Math 4009 Ordinary Differential Equations

MATH 4009 Catalogue Description

Three credits. Three hours of lecture per week. Prerequisite: MATH 3152. Recommended MATH 4031 (Linear Algebra)

Ordinary differential equations of the first order. Linear differential equations with constant coefficients. Linear differential equations of the second order. Systems of differential equations. Applications.

General Information

• Generic Course Objectives
• Classroom Behaviour
• On the use of electronic apparati
• In Praise of Lectures

Syllabus

Download Syllabus (pdf)

Miscelleneous Notes

1. Ordinary Differential Equations – Introduction
2. Separable ODE’s
3. Scaling of First and Second Order Linear Equations (nondimensionalization)
4. Elementary Symmetry Properties
5. Upper and Lower Fences
6. Linear ODE’s
7. First Order Linear ODE’s
8. Second Order Linear ODE’s
9. Forced Damped Oscillatory Systems
10. Method of Variation of Parameters
11. Exact Differential Equations, Integrating Factors and Vector Fields
12. Convolution and Time Invariant Linear Systems
13. Forced Oscillator – Steady State Solution by Fourier Transform
14. Linear Systems
15. The Jordan Normal Form
16. Existence and Uniqueness – Bielecki Renorming Technique

Practice Problems and Solutions

1. Exam 1 –Practice Problems

Exercise Sets

1. Elementary ODE’s
2. Autonomous Differential Equations
3. Linear Differential Equations
4. First Order Linear Differential Equations
5. Homogeneous Differential Equations
6. Second order Linear Differential Equations
7. Simple Harmonic Motion
8. The Wronskian
9. Variation of Parameters
10. Reduction of Order