Math 1270:       Ordinary Differential Equations 1       Fall 2006       

Instructor: David Swigon

Office: Thackeray 519, 412-624-4689, swigon@pitt.edu

Lectures:  MW 6:00-7:15pm, Thackeray 524

Office Hours: MW 2:00-3:00pm, Thackeray 519, or by appointment.

Course Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math1270.html

Course Description

This course is covers the theory of ordinary differential equations (ODEs) at the undergraduate level.  The topics include classical methods of solving first order ODEs, linear higher-order ODEs and systems of first order linear and nonlinear ODEs. Geometric qualitative methods for autonomous systems of first order ODEs and solution of boundary value problems will be briefly discussed. 

Prerequisites

Single-variable calculus (Math 0420, 0450, or equivalent) including Taylor series, linear algebra (Math 1180, 1185 or equivalent) including eigenvalues and eigenvectors.

Textbook

W.E. Boyce & R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 8th edition, John Wiley & Sons, 2004. ISBN 0471433381

(Available at The Book Center on Fifth Ave.)

Grading Scheme

Homework Assignments: 30%

Midterm Exam: 30%

Final Exam: 40%

Schedule

Each week we will cover approximately one chapter of the book.  The precise schedule and a list of homework problems is posted below.  Homework is due at the beginning of a class one week after it was assigned. You may work with other students on homework but do not submit solutions that are identical copies of each other, as such will be discarded. 

Some homework assignments will require the use of a computer software to perform numerical computation or symbolic manipulation. You may use any computer program (e.g., XPP, ODE Architect, MATLAB, Maple, Mathematica)  in solving the homework. Each such use should be explicitly documented (e.g., “eigenvalues computed with MATLAB”).  A list of appropriate computer programs is given below.

Program

Utility

Availability

XPP, XPPAUT,
WINPP

Numerical solution of ODEs with GUI

Free for download, Windows and Unix versions

ODE Architect

Numerical solution of ODEs with GUI

Free with the Textbook

MATLAB

Numerical solution of ODEs, Symbolic manipulation, Matrix algebra

Benedum and GSCC computer labs, Windows/OSX/Linux/Unix version for $10 from Pitt SLS

Maple

Numerical solution of ODEs, Symbolic manipulation, Matrix algebra

Benedum and GSCC computer labs

Mathematica

Numerical solution of ODEs, Symbolic manipulation, Matrix algebra

Benedum and GSCC computer labs, Windows/OSX/Linux/Unix version for $10 from Pitt SLS

Syllabus

Week

Reading

Topics

Homework

Notes

Aug 28 – Sep 1

1.1-4

2.1-2

Introduction, Classification, First order ODEs – linear equations, Separable equations

HW#1

Due Sep 6

 

Labor Day

Sep 6 – Sep 8

2.3, 2.5

Models using 1st order ODEs, Autonomous equations and population dynamics

HW #2

Due Sep 13

 

Sep 11 – Sep 15

2.4, 2.6, 2.8

Exact equations and integrating factors, Existence and uniqueness of solutions

HW #3

Due Sep 20

 

Sep 18 – Sep 22

8.1-3

Numerical solution of ODEs – Euler method, Improved Euler method and Runge-Kutta method, Error & Stabillity

HW #4

Due Sep 27

 

Sep 25 – Sep 29

3.1, 3.4-5

Higher order ODEs – Homogeneous equations with constant coefficients, Complex roots, Repeated roots

HW #5

Due Oct 4

 

Oct 2 – Oct 6

3.2-3, 3.6

Fundamental solutions of linear homogeneous equations, Linear Independence and the Wronskian, Nonhomogeneous equations – undetermined coefficients

HW #6

Due Oct 11

 

Oct 9 – Oct 13

3.7-8

Variation of parameters, Vibrations, Review

Practice problems

 

Oct 16

 

Midterm Exam

Covers Chapters 1-3

 

 

Oct 18 – Oct 20

7.2-3

Review of matrices, systems of linear equations, eigenvalues, eigenvectors

 

 

Oct 25 – Oct 27

7.1, 7.4

Systems of first order linear ODEs, Homogeneous systems with constant coefficients

HW #8

Due Nov 1

 

Oct 30 – Nov 3

7.5-8

Repeated eigenvalues, Complex eigenvalues, Fundamental matrices

HW #9

Due Nov 8

 

Nov 6 – Nov 10

7.7,

Matrix exponential, Nonhomogeneous linear systems

HW #10

Due Nov 15

 

Nov 13 – Nov 17

7.9

Nonhomogeneous linear systems

 

 

Nov 20

Thanksgiving

7.1, 7.9

RLC circuits

 

 

Nov 27 – Dec 1

6.1-2

Laplace transform, solution of IVP

HW #11

Due Dec 4

 

Dec 4 – Dec 8

9.7-8

Step functions

Review

 

 

Dec 15

 

Final Exam

6:00pm-8:00pm, Thack 524

Solution to sample final