These notes have equal standing with the text as a basis for the course.

Suggested exercises, where shown, are based on the Kelley - Peterson text.

(see Course Description for text details).

These notes are provided primarily in the form of .pdf files which the student

can access with Acrobat Reader, which is freely available from the Adobe website. Some notes are provided as MSWord files.

A notation (Information) following the hyperlink indicates that the
material

is for the student's information only and will not be explicitly tested
on

exams, etc.

Math 4245 Notes for Fall, 2013.

Solution of Equations (Information)

Posted August 24, 2013.

Lecture of Tuesday, August 27, 2013.

Introduction to First Order Differential Equations

Posted August 24, 2013.

Lecture of Thursday, August 29, 2013.

Linear First Order Equations

Posted August 27, 2013.

Example from lecture of August 29.MSWord file.

Lecture of Tuesday, Sept. 3, 2013.

Separable First Order Equations

Posted August 29, 2013.

Lecture of Tuesday, September 10, 2013.

Exact Differential Equations

Posted September 10, 2013. Note QuickCheck exercises at end of notes.

Second Order Differential Equations

Posted September 10, 2013.

Lecture of Thursday, September 12, 2013.

Linear Second Order Equations

Posted September 17, 2013.

Complex Roots of the Characteristic Equation

Posted September 17, 2013.

Lecture of Tuesday, September 17, 2013.

Repeated Real Roots; Reduction of Order

Posted September 17, 2013; Note the QuickCheck exercises.

Inhomogeneous Second Order Equations

Posted September 17, 2013.

Lecture of Tuesday, September 24, 2013.

Systems of Differential Equations

Posted September 24, 2013.

Using Complex Numbers (information)

Posted September 24, 2013.

Lecture of Thursday, September 26, 2013.

Linear Systems of Differential Equations

Posted September 24, 2013.

Lecture of Tuesday, October 8, 2013.

Constant Coefficient Linear Systems

Posted October 17, 2013.

Lecture of Thursday, October 10, 2013.

Linear Systems with Complex Eigenvalues

Posted October 17, 2013.

Lecture of Tuesday, October 15, 2013.

Inhomogeneous Linear Systems

Posted October 17, 2013.

Suggested Exercises: pp. 78 - 82 in Kelley and Peterson. Do a representative selection.

Not to be turned in.

Lecture of Thursday, October 17, 2013.

General Systems in R^n; Vector Functions MSWord file.

Posted October 17, 2013.

Lecture of Tuesday, October 22, 2013.

Invariant Sets MSWord file.

Posted October 22, 2013.

Lecture of Thursday, October 24, 2013.

Critical Points MSWord file.

Posted October 22, 2013.

Lecture of Tuesday, October 29, and Thursday, October 31, 2013.

Stability and Asymptotic Stability MSWord file.

Re-posted, following corrections and additions, October 29, 2013.

Lectures of Thursday, November 9, and Tuesday, November 12, 2013.

Liapounov Theory MSWord file.

Posted November 12, 2013.

Lecture of Tuesday, November 19, 2013.

LaSalle Invariant Set Theorem MSWord file.

Posted November 19, 2013.

Lecture of Thursday, November 21, 2013.

Stabilization via Linear Feedback MSWord file.

Posted November 21, 2013.

Periodic Solutions and Orbits MSWord file.

Posted December 8, 2013.

Poincare-Bendixson Theorem MSWord file.

Posted December 8, 2013.