11-Differential Equations

Overview

This textbook introduces the theory and applications of differential equations, beginning with first-order methods and progressing through higher-order equations, systems, Laplace transforms, numerical methods, and partial differential equations. Students learn both analytical and computational techniques for solving dynamic systems.

Table of Contents

1. Chapter 1: What Differential Equations Study
2. Chapter 2: Differential Equations Overview
3. Chapter 3: Separable Differential Equations
4. Chapter 4: Linear First-Order Equations
5. Chapter 5: First-Order Differential Equations
6. Chapter 6: Second-Order Linear Equations
7. Chapter 7: Mechanical Vibrations
8. Chapter 8: Nonhomogeneous Differential Equations
9. Chapter 9: Systems of Differential Equations
10. Chapter 10: Laplace Transforms
11. Chapter 11: Numerical Methods
12. Chapter 12: Advanced Differential Equations Topics
13. Chapter 13: Introduction to Partial Differential Equations
14. Chapter 14: Differential Equations Capstone

Learning Outcomes

• Classify and model real-world problems using differential equations.
• Solve first-order and higher-order differential equations using standard techniques.
• Analyze physical systems such as oscillations and mechanical vibrations.
• Apply Laplace transforms to solve linear differential equations.
• Use numerical methods for approximate solutions.
• Analyze systems of differential equations and dynamic interactions.
• Understand introductory partial differential equations.