Introduction to Calculus (Differentiation)

Class Description

Calculus is a fundamental branch of mathematics that deals with the concept of change. It provides us with a powerful toolkit for understanding and modeling how things vary and evolve. This introductory calculus lesson aims to provide you with a solid foundation in the key concepts and techniques of calculus.

Lesson Outline:

1. Understanding Limits:

Definition of a limit
Evaluating limits algebraically and graphically
One-sided limits
Limits at infinity

2. Differentiation:
Definition of a derivative
Derivative rules (power rule, product rule, quotient rule, chain rule)
Calculating derivatives of common functions
Applications of derivatives (related rates, optimization)

3. Applications of Differentiation:
- Curve sketching
- Optimization problems
- Related rates problems
- Approximation using differentials