1. FUNCTIONS.

Real Numbers, Inequalities, and Lines.

Exponents.

Functions: Linear and Quadratic.

Functions: Polynomial, Rational, and Exponential.

2. DERIVATIVES AND THEIR USES.

Limits and Continuity.

Rates of Change, Slopes, and Derivatives.

Some Differentiation Formulas.

The Product and Quotient Rules.

HigherOrder Derivatives.

The Chain Rule and the Generalized Power Rule.

Nondifferentiable Functions.

3. FURTHER APPLICATIONS OF DERIVATIVES.

Graphing Using the First Derivative.

Graphing Using the First and Second Derivatives.

Optimization.

Further Applications of Optimization.

Optimizing Lot Size and Harvest Size.

Implicit Differentiation and Related Rates.

4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Exponential Functions.

Logarithmic Functions.

Differentiation of Logarithmic and Exponential Functions.

Two Applications to Economics: Relative Rates and Elasticity of Demand.

5. INTEGRATION AND ITS APPLICATIONS.

Antiderivatives and Indefinite Integrals.

Integration Using Logarithmic and Exponential Functions.

Definite Integrals and Areas.

Further Applications of Definite Integrals: Average Value and Area Between Curves.

Two Applications to Economics: Consumers' Surplus and Income Distribution.

Integration by Substitution.

6. INTEGRATION TECHNIQUES.

Integration by Parts.

Integration Using Tables.

Improper Integrals.

Numerical Integration.

7. CALCULUS OF SEVERAL VARIABLES.

Functions of Several Variables.

Partial Derivatives.

Optimizing Functions of Several Variables.

Least Squares.

Lagrange Multipliers and Constrained Optimization.

Total Differentials and Approximate Changes.

Multiple Integrals.

8. TRIGONOMETRIC FUNCTIONS.

Triangles, Angles, and Radian Measure.

Sine and Cosine Functions.

Derivatives of Sine and Cosine Functions.

Integrals of Sine and Cosine Functions.

Other Trigonometric Functions.

9. DIFFERENTIAL EQUATIONS.

Separation of Variables.

Further Applications of Differential Equations: Three Models of Growth.

FirstOrder Linear Differential Equations.

Approximate Solutions of Differential Equations: Euler's Method.

10. SEQUENCES AND SERIES.

Geometric Series.

Taylor Polynomials.

Taylor Series.

Newton's Method.

11. PROBABILITY.

Discrete Probability.

Continuous Probability.

Uniform and Exponential Random Variables.

Normal Random Variables.
