Functions and Their Graphs. Some Important Functions. The Algebra of Functions. Zeros of Functions — The Quadratic Formula and Factoring. Exponents and Power Functions. Functions and Graphs in Applications. Appendix: Graphing Functions Using Technology.
1. The Derivative.
The Slope of a Straight Line. The Slope of a Curve at a Point. The Derivative. Limits and the Derivative. Differentiability and Continuity. Some Rules for Differentiation. More About Derivatives. The Derivative as a Rate of Change.
2. Applications of the Derivative.
Describing Graphs of Functions. The First and Second Derivative Rules. Curve Sketching (Introduction.) Curve Sketching (Conclusion.) Optimization Problems. Further Optimization Problems. Applications of Derivatives to Business and Economics.
3. Techniques of Differentiation.
The Product and Quotient Rules. The Chain Rule and the General Power Rule. Implicit Differentiation and Related Rates.
4. The Exponential and Natural Logarithm Functions.
Exponential Functions. The Exponential Function e^x. Differentiation of Exponential Functions. The Natural Logarithm Function. The Derivative of ln x. Properties of the Natural Logarithm Function.
5. Applications of the Exponential and Natural Logarithm Functions.
Exponential Growth and Decay. Compound Interest.Applications of the Natural Logarithm Function to Economics. Further Exponential Models.
6. The Definite Integral.
Antidifferentiation. Areas and Reimann Sums. Definite Integrals and the Fundamental Theorem. Areas in the xy-Plane. Applications of the Definite Integral.
7. Functions of Several Variables.
Examples of Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables. Lagrange Multipliers and Constrained Optimization. The Method of Least Squares. Nonlinear Regression. Double Integrals.
8. The Trigonometric Functions.
Radian Measure of Angles. The Sine and the Cosine. Differentiation of sin t and cos t. The Tangent and Other Trigonometric Functions.