| Topics to be covered | |
|---|---|
| Chapter 6 | Transcendental functions |
| 6.1 | Inverse functions and their derivatives |
| 6.2 | Natural logarithms |
| 6.3 | The exponential function |
| 6.4 | a to the x and log x to the base a |
| 6.5 | Growth and decay |
| 6.6 | L'Hopital's rule |
| 6.7 | Relative rates of growth |
| 6.8 | Inverse trigonometric functions |
| 6.9 | Derivatives of inverse trigonometric functions; integrals |
| 6.10 | Hyperbolic functions |
| 6.11 | First order differential equations |
| 6.12 | Euler's numerical method; Slope fields |
| Chapter 7 | Techniques of Integration |
| 7.1 | Basic integration formulas |
| 7.2 | Integration by parts |
| 7.3 | Partial fractions |
| 7.4 | Trigonometric substitutions |
| 7.6 | Improper integrals |
| Chapter 8 | Infinite series |
| 8.1 | Limits of sequences of numbers |
| 8.2 | Theorems for calculating limits of sequences |
| 8.3 | Infinite series |
| 8.4 | The integral test for series of nonnegative terms |
| 8.5 | Comparison tests for series of nonnegative terms |
| 8.6 | The ratio and root tests for series of nonnegative terms |
| 8.7 | Alternating series, absolute and conditional convergence |
| 8.8 | Power series |
| 8.9 | Taylor and Maclaurin series |
| 8.10 | Convergence of Taylor series; error estimates |
| 8.11 | Applications of power series |
| Chapter 9 | Conic Sections, Parametrized Curves, and Polar Coordinates |
| 9.1 | Conic sections and quadratic equations |
| 9.2 | Classifying conic sections by eccentricity |
| 9.4 | Parametrizations of plane curves |
| 9.5 | Calculus with parametrized curves |
| 9.6 | Polar coordinates |
| 9.8 | Polar equations for conic sections |
| 9.9 | Integration in polar coordinates |
| Handout: The Complex numbers |