Introduction to and Classification of
Differential Equations
First Order Equations
Linear, separable and exact equations
Introduction to symbolic solutions using a MSS
Existence and uniqueness of solutions
Properties of nonlinear vs. linear equations
Qualitative methods for autonomous equations
Plotting direction fields using a MSS
Models and applications
Numerical Methods
Introduction to a numerical solver in a MSS
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
Homogeneous linear equations with constant coefficients
Reduction of order
Methods of undetermined coefficients and variation
of parameters for non-homogeneous equations
Symbolic and numerical solutions using a MSS
Mechanical and electrical vibrations
Laplace Transforms
Definition and calculation of transforms
Applications to differential equations
with discontinuous forcing functions
First Order Linear Systems
General theory
Eigenvalue-eigenvector method for systems
with constant coefficients
Finding eigenpairs and solving linear systems
with a MSS
The phase plane and parametric plotting
with a MSS
First Order Systems in the Plane
Autonomous systems and critical points
Stability and phase plane analysis of almost linear systems
Linearized stability analysis and plotting vector fields
using a MSS
Numerical solutions and phase portraits of nonlinear systems
using a MSS
Models and applications