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