Differential Equations: Lecture 1.1-1.2 Definitions and Terminology and Initial Value Problems

This is an actual classroom lecture. This is the very first day of class in Differential Equations. We covered most of Chapter 1 which is mainly definitions, terminology, and initial value problems. Just tons of theory here.
Here is the book for the lectures https://amzn.to/4ajOMyW (affiliate link).

There are lots of notes and tons of definitions in this lecture.

Summary of Some of the Topics
- Definition of a Differential Equation
- Motivation for Differential Equations
- Types of Differential Equations
- Order of a Differential Equation
- Linear versus Nonlinear Differential Equations
- Solutions to Differential Equations
- One parameter families and two parameter families of solutions
- Particular Solutions
- Explicit versus implicit solutions
- The trivial solution
- The General solution
- Singular solutions
- The interval of definition
- Initial Value problems


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