MATH 225 Spring 2022

Chapter 1: Review and Introduction (2 weeks)

Integration Review

Mathematical Models and Solutions

Qualitative Methods: Phase Lines and Direction Fields

Definitions, Classification, and Terminology

First Order Differential Equations (2½ weeks)

Separable Equations

Linear Equations: Method of Integrating Factors

Modeling with First Order Equations

Differences Between Linear and Nonlinear Equations

Autonomous Equations and Population Dynamics

Systems of Two First Order Equations (2½ weeks)

Matrices and Linear Algebra

Systems of Two First Order Linear Differential Equations

Homogeneous Linear Systems with Constant Coefficients

Complex Eigenvalues

Repeated Eigenvalues

Systems of First Order Linear Equations (3 weeks)

Definitions and Examples

Basic Theory of First Order Linear Systems

Homogeneous Linear Systems with Constant Coefficients

Nondefective Matrices with Complex Eigenvalues

Fundamental Matrices and the Exponential of a Matrix

Nonhomogeneous Linear Systems

Nonlinear Differential Equations and Stability (2 -3 weeks)

Autonomous Systems and Stability

Almost Linear Systems

Competing Species

Predator-Prey Equations

Periodic Solutions and Limit Cycles

Chaos and Strange Attractors: The Lorenz Equations