| Lecture | Text | Topics | Suggested Problems |
|---|---|---|---|
| 1 |
Appendices A,B,D; 1.1-1.5 |
Review of real numbers, absolute value, inequalities, lines, functions, exponential and trig functions |
App. A: 6, 7, 23, 28, 49, 52, 61, 62 App. B: 1, 7, 23, 25, 29, 35 App. D: 15, 19, 27, 31, 67, 74 1.1: 2, 7, 8, 19, 21, 22, 25, 38, 50, 51 1.2: 4, 11, 15, 16 1.3: 4, 5, 9, 16, 20, 23, 27, 36, 53 1.4: 1, 14, 15, 19, 25, 27 1.5: 11, 13, 17, 18, 22 |
| 2 | Appendix D, 1.6 | Inverse functions; logs and inverse trig functions | 1.6: 6, 12, 14, 26, 27, 35, 38, 48, 49, 50, 52 |
| 3 | 2.1, 2.2 | Tangents and velocity; limits |
2.1: 1, 3, 6, 8 2.2: 5, 6, 8, 9, 14, 19, 23, 27, 28, 30, 31 |
| 4 | 2.3, 2.4 | Limit laws and definition of limit |
2.3: 1, 3, 6, 7, 10, 13, 20, 26, 29, 37, 38, 40, 47, 58 2.4: 1, 3, 4, 6, 7, 20, 41, 42 |
| 5 | 2.5 | Continuity; Intermediate Value Theorem | 2.5: 3, 4, 15, 16, 19, 20, 25, 26, 37, 40, 47, 50, 51 |
| 6 | 2.6 | Infinity; asymptotes | 2.6: 4, 11, 16, 18, 19, 23, 26, 39, 40, 55, 58 |
| 7 | 2.7, 2.8, 2.9 | Rates of change; derivatives |
2.7: 5, 8, 11, 12, 15 2.8: 3, 7, 11, 15, 16 2.9: 2, 4, 11, 22, 26, 33, 34, 37, 41 |
| 8 | 3.1, 3.2 | Differentiation formulas; derivs of exponential functions |
3.1: 5, 7, 13, 16, 20, 33, 39, 46, 51, 54, 57 3.2: 3, 4, 5, 8, 9, 20, 27, 41, 42 |
| 9 | 3.3, 3.4 | Rates of change; derivatives of trig functions |
3.3: 3, 8, 13, 18, 25, 31 3.4: 3, 5, 8, 10, 13, 16, 18, 23, 29, 35, 36, 39 |
| 10 | 3.5, 3.6 | The chain rule; implicit differentiation |
3.5: 1, 2, 9, 14, 15, 16, 21, 22, 25, 33, 35, 44, 47 3.6: 3, 9, 16, 29, 41-44, 47, 48 |
| 11 | First exam (usual class time and place) | ||
| 12 | 3.6, 3.7, 3.8 |
Derivs of logs and inverse trig functions; higher derivs |
3.7: 1, 5, 8, 11, 19, 20, 39, 48, 51, 57 3.8: 3, 4, 7, 8, 13, 15, 24, 25, 26, 32, 35, 38, 41 |
| 13 | 3.10 | Related rates | 3.10: 1, 6, 14, 23, 24, 31 |
| 14 | 3.11, 4.9 | Linear approximation; Newton's Method |
3.11: 5, 7, 10, 13, 32, 36, 42 4.9: 1, 5, 14, 36 |
| 15 | 4.4 | L'Hôpital's Rule | 4.4: 1, 2, 3, 7, 10, 15, 21, 22, 29, 36, 37, 38, 47, 53, 54, 68 |
| 16 | 4.1, 4.2 | Max and min; the Mean Value Theorem |
4.1: 3, 22, 34, 39, 46, 55, 61, 62, 65, 68, 77 4.2: 5, 11, 14, 17, 23, 24, 29 |
| 17 | 4.3 | f´(x), f´´(x), and the graph of f | 4.3: 1, 5, 7, 11, 21, 22, 31, 32, 33, 36, 37, 42, 45, 47 |
| 18 | 4.5, 4.6 | Sketching graphs |
4.5: 3, 18, 30, 35, 45, 48 4.6: 7, 14, 15, 26, 27 |
| 19 | 4.7 | Applied max/min | 4.7: 2, 9, 17, 22, 27, 33, 40, 56 |
| 20 | 4.10 | Antiderivatives | 4.10: 3, 10, 12, 15, 25, 28, 35, 40, 48, 53, 55, 60, 63 |
| 21 | 5.1, Appendix E | Area; distance; sigma notation |
5.1: 4, 11, 18, 21 App. E: 1, 6, 12, 14, 25, 30, 44 |
| 22 | Second exam (usual class time and place) | ||
| 23 | 5.2 | The definite integral | 5.2: 3, 5, 12, 23, 33, 34, 37, 38, 48, 49, 53, 54 |
| 24 | 5.3, 5.4 | The Fundamental Theorem of Calculus |
5.3: 2, 8, 11, 17, 18, 25, 30, 31, 35, 37, 68 5.4: 1, 2, 5, 7, 8, 10, 11, 18, 19, 22, 29, 30, 38, 47, 54, 55 |
| 25 | 5.5 | Substitution rule | 5.5: 1, 3, 4, 5, 10, 12, 19, 20, 21, 25, 32, 44, 51, 53, 58, 63, 66, 68 |
| 26 | 6.1 | Computation of areas | 6.1: 1, 2, 3, 4, 9, 14, 17, 18, 43, 44, 45 |
| 27 | 5.6 | Logarithm defined as an integral | 5.6: 1, 3 |
| 28 | Catch up or review for final exam | ||