Course Overview

Comprehensive study of differential equations. Key areas included:

Ordinary Differential Equations

• First-order equations
• Linear second-order equations
• Systems of ODEs
• Boundary value problems

Solution Methods

• Separation of variables
• Variation of parameters
• Series solutions
• Laplace transforms

Partial Differential Equations

• Heat equation
• Wave equation
• Laplace's equation
• Method of characteristics

Numerical Methods

• Euler's method
• Runge-Kutta methods
• Finite difference methods
• Stability analysis

Applications

• Physics problems
• Population dynamics
• Circuit analysis
• Control systems