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Differential Equations

Explore the mathematics of change and discover how differential equations model real-world phenomena.

First Order ODEs

Introduction to basic differential equations

Topics covered:

  • Separation of Variables
  • Linear First Order ODEs
  • Exact Equations
  • Growth and Decay Models

Second Order ODEs

Understanding higher order differential equations

Topics covered:

  • Homogeneous Equations
  • Non-homogeneous Equations
  • Method of Undetermined Coefficients
  • Variation of Parameters
  • Springs and Oscillations

Systems of ODEs

Working with multiple coupled equations

Topics covered:

  • Phase Plane Analysis
  • Eigenvalues and Eigenvectors
  • Stability Analysis
  • Coupled Oscillators
  • Predator-Prey Systems

Applications

Real-world applications and numerical methods

Topics covered:

  • Numerical Methods
  • Circuit Analysis
  • Population Dynamics
  • Chemical Reactions
  • Control Systems