Differential Equations and Applications
( 25 Modules )

Module #1
Introduction to Differential Equations
Definition, types, and importance of differential equations

Module #2
Basic Concepts and Notations
Understanding derivatives, slopes, and rates of change

Module #3
Separable Variables
Solving separable differential equations and population growth models

Module #4
Linear First-Order Differential Equations
Solving linear first-order differential equations using integrating factors

Module #5
Applications to Population Dynamics
Modeling population growth and decay using differential equations

Module #6
Applications to Chemical Reactions
Modeling chemical reactions using differential equations

Module #7
Higher-Order Linear Differential Equations
Solving higher-order linear differential equations using undetermined coefficients

Module #8
Homogeneous Linear Differential Equations
Solving homogeneous linear differential equations using characteristic equations

Module #9
Non-Homogeneous Linear Differential Equations
Solving non-homogeneous linear differential equations using variation of parameters

Module #10
Laplace Transforms
Introduction to Laplace transforms and their applications to differential equations

Module #11
Laplace Transform Applications
Solving differential equations using Laplace transforms

Module #12
Systems of Linear Differential Equations
Solving systems of linear differential equations using eigenvalues and eigenvectors

Module #13
Matrix Methods for Systems
Using matrices to solve systems of linear differential equations

Module #14
Numerical Methods for Differential Equations
Introduction to numerical methods for solving differential equations

Module #15
Eulers Method
Using Eulers method to approximate solutions of differential equations

Module #16
Runge-Kutta Methods
Using Runge-Kutta methods to approximate solutions of differential equations

Module #17
Boundary Value Problems
Solving boundary value problems using shooting methods and finite difference methods

Module #18
Stability Analysis
Analyzing stability of equilibrium solutions using linearization and eigenvalues

Module #19
Applications to Electrical Circuits
Modeling electrical circuits using differential equations

Module #20
Applications to Mechanical Systems
Modeling mechanical systems using differential equations

Module #21
Applications to Epidemiology
Modeling disease spread using differential equations

Module #22
Applications to Economics
Modeling economic systems using differential equations

Module #23
Phase Portraits
Analyzing phase portraits of nonlinear differential equations

Module #24
Bifurcation Analysis
Analyzing bifurcations of nonlinear differential equations

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Differential Equations and Applications career

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Differential Equations and Applications ( 25 Modules )

Differential Equations and Applications
( 25 Modules )