## Ordinary Differential Equations Spring 2012

### Instructor: Bard Ermentrout

#### Office Hours: MW 1:00-2:00 PM Office: Thackeray 502 Phone: 624-8324 EMAIL: bard+@pitt.edu WWW: http://www.pitt.edu/~phase

All homework is due the week following the assignment. Grades will be based on:
• Written homework 30%
• Projects 20%
• 2 Exams 50% (Midterm and Final)

The book is Elementary Differential Equations and Boundary Value Problems The authors are Boyce and DiPrima

Please note This is the ninth edition!

### Syllabus:

• 1/4: 1.1; 1/6-1/9:2.1

Homework due: 1/13: 1.1:15-20,23,24,26,29,30;2.1:13,15,16,31,32

• Here is a handout for using XPP and doing some of the computer problems How to plot
• Simple XPP code for direction fields
• Run this in XPP. Click on (D)ir.field (S)caled and then Reture to accept the default. See the nice direction fields!
• Click (I)nitialconds m(I)ce and click around on the screen near the dashed line. See the trajectories. Tap ESC when done.
• Take a screen shot of this to print it if you want
• 1/9-1/13: Homework due 1/20 2.2:1,5,8,9,10,17,31,37,36; 2.3:2,9,19,29,32;
• 1/18-1/20: 2.4-2.7 (we already did a bunch of 2.6) HW Due 1/27 2.4:1,3,5,7,14,15,23,27,28; 2.5: 1,3,4,8,11,13,20,25;
• 1/23-1/27 2.6,2.7,2.8,3.1 Homework Due Feb 3
• 2.6:1,3,5,9,13,15,18,19,25;
• 2.8:5a-c; 3.1:1,7,9,12,17,20,23,28
• Rocket execercise and numerical exercise OPTIONAL DUE FEB 3
• Week of Jan 30: Sections 3.2 and 3.3. HOMEWORK DUE Feb 10
• 3.2: 1,2,4,7,12,13,16,17,23,28,29
• 3.3: 1,4,6,10,15,21,34,35,39
• Week of Feb 6: Sections 3.4-3.6. Homework due Feb 17
• 3.4:7,`11,12,17,20,21
• 3.5: 1,4,8,12,14,18
• 3.6: 1,2,9,13
• Week of Feb 13: sections 3.7,3.8,4.1 Homework due Feb 24
• Week of Feb 20:
• 4.1:3,6,7,11,15,24 (you can assume without proving it, the result of problem 20 on page 225) This is the only HW due on MARCH 02
• Read pages 3-5 of this handout
• Sample examp 1
• There will be a review Friday and we will go over what you need for monday
• MONDAY FEB 27 EXAM 1
• Week of Feb 27:
• Monday Exam 1
• Wed,Fri Rest of chapter 4 in the book
• HW due March 16: Handout p3:1,2,3; Handout p5,6:1,2,3; 4.2:11,18,21;4.3:1(see 4.2,11);4.4:1
• Week of March 12:
• M-F chapters 7.3-7.5
• HW Due March 23
• 7.1:1,4,6,23
• 7.3:1,4,15,18,21,23
• 7.4:2abc,6
• Week of March 18
• 7.6-7.8
• Homework due March 30
• 7.5:1,2,5,7,11,15,16,20,24,25,27,31
• 7.6:1,3,5,13,14,28
• 7.7:1,3,5
• Let A be a 3x3 matrix with eigenvalues -1, -1+2 i. Express exp(At) in terms of the matrix A. (Use Fulmer's method)
• Use Fulmer's method to do problem 1 in 7.7
• Week of March 25
• 7.8-7.9, 9.1
• Homework due April 6
• 7.8:1,2,11
• 7.9:3,12
• 9.1: 1,3,5,6,13
• Homework due Apr 13:
• 9.2:1,4,5,9,17
• 9.3:1,2,5,10
• For the following differential equation, find all the equilibria, their stability, and sketch the nullclines and direction fields. Sketch the separatrices of any saddle points and sketch some trajectories

x'=(2*x-y)*(1-x-y)

y'=(x-1)*(1/2-y)