# 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