1. Linear Functions.
Slopes and Equations of Lines.
Linear Functions and Applications.
The Least Squares Line.
2. Nonlinear Functions.
Properties of Functions.
Quadratic Functions; Translation and Reflection.
Polynomial and Rational Functions.
Applications. Growth and Decay; Mathematics of Finance.
3. The Derivative.
Rates of Change.
Definition of the Derivative.
4. Calculating the Derivative.
Techniques for Finding Derivatives.
Derivatives of Products and Quotients.
The Chain Rule.
Derivatives of Exponential Functions.
Derivatives of Logarithmic Functions.
5. Graphs and the Derivative.
Increasing and Decreasing Functions.
Higher Derivatives, Concavity, and the Second Derivative Test.
6. Applications of the Derivative.
Applications of Extrema.
Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand.
Differentials: Linear Approximation.
Area and the Definite Integral.
The Fundamental Theorem of Calculus.
The Area Between Two Curves.
8. Further Techniques and Applications of Integration.
Integration by Parts.
Volume and Average Value.
Continuous Money Flow.
9. Multivariable Calculus.
Functions of Several Variables.
Maxima and Minima.
Total Differentials and Approximations.
10. Differential Equations.
Solutions of Elementary and Separable Differential Equations.
Linear First-Order Differential Equations.
Applications of Differential Equations.
11. Probability and Calculus.
Continuous Probability Models.
Expected Value and Variance of Continuous Random Variables.
Special Probability Density Functions.
12. Sequences and Series.
Annuities: An Application of Sequences.
Taylor Polynomials at 0.
13. The Trigonometric Functions.
Definitions of the Trigonometric Functions.
Derivatives of Trigonometric Functions.
Integrals of Trigonometric Functions.
Table 1. Formulas from Geometry.
Table 2. Area Under a Normal Curve.
Table 3. Integrals.
Table 4. Integrals Involving Trigonometric Functions.