|
Planned Date |
Topic |
Important ideas |
| Week 1 |
Review of Precalculus | functions (definition, one-to-one, inverses, symmetry); trigonometry (basic definitions, properties, inverses); logarithmic and exponential functions (basic definitions, properties) |
| Weeks 2—3 | Limits | definition of the limit (intuitive and precise); properties; limits at and of infinity; the Squeeze Theorem; continuity; the Intermediate Value Theorem; using the Method of Bisection to find roots |
| Weeks 4—6 |
Derivatives | definition of the derivative (intuitive and precise); basic properties; derivatives of polynomials; derivatives of trigonometric functions; derivatives of exponential and logarithmic functions; the Mean Value Theorem for derivatives |
| Weeks 6—9 | Applications of differentiation | Newton's method to find roots; linear approximation; related rates; optimization; sketching the shape of a graph; L'Hôpital's Rule |