# MATH 341, Section 0201, Spring 2014

## ANNOUNCEMENTS

My regular office hour schedule is no longer in effect. I will have two special extended office hours: Wednesday May 14 from 12-2pm and Friday May 16 from 3-5pm. If my office (MTH4408) gets too full, we may move to our regular classroom.

Recall from the syllabus that our final examination will be on Tuesday, May 20 from 8-10am. It will be in our regular classroom.

## Wave Equation Animation

Here is wave.m, the simple program I used in class to animate solutions to the wave equation. The comments in the program explain how to use it.

## Computer Assignments

Here is Computer Assignment 3, due Friday May 9, and the associated Handout on Least Squares.

## Weekly Homework Assignments

All problems in this section are from the textbook. This homework is not to be turned in; a quiz drawn from the assigned problems will be given on the due date.

### Homework Assignment 12 Due Wednesday, May 7

Section 5.7: 1, 2, 5, 7, 8
Section 5.8: 1, 2, 5, 8, 9, 10
Section 6.2: 2, 6, 7, 8, 10, 11
Section 6.3: 1, 3, 4
Section 6.4: 4, 6

Notes: In the book's solution to Problem 5.7.5, change the last 2 to 10. For Problem 5.7.8, change the interval to 0 < x < l, and replace g in the integral with its odd periodic extension. In the book's solution to Problem 5.8.5, change b to a in the first numerator. For Problem 6.3.3, the interval for x is the whole real line. For Problem 6.3.4, start with k = 1, not k = 0.

### Homework Assignment 11 Due Wednesday, April 30

Section 5.1: 1, 3, 4, 5, 7, 8
Section 5.3: 1, 3, 5, 9a, 10
Section 5.4: 3, 4, 6, 11, 16, 17, 18
Section 5.5: 1, 5, 7
Section 5.6: 1a, 1d, 2c, 4

Note: In the book's solution to Problem 5.3.9, change one (but not both) of the μ's to -μ.

### Homework Assignment 10 Due Friday, April 18

Section 4.4: 5, 7, 9, 10, 13
Section 4.5.2: 4
Section 4.6: 1, 10
Section 4.7: 6, 8, 11, 12
Section 4.8: 7, 8, 11, 12
Section 4.10: 1, 5
Section 4.12: 2

Notes: In Problem 4.6.10, please change z2 to z3; the problem is wrong as stated. In Problem 4.7.11, you may assume that m = k = 1. You should have a different phase portrait representing each of the three cases mentioned in the problem. Finally, part (a) of Problem 4.12.2 is a bit tricky; however, you should be able to answer part (b) without solving part (a).

### Homework Assignment 9 Due Friday, April 11

Section 4.1: 1, 2, 7, 8
Section 4.2: 1, 3, 6, 7, 8, 16
Section 4.3: 3, 4, 5, 6, 8, 9, 13, 16, 18

### Homework Assignment 8 Due Friday, April 4

Section 3.8: 1, 5, 7, 11, 15, 16, 18, 19
Section 3.9: 1, 3, 5, 7, 8, 9
Section 3.10: 1, 7, 9, 17
Section 3.11: 5, 9, 11, 12, 13, 14, 15, 16
Section 3.12: 1, 4

The book's answers to Problems 3.9.1 and 3.9.7 have typographical errors. For 3.9.1, the first 2 should be 2cost, and the 1 below it should be cost. For 3.9.7, the vector after the + sign should be multiplied by e-t, and the third square root of 2 in its first coordinate should be just 2.

### Homework Assignment 7 Due Friday, March 28

Section 2.11: 1, 2, 3, 5, 9, 10
Section 2.12: 3, 5, 7, 8
Section 2.15: 6, 7
Section 3.1: 1, 4
Section 3.4: 1, 5, 9, 11

The answer in the book for Problem 2.11.9 is wrong; in the term multiplying H2(t), change 1 to 2, change 2t to 3t, and change 7 to 10. For Problem 2.12.3, the answer in the back of the book is given in terms of the functions coshx = (ex + e-x)/2 and sinhx = (ex - e-x)/2. These functions also appear often in inverse Laplace transforms found by MATLAB.

### Homework Assignment 6 Due Friday, March 14

Section 2.8: 1, 5, 7, 11
Section 2.8.1: 1, 5, 7
Section 2.8.2: 7, 8, 9, 11, 23
Section 2.9: 3, 9, 17, 19, 20, 22, 23
Section 2.10: 1, 2, 3, 5, 7a, 19, 20, 21

You are welcome to use MATLAB to perform inverse Laplace transforms as needed. You should not rely on MATLAB to do the required forward Laplace transforms, since you will be expected to do them on the quizzes and exams.

### Homework Assignment 5 Due Wednesday March 5 (was Monday, March 3)

Section 2.3: 1, 3, 4
Section 2.4: 1, 2, 6, 7, 9, 11
Section 2.5: 1, 2, 5, 7, 11, 14
Section 2.6: 1, 5, 7, 9, 10, 12, 13
Section 2.6.2: 3

For Problem 2.6.9, the answer in the back of the book is off by a factor of 2 (cross out the 2 in the denominator of the first fraction).

### Homework Assignment 4 Due Monday, February 24

Section 2.1: 5, 7, 9, 10, 12, 15
Section 2.2: 1, 3, 5, 6, 9, 10
Section 2.2.1: 3, 6, 9, 11
Section 2.2.2: 1, 3, 8, 13, 17

### Homework Assignment 3 Due Wednesday, February 19 (was Monday, February 17)

Section 1.10: 1, 2, 5, 7, 11, 14, 19
Section 1.13: 1, 2, 6
Section 1.13.1: 1, 2, 5, 6, 8
Section 1.15: 2
Section 1.16: 2

For Problem 1.10.19, use y(0) = -1 instead, and change sin to -cos in the answer in the back of the book.

For Problems 1.13.1, 1.13.2, 1.15.2, and 1.16.2, do not use h = 0.1 and h = 0.025. Instead, do them by hand with h = 1 and h = 0.5.

### Homework Assignment 2 Due Monday, February 10

Section 1.5: 2a, 3, 4, 6, 7, 9, 12
Section 1.7: 3, 6, 7, 9, 10, 11
Section 1.8: 3, 4, 7, 10, 11, 18
Section 1.9: 3, 4, 6, 7, 8, 9, 11, 17

In Problem 1.5.3, find a value of a from the data given, using the Malthusian model; don't worry if it doesn't match exactly the answer in the back of the book. One possible interpretation is that you are finding a lower bound on the natural growth rate for the fish; if the model included a negative term representing fishing before 1899, then in order to fit the data, the value of a would have to be larger to compensate. Another possible interpretation is that the value of a is uncertain because how many fish arrived in 1879 versue 1881 is not given, but you can still bound it above and below.

For Problem 1.7.11a, in the answer in the the back of the book, the exponent 3 should be 2.

### Homework Assignment 1 Due Monday, February 3

Section 1.2: 2, 4, 5, 6, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22
Section 1.3: 2, 5, 7, 8
Section 1.4: 1, 2, 4, 5, 6, 9, 10, 12

## Old Computer Assignments

Here is Computer Assignment 2, due Wednesday April 9.

Here is Computer Assignment 1 and the associated program myeuler.m, due Friday February 21.

Most of the topics we will cover are also discussed in the Course Notes for MATH 246 by David Levermore (use your university Directory ID and Password when prompted). These notes also include some topics not in our textbook, in particular graphical methods for first-order equations, and many MATLAB examples.

## Computing Resources

You can find a brief introduction to MATLAB along with examples of graphing and calculus commands in the MATLAB materials for MATH 241 by Paul Green and Jonathan Rosenberg. For a more detailed introduction and discussion of using MATLAB for ordinary differential equations, see Hunt, Lipsman, Osborn, Rosenberg et al., Differential Equations with MATLAB, 3rd edition, ISBN 9781118376805 (this book is used in MATH 246).

MATLAB is available in many of the campus computer laboratories and for download via TERPware.

Schedule of MATLAB tutoring provided by the Department of Mathematics.

ODE Software for MATLAB by John Polking includes the programs dfield8.m and pplane8.m for visualizing ordinary differential equations and their solutions.

Here is the syllabus in case you have misplaced your copy. You can also find my office hours and contact information on my home page.

Updated: 12 May 2014