Differential Equations

Course Description

Differential equations are the mathematical equations that relate a function with its derivatives. They describe how systems change over time and are fundamental to understanding natural phenomena in physics, engineering, biology, economics, and many other fields. This course provides comprehensive coverage of both the theory and practical applications of differential equations.

You'll begin with first-order differential equations, learning various solution techniques including separation of variables, integrating factors, and exact equations. The course then progresses to higher-order linear differential equations, where you'll master the method of undetermined coefficients, variation of parameters, and power series solutions.

A major focus is on systems of differential equations and their applications to real-world problems. You'll learn matrix methods, eigenvalue approaches, and phase plane analysis. The Laplace transform section teaches you a powerful tool for solving initial value problems and understanding system behavior in engineering applications.

The course culminates with an introduction to partial differential equations, covering the heat equation, wave equation, and Laplace's equation. You'll learn separation of variables, Fourier series, and numerical methods for solving PDEs. Throughout the course, emphasis is placed on modeling real-world phenomena including population dynamics, mechanical vibrations, heat transfer, and electrical circuits. Perfect for engineering students, physics majors, and anyone working in technical fields requiring mathematical modeling.