Differential Equations
( 24 Modules )

Module #1
Introduction to Differential Equations
Overview of differential equations, types, and applications

Module #2
Basic Concepts
Definitions, terminology, and notation

Module #3
Separable Variables
Method of separation of variables, examples and applications

Module #4
Linear First-Order Equations
Integrating factor method, examples, and applications

Module #5
Applications of First-Order Equations
Population growth, chemical reactions, and electrical circuits

Module #6
Higher-Order Linear Equations
Introduction to higher-order linear equations, homogeneous and non-homogeneous equations

Module #7
Undetermined Coefficients Method
Method of undetermined coefficients, examples, and applications

Module #8
Variation of Parameters Method
Method of variation of parameters, examples, and applications

Module #9
Laplace Transforms
Introduction to Laplace transforms, properties, and applications

Module #10
Laplace Transforms and Differential Equations
Using Laplace transforms to solve differential equations

Module #11
Systems of Linear Equations
Introduction to systems of linear equations, matrix methods, and eigenvalues

Module #12
Matrix Exponential
Definition and properties of matrix exponential, applications to systems of differential equations

Module #13
Numerical Methods
Introduction to numerical methods, Eulers method, and Runge-Kutta methods

Module #14
Stability and Instability
Stability and instability of equilibrium solutions, phase portraits

Module #15
Phase Plane Analysis
Phase plane analysis, direction fields, and autonomous systems

Module #16
Linear Autonomous Systems
Linear autonomous systems, eigenvalues, and eigenvectors

Module #17
Nonlinear Autonomous Systems
Nonlinear autonomous systems, phase portraits, and bifurcations

Module #18
Boundary Value Problems
Introduction to boundary value problems, types, and applications

Module #19
Sturm-Liouville Problems
Sturm-Liouville problems, eigenvalues, and eigenfunctions

Module #20
Fourier Series and Differential Equations
Fourier series and their applications to differential equations

Module #21
Differential Equations in Physics
Applications of differential equations in physics, mechanics, and electromagnetism

Module #22
Differential Equations in Biology
Applications of differential equations in biology, population dynamics, and epidemiology

Module #23
Differential Equations in Engineering
Applications of differential equations in engineering, electrical circuits, and control systems

Module #24
Course Wrap-Up & Conclusion
Planning next steps in Differential Equations career

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