R.3 Rational Expressions.
1. Linear Functions.
Linear Functions and Applications.
The Least Squares Line.
2. Nonlinear 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.
Derivatives of Products and Quotients.
The Chain Rule.
Derivatives of Exponential Functions.
Derivatives of Logarithmic Functions.
5. Graphs and the Derivative.
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.
Volume and Average Value.
Continuous Money Flow.
9. Multivariable Calculus.
Maxima and Minima.
Total Differentials and Approximations.
10. Differential Equations.
Linear First-Order Differential Equations.
Applications of Differential Equations.
11. Probability and Calculus.
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.
Derivatives of Trigonometric Functions.
Integrals of Trigonometric Functions.
Table 2. Area Under a Normal Curve.
Table 3. Integrals.
Table 4. Integrals Involving Trigonometric Functions.