# Calculus

Calculus Curriculum

1: Functions

- Definitions
- Special Functions
- Polynomials and Other Rational Functions
- Trigonometric Functions

2. Limits and Continuity

- Definitions and Examples
- Asymptotes
- Theorems on Limits
- Limit of a Quotient of Polynomials
- Other Basic Limits
- Continuity

3: Differentiation

- Definition of Derivative
- Formulas
- The Chain Rule: the Derivative of a Composite Function
- Differentiability and Continuity
- Estimating a Derivative

4: Applications of Differential Calculus

- Slope: Critical Points
- Tangents and Normals
- Increasing and Decreasing Functions
- Maximum, Minimum, and Inflection Points: Definitions
- Maximum, Minimum, and Inflection Points: Curve Sketching
- Optimization: Problems Involving Maxima and Minima
- Relating a Function and Its Derivatives Graphically
- Motion Along A Line
- Motion Along A Curve: Velocity and Acceleration Vectors

5: Antidifferentiation

- Antiderivitives
- Basic Formulas

6: Definite Intergrals

- Fundamental Theorem of Calculus
- Properties of Definite Integrals
- Approximations of the Definite Integral; Riemann Sums

7: Further Applications of Integration

- Motion Along a Straight Line
- Motion Along a Plane Curve