1. FUNCTIONS AND MODELS (Review)

Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms.

2. LIMITS AND DERIVATIVES.

The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. The Derivative as a Function.

3. DIFFERENTIATION RULES.

Derivatives of Polynomials and Exponential Functions. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Derivatives of Logarithmic Functions. Related Rates. Linear Approximations and Differentials.

4. APPLICATIONS OF DIFFERENTIATION.

Maximum and Minimum Values. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and lâ€™Hospitalâ€™s Rule. Summary of Curve Sketching. Optimization Problems. Antiderivatives.

5. INTEGRALS.

Areas and Distances. The Definite Integral. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. The Substitution Rule.

6. APPLICATIONS OF INTEGRATION.

Areas Between Curves. Volume by Slicing and/or Shells. Average Value of a Function.