- Math 141 (Calculus II) or its equivalent;
- Either Math 240 (Calculus III) or ENES102 or PHYS161 or PHYS171 or some other course with an adequate coverage of vectors.

** Introduction to and Classification of
Differential Equations **

** First-Order Equations **

Linear, separable and exact equations

Introduction to symbolic solutions using MATLAB

Existence and uniqueness of solutions

Properties of nonlinear vs. linear equations

Qualitative methods for autonomous equations

Plotting direction fields using MATLAB

Models and applications

** Numerical Methods **

Introduction to a numerical solver in MATLAB

Elementary numerical methods: Euler, improved Euler, Runge-Kutta

Local and global error, reliability of numerical methods

** Higher-Order Linear Equations **

General theory of linear equations

Reduction of order

Homogeneous linear equations with constant coefficients

Methods of undetermined coefficients, variation of parameters,
and Green functions for nonhomogeneous equations

Symbolic and numerical solutions using MATLAB

Mechanical vibrations

** Laplace Transforms **

Definition and calculation of Laplace transforms

Applications to differential equations
with piecewise continuous forcing functions

** First-Order Linear Systems **

General theory

Systems with constant coefficients and matrix exponentials

Eigenpairs and special solutions

Finding eigenpairs and solving linear systems
with MATLAB

The phase plane and parametric plotting
with MATLAB

** First-Order Systems in the Plane **

Autonomous systems and stationary solutions

Linearized stability and phase plane analysis

Linearized stability analysis and plotting vector fields
using MATLAB

Numerical solutions and phase portraits of nonlinear systems
using MATLAB

Models and applications