Differential Equations for Engineers Course Syllabus

Overview: This course provides a comprehensive introduction to differential equations with a focus on applications in engineering. Structured into six modules, it covers first-order, second-order, and systems of differential equations, along with Laplace transforms, series solutions, and an introduction to partial differential equations. With approximately 24 hours of content, learners will engage in interactive exercises, quizzes, and real-world problem-solving to build strong analytical foundations. The course is designed for beginners and ideal for those pursuing careers or advanced studies in engineering, data science, or computational modeling.

Module 1: First-Order Differential Equations

Estimated time: 4 hours

• Introduction to differential equations and classification
• Separable first-order differential equations
• Linear first-order differential equations and integrating factors
• Applications: compound interest, terminal velocity, and RC circuits

Module 2: Homogeneous Linear Differential Equations

Estimated time: 4 hours

• Second-order linear differential equations with constant coefficients
• Superposition principle and general solutions
• Wronskian and linear independence
• Characteristic equations and solution forms

Module 3: Inhomogeneous Linear Differential Equations

Estimated time: 4 hours

• Non-homogeneous equations and particular solutions
• Method of undetermined coefficients
• Variation of parameters
• Applications: RLC circuits, mass-spring systems, and pendulums

Module 4: The Laplace Transform and Series Solution Methods

Estimated time: 4 hours

• Laplace transform and its properties
• Solving ODEs with discontinuous and impulsive forcing functions
• Series solutions for linear ordinary differential equations

Module 5: Systems of Differential Equations

Estimated time: 4 hours

• Coupled systems of first-order linear differential equations
• Matrix methods and eigenvalue problems
• Applications: coupled harmonic oscillators

Module 6: Partial Differential Equations

Estimated time: 4 hours

• Introduction to partial differential equations
• Classification of PDEs (elliptic, parabolic, hyperbolic)
• Basic solution techniques and engineering applications

Prerequisites

• Basic knowledge of calculus (derivatives and integrals)
• Familiarity with linear algebra concepts (vectors and matrices)
• Understanding of fundamental physics concepts (e.g., circuits and mechanics)

What You'll Be Able to Do After

• Solve separable and linear first-order differential equations and apply them to real-world problems
• Analyze homogeneous and inhomogeneous second-order differential equations, including resonance phenomena
• Utilize the Laplace transform and series methods to solve linear ordinary differential equations
• Model and solve systems of linear differential equations using matrix methods
• Understand the basics of partial differential equations and their applications