# MA 320 Differential Equations

### Videos

**First order equations**

Introduction to differentrial equations

Separable differentrial equations

Linear and Bernoulli's differential equations

Exact equations

Homogeneous equations

Autonomous equations

Modeling with first order differential equations, part 1

Modeling with first order differential equations, part 2

The first assignment questions

First order differential equations in Matlab

Euler's method in Matlab

Exam 1 material review

**Second and higher order equations**

Second order linear equations with constant coefficients

Higher order linear equations with constant coefficients

Variation of parameters

Undetermined coefficients, part 1

Undetermined coefficients, part 2

Applications of second order differential equations

The second assignment questions

Second order differential equations in Matlab

Exam 2 material review

**Laplace Transform**

Introduction to the Laplace transform

The inverse Laplace transform

Step, box, and impulse functions

Examples with ramp and impulse functions

Convolutions. Examples with box function and convolution

Solving systems of equations using the Laplace transform

The third assignment questions

Exam 3 material review

**Systems of differential equations**

Introduction to systems. Equilibrium points. Nodes and spirals

Saddle and center

Applications of systems. Predator-prey and hunter models

Practice problems. Systems in Matlab

Stability and type analysis

The second project questions

Systems with infinitely many critical points

More examples with systems

**Review for the final exam.**

Systems review

Review of the exam 1 to 3 material

Final exams message

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