Master Differential Equations

Learn everything from Differential Equations, then test your knowledge with 130+ practice questions

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“I would recommend this class to anyone going to college, in college, or out of college. These classes are some of the best reference materials you’ll ever have.”

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Course Summary

Learn everything you need to know to get through Differential Equations and prepare you to go onto the next level with a solid understanding of what’s going on. Video explanations, text notes, and quiz questions that won’t affect your class grade help you “get it” in a way textbooks never explain.

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Course outline

The curriculum includes:

Introduction to differential equations
- Sketching direction fields
Euler's method
Separable differential equations
- Separable differential equations
- Change of variable
- Initial value problems
- Mixing problems
- Orthogonal trajectories
Logistic models
- Population growth
- Logistic growth models
- Predator-prey systems
- Equilibrium solutions and stability
Exact differential equations
- Exact differential equations
- Exact differential equations initial value problems
Linear differential equations
- Linear differential equations
- Electrical circuits
- Initial value problems
Second-order homogeneous differential equations
- Distinct real roots
- Equal real roots
- Complex conjugate roots
- Initial value problems
- Boundary value problems
- Working backwards
- Linear dependence and independence

Second-order nonhomogeneous differential equations
- Undetermined coefficieints
- Variation of parameters
- Variation of parameters with a system of equations
- Variation of parameters with Cramer's rule
- Initial value problems
Laplace transforms
- Laplace transforms using the definition
- Laplace transforms using the table
Methods of Laplace transforms
- Laplace transforms and initial value problems
- Laplace transforms and integration by parts
- Inverse Laplace transforms
- Nonconstant coefficients
- Step functions
- Step functions initial value problems
Advanced Laplace transforms
- Dirac delta functions
- Convolution integrals and initial value problems
- Gamma and beta functions