# Differential Equations

### Videos

First order equations
Introduction to differentrial equations (Mon Aug 30, 2021)
Separable differentrial equations (Th Sept 2, 2021)
Linear and Bernoulli's differential equations (Fri Sept 3, 2021)
Exact equations (Tue by Mon schedule, Sept 7, 2021)
Homogeneous equations (Fri Sept 10, 2021)
Autonomous equations (Mon Sept 13, 2021)
Modeling with first order differential equations, part 1 (Fri Sept 17, 2021)
Modeling with first order differential equations, part 2 (Mon Sept 20, 2021)
The first assignment questions (Th Sept 23, 2021)
First order differential equations in Matlab (Th Sept 9, 2021)
Euler's method in Matlab (Th Sept 16, 2021)
Exam 1 material review (Th Sept 30, 2021)

Second and higher order equations
Second order linear equations with constant coefficients (Fri Sept 24, 2021)
Higher order linear equations with constant coefficients (Mon Sept 27, 2021)
Variation of parameters (Mon Oct 4, 2021)
Undetermined coefficients, part 1 (Th Oct 7, 2021)
Undetermined coefficients part 2 and intro to applications (Fri Oct 8 and Fri Oct 15, 2021)
Applications of the second order differential equations, part 1 (Fri Oct 15, 2021)
Applications of the second order differential equations, part 2 (Mon Oct 18, 2021)
Second order differential equations in Matlab (mostly on Th Oct 14, parts of Mon Oct 18, and Th Oct 21, 2021)
Exam 2 material review (Th Oct 28, 2021)

Laplace Transform
Introduction to the Laplace transform (Fri Oct 22, 2021)
The inverse Laplace transform (Mon Oct 25, 2021)
Step, box, and impulse functions (Mon Oct 25, and Mon Nov 1, 2021)
Examples with impulse and ramp functions (Th Nov 4 and Fri Nov 5, 2021)
Convolutions. Examples with box function and convolution (Mon Nov 1 and Mon Nov 8, 2021)
Solving systems of equations using the Laplace transform (Fri Nov 12, 2021)
The third assignment questions (Th Nov 11, 2021)
Exam 3 material review (Th Nov 18, 2021)

Systems of differential equations
Introduction to systems. Equilibrium points. Nodes and spirals (Mon Nov 15, 2021)
Saddle and center (Mon Nov 15 and Mon Nov 22, 201)
Applications of systems. Predator-prey and hunter models (Mon Nov 22, 2021)
Practice problems. Systems in Matlab (Mon Nov 29 and Th Dec 2, 2021)
Stability and type analysis (Fri Dec 3, 2021)
The third project questions (Th Dec 2, 2021)
Systems with infinitely many critical points (Mon Dec 6, 2021)
More examples with systems (Mon Nov 29 and Th Dec 2, 2021)

Review for the final exam.
Systems review (Th Dec 9, 2021)
Review of the exam 1 to 3 material (Fri Dec 10, 2021)
Final exams message