Course Description
This course includes the study of first-order differential equations, second and higher-order linear differential equations, systems of linear and nonlinear first-order differential equations, numerical methods, and their applications.
Textbook and Reference Materials
Required Textbook:
Elementary Differential Equations, 2nd Edition, by Kohler and Johnson
References:
An Introduction to Ordinary Differential Equations, James C. Robinson
Elementary Differential Equations with Boundary Value Problems, William F. Trench
Sections Taught
Introduction to Differential Equations, Direction Fields
First Order Linear Differential Equations
Existence and Uniqueness
Solving the Homogeneous Equation
Integrating Factors
Discontinuous Coefficients
Introduction to Mathematical Modeling
Population Dynamics, Radioactive Decay, and Half-Life
First Order Nonlinear Equations
Separable Equations
Applications to Mechanics
Euler's Method
Second Order Linear Differential Equations
Existence and Uniqueness
General Solutions
Constant Coefficient Equations
Repeated Roots
Complex Roots
Unforced Mechanical Vibrations
The General Solution of the Linear Nonhomogeneous Equation
The Method of Undetermined Coefficients
The Method of Variation of Parameters
Forced Mechanical Vibrations
Higher Order Linear Differential Equations
Higher Order Linear Homogeneous Constant Coefficient Differential Equations
Introduction to First Order Linear Systems
Existence and Uniqueness
Homogeneous Linear Systems
Constant Coefficient Equations
Real Eigenvalues and the Phase Plane
Complex Eigenvalues
Repeated Eigenvalues
Nonhomogeneous Linear Systems
Euler's Method
Introduction to Nonlinear Systems
Equilibrium Solutions and Direction Fields
Stability
Linearization and the Local Picture
Two-Dimensional Linear Systems