| By the end of this course, the student will be able to: |
| 1. Compute limits: |
| · algebraically |
| · graphically |
| 2. Compute derivatives involving: |
| · the definition of the derivative |
| · polynomials |
| · exponential functions |
| · trigonometric functions |
| · inverse trigonometric functions |
| · logarithmic functions |
| · the product rule |
| · the quotient rule |
| · the chain rule |
| 3. Apply derivatives to various topics: |
| · tangent lines |
| · related rates |
| · minimum and maximum values |
| · concavity |
| · L'Hospital's Rule |
| · optimization |
| · other |
| 4. Compute integrals involving: |
| · Riemann sums |
| · indefinite integrals of polynomials |
| · indefinite integrals of exponential functions |
| · indefinite integrals of trigonometric functions |
| · indefinite integrals of inverse trigonometric functions |
| · definite integrals |
| · substitution |
| 5. Apply integrals to various topics: |
| · area |
| · average value of a function |
| · other |