Module 1: Introduction to Differential Equations
Begin your journey into differential equations by learning the key terminology, visualizing solutions with direction fields, understanding existence and uniqueness theorems, and approximating solutions numerically.
Your Progress
Learning Objectives
By the end of this module, you will be able to:
- Define what a differential equation is and distinguish ODEs from PDEs
- Classify DEs by order, linearity, and autonomy
- Sketch direction fields and identify solution curves
- State the Existence and Uniqueness Theorem for first-order IVPs
- Apply Euler's method to approximate solutions numerically
- Verify that a given function is a solution to a differential equation
Module Lessons
What Is a Differential Equation?
Learn the definition of a DE, classify by order and linearity, and verify solutions by substitution.
30-40 minutes
Direction Fields and Solution Curves
Visualize differential equations through slope fields and sketch solution curves without solving.
30-35 minutes
Existence and Uniqueness of Solutions
Understand when an IVP has a solution, when that solution is unique, and what can go wrong.
25-30 minutes
Euler's Method for Numerical Approximation
Approximate solutions step-by-step when an analytic formula is unavailable.
30-35 minutes
After the Lessons
Practice Problems
Apply what you learned with 10 problems covering classification, direction fields, existence/uniqueness, and Euler's method.
Practice ProblemsModule Quiz
Test your understanding with a 10-question quiz. Detailed solutions included!
Take Module QuizStudy Materials
Printable study guide and quick reference card for exam prep.