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