Engineering Mathematics IV:

Differential Equations

22m:34, Fall 2003
Instructor: Frederick M. Goodman

New Stuff

Sample exams from Professor Radulescu -- look below under Review and Practice Sheets.

Contact Information:


325G Maclean Hall

phone: 335-0791


goodman at math dot uiowa dot edu

Please put "math 34" in the subject line.

Office Hours:

M and W 4:30-5:30

may be changed if conflicts arise

Paper Mail:

Frederick Goodman
Department of Mathematics MLH
The University of Iowa
Iowa City, IA 52242

Class Hours:

Tuesdays and Thursdays at 1:05-2:20 in MLH 110


Elsa Su:


Click here to read the syllabus.


Boyce and DiPrima, Elementary Differential Equations, 7th edition

This text is required.

Note: the textbook includes a CD containing:

  1. An electronic copy of the entire text!
  2. An electronic copy of the student solutions manual. (So you should not purchase the solutions manual.)
  3. A program ODE Architect for exploring differential equations.
  4. An electronic copy of the lab book ODE Architect Companion.


Assignment lists:

There will be weekly assignments, due on Thursdays in class. Details will appear here as the assignments are made.

Assignment 1, Due Thursday Sept. 4.

Assignment 2, Due Thursday Sept. 11.

Assignment 3. Due Thursday Sept 18.

Assignment 4. Due Thursday Sept. 25.

Assignment 5. Due Thursday Oct 2.

Assignment 6, Due Thursday Oct. 16.

Assignment 7, Due Thursday Oct. 23.

Assignment 8, Due Thursday Oct. 30.

Assignment 9, Due Thursday Nov 6.

Here are some Mathematica solutions for assignment 9. (Thanks to Matt for the suggestion.)

Assignment 10, Due Thursday Nov 20.

Assignment 11, Due Thursday Dec 4.

Optional Last Assignment

Mathematica Tutorials:

Mathematica Lesson 1: Getting started.

Mathematica Lesson 2: Mathematica as a scientific calculator.

Mathematica Lesson 3: Mathematica as a symbolic calculator.

Mathematica Lesson 4: Mathematica for calculus and graphing.

Mathematica Lesson 5: Solving equations (including differential equations.)

Mathematica Lesson 6: Some useful advanced techniques.


Note: some students have reported difficulty opening Mathematica files with in Windows. This is not the fault of these files but rather something to do with the way Mathematica and Windows are set up on some of the university computers. The following procedure will work:

1. Click on the www link to the file you want to use and, when the dialogue box pops up and asks what you want to do with the file, chose save to disk. Save it to some convenient location, like the desktop, or your own floppy drive.

2. Start the Mathematica program.

3. Open the desired file from within the Mathematica program; i.e. on the main Mathematica menu bar do File -> Open . A file browser will pop up, and you can choose your file.

Programs for drawing direction fields and solution curves.

ODE Architect

Advantages: You own it and it runs on your home computer.

Disadvantages: It runs only on your home computer.

Tutorials: There is a brief online tutorial here. The multimedia version of ODE Architect on your CD has built-in tutorials.


Java applet available online here. To start the program, open the link in your internet browser, wait briefly for the java applet to load, and click on the button for DFIELD2002.2. Note: Menus for the applet will be located either in your browser's menu field, to the right of other usual items, or at the top of the direction field window. Printing is done from the applet's file menu, not the browser's file menu!

Advantages: Works very well and available on every computer with an internet connection.

Disadvantages: Can get "tied up" at "difficult" points on a solution curve. Tricky to set up printing from Internet Explorer; see the instructions regarding printing on the link page.


Advantages: Works very well, you can install in your computer account, integrates well with Mathematica.

Disadvantages: Commercial product ($30 from Requires Mathematica to work, so can't be used at home.

Note on installing VisualDSolve: Click here for information.


There will be two midterm exams, each 75 minutes in duration.

Text of the first exam

Text of the second exam, and solutions.

There will be a final exam at the time specified in the Fall 2003 course schedule, namely at

noon on Tuesday Dec. 16, in our regular classroom.

(Classes meeting at a time other than on the half-hour are tested with classes of the preceding half-hour. Since our class meets at 1:05 on Tuesdays and Thursdays, our exam is at the same time as those of 12:30 Tuesday classes -- exam period 9)

All exams will be comprehensive.

Demonstrations and discussions (online "handouts"):

Remarks on practical mathematics and learning in this course!

Solution to Exercise 2.3.32

Mathematica Demo: detailed solution of 2nd order constant coefficient differential equations.

Mathematica Demo: efficient template for solving 2nd order constant coefficient differential equations. Useful for checking your homework or for doing applied problems.

Mathematica Demo: detailed solution of higher order constant coefficient differential equations.

Review and Practice sheets:

Review for first midterm exam.

Review for the second midterm exam.

Professor Radulescu's review for the first midterm.

Professor Radulescu's review for the second midterm.

Professor Radulescu's review for the final.


Some Web Resources:

  1. You can get a free reader for Mathematica notebooks, which allows you to read prepared Mathematica notebooks but not to edit them or to run Mathematica.
  2. Engineering computer labs information here.


Fred Goodman
Fall 2003