MAT 5653

From Department of Mathematics at UTSA
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Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

Basic Concepts of Ordinary Differential Equations

Week 2

Equilibrium Points, Phase Plane

Week 3

ODE Models in Science and Engineering

Week 4

Picard-Lindeloef Theorem and Applications

  • Picard Iteration, Contraction
Week 5

Peano Theorem

Week 6

Dependence of Solutions on Initial Values, Maximal Interval of Existence

Week 7

Conservative Systems

Week 8

Linear Systems and Exponentials

Week 9

Stable Manifold Theorem

Week 10

Hartman-Grobman Theorem

Week 11

Stability and Lyapunov functions

Week 12

Introduction to Bifurcation Theory/Hopf Bifurcation

Week 13

Epidemic and Population Models

Week 14

Review, advanced topics