug 25)
               GL   Chapter 1:  Section 1.3: 1, 2, 4
                                           Section 1.4: 1       (not Section 1.8 number 2)
               ZT    Read Ch 1.

          

*********************************************************
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 1.1:  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 (reason this result geometrically only), 3.2 (use 3.1), (3.3), 3.4, 3.6 b,c

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.

 

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 3:

1.1, 1.2

2.1a,c,e,g; 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).

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

6.1, 6.6, 6.9

 

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

3.1 (hint)

4.2,  4.4

6.1, 6.2a,b

7.5, 7.7

9.1, 9.2, 9.3

 

ZT Chapter 6:

1.1, 1.2, 1.3, 1.4

2.1, 2.2, 2.3

4.1 (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, 1.2 (for 1.2b, see p. 59, number 1.1), 1.3 (you need 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) 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).

5.2 (5 pts extra credit - do not have to do)

7.2, 7.3, 7.4 (Series solution is valid only for r<a, so one must integrate first and then take limits), 7.6, 7.7a,b,c (Take advantage of whether function is even or odd).

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

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

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

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