MATH 341, Section 0101, Spring 2009

ANNOUNCEMENTS

My office hour on Wednesday May 13 is moved to 11-12. On Thursday May 14 my office hour will be 2:15-3:15 as usual.

Please fill out the online course evaluation for this and other courses you are taking this semester.

The final exam will be Saturday May 16 from 8:00am-10:00am in our regular classroom.

Weekly Homework Assignments

This homework is not to be turned in; a quiz drawn from the assigned problems will be given on the due date. All problems are from Braun's book except those designated "Colley".

Homework Assignment 11.5
Due Saturday, May 16

Section 5.5: 1, 5, 7
Section 5.6: 1a, 1d, 2c, 4

These problems are additional study problems for the final exam.

Homework Assignment 11
Due Wednesday, May 6

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

Homework Assignment 10
Due Wednesday, April 29

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 Wednesday, April 22

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 Wednesday, April 15

Section 3.1: 1, 4
Section 3.4: 5, 11
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

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 7.5
Additional study problems for the exam on Monday, April 6

Section 2.11: 1, 2, 3, 5, 9, 10
Section 2.12: 3, 5, 7, 8
Section 2.15: 6, 7

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 7
Due Monday, March 30

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 6
Due Monday, March 23

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 5
Due Monday, March 9

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 4
Due Monday, February 23

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, the answer in the back of the book should say cos, not sin.

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. You can use the program myeuler.m from Chapter 7 of Differential Equations with MATLAB to see what happens for the smaller values of h.

Homework Assignment 3
Due Monday, February 16

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, you should get a specific value of a from the data given, using the Malthusian model. Your answer is a "lower bound" in the sense that if the logistic term -bp2 were present in the model, in order to fit the data the value of a would have to be larger to compensate.

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

Homework Assignment 2
Due Monday, February 9

Colley Section 4.4: 1, 2
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

For a bit more detail on carbon-14 dating, click here.

Homework Assignment 1
Due Monday, February 2

Colley Section 4.1: 9, 11, 13, 14, 15, 20, 21
Colley Section 4.2: 3, 11, 17, 19, 22, 30, 32, 46
Colley Section 4.3: 1, 3, 5, 7, 17, 18, 19, 21, 24, 29, 31, 32

In Problem 4.3.31b, take "extrema" to mean "global extrema".

Computer Assignments

Computer Assignment 2
Due Friday, May 1

Problem 5 from the handout.

Computer Assignment 1
Due Wednesday, March 11 (was Friday, March 6)

Problems 2 and 16 from the handout.

Note: For Problem 2a, the newest version of MATLAB (R2008b) fails to solve the second differential equation. Other versions may give answers in terms of complex numbers and/or hyperbolic functions, which are defined in terms of the exponential function. Expressing the solution in terms of real numbers and exponentials, as you would if you solved the problem by hand, makes it easier to see the value of t at which the solution goes to infinity. So, you are welcome to solve the differential equation by hand or to rewrite the solution given by MATLAB if it helps you answer the question. You can rewrite the solution by hand or by applying commands like expand and simplify to the output of dsolve. In the MATLAB versions I've tried, I find that applying expand and then applying simplify gets rid of any complex numbers. Applying simple instead of simplify rewrites the solution in a variety of forms, one of which is in terms of the exponential function.

For Problem 16, dy/dx should be dy/dt.

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, 2nd edition, ISBN 978-0-4-7171812-3 (this book is used in MATH 246).

ODE Software for MATLAB by John Polking includes the programs dfield7.m and pplane7.m for visualizing ordinary differential equations and their solutions.

Schedule of MATLAB tutoring provided by the Department of Mathematics. See also the Department's links to resources for undergraduate students.

General information on computing resources available to UMCP students. See also the list of computer laboratories provided by the College of Engineering.

Home page of The Mathworks, makers of MATLAB. Go here for technical support, information on the Student Version, etc.

More links to MATLAB information and tutorials from Indiana University.

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: 13 May 2009