Currently (Summer I, 2009), I am teaching Differential and Integral Calculus, 21-120. Lectures are 10:30–11:50 daily, in Wean Hall 8427. Syllabus (pdf)
N.B. Scheduled topics are provisional until covered. All homework assignments are from Stewart “Essential Calculus: Early Transcendentals“, and are due in class two lectures later.
| Date | Topic(s) | Homework |
| Mon 18 May | Introduction and overview; definiton of a function. (Stewart 1.1) | 1.1: 3–6, 14, 48, 54. |
| Tue 19 | A gallery of essential functions (Stewart 1.2); a look ahead towards differentiation. | 1.1: 20, 56. 1.2: 10, 30. |
| Wed 20 | Introduction to limits. (Stewart 1.3) | 1.2: 36. 1.3: 4, 34, 20. |
| Thu 21 | More on limits: the limit laws. (Stewart 1.3, 1.4) | 1.3: 20, 24, 42. 1.4: 6. |
| Fri 22 | More limits; continuity. (Stewart 1.5) | 1.4: 38. 1.5: 10, 26, 30. |
| Mon 25 May | Memorial Day; no class. | |
| Tue 26 | More on limits and continuity: the Squeeze Theorem, the Indermediate Value Theorem. (Stewart 1.4, 1.5) | 1.4: 20, 28. 1.5: 8, 36, 24. |
| Wed 27 | Introduction to derivatives: slopes, velocities, tangent lines. (Stewart 2.1) | 2.1: 2, 10, 14, 38. |
| Thu 28 | First properties of derivatives; some important derivatives. (Stewart 2.1, 2.2) | 2.1: 44. 2.2: 4–11, 14, 22, 27–30 |
| Fri 29 | Rules for differentiation: polynomials, sums and constant multiples, and the product rule. (Stewart 2.2, 2.3, 2.4) | 2.3: 4, 20, 28, 52, 64. 2.4: 6. |
| Mon 1 June | Trig limits and derivatives; higher derivatives, acceleration. (Stuart 1.3, 2.2, 2.3) | 2.3: 22, 56. 2.4: 30, 47. |
| Tue 2 | The Chain Rule (Stewart 2.5) | 2.4: 2, 22, 38. 2.5: 44, 64. |
| Wed 3 | Implicit derivatives; related rates. (Stewart 2.6, 2.7) | 2.6: 18, 30. 2.7: 16. |
| Thu 4 | Maxima and minima of functions; the mean value theorem. (Stewart 4.1, 4.2) | 2.7: 30. 4.1: 6, 44. 4.2: 20. 4.3: 24. (For Tue 9.) |
| Fri 5 | Derivatives in curve sketching (Stewart 4.3); review for midterm. Review sheet: plain, with hints, with solutions. | — |
| Mon 8 | Midterm exam. | — |
| Tue 9 | Limits involving infinity (Stewart 1.6) | 1.6: 2, 14, 18, 22, 26, 44. |
| Wed 10 | Integration: introduction (Stewart 5.1) | 5.1: 2, 8, 20. |
| Thu 11 | The Riemann Integral; the Fundamental Theorem of Calculus I. (Stewart 5.2) | 5.2: 6, 16, 20, 45. 5.3: 8. |
| Fri 12 | Calculating integrals: first techniques. (Stewart 5.3) | 5.3: 14, 38, 46, 52, 58. 5.5: 2. |
| Mon 15 | Integration by substitution (Stewart 5.5); the Fundamental Theorem of Calculus II (Stewart 5.4). | 5.5: 4, 14, 46, 60. |
| Tue 16 | Odds and ends of integration (Stewart 5.1–5). Integration by parts (Stewart 6.1). | 5.4: 8, 10, 26. 6.1: 6. |
| Wed 17 | Applications of integration: areas and volume. (Stewart 7.1–2) | 7.1: 2, 22. 7.2: 8, 28. |
| Thu 18 | Exponential and log functions: introduction (Stewart 3.1–3) | 3.1: 18. 3.2: 50. 3.3: 12, 56, 60. |
| Fri 19 | Exponential and log functions: calculus, and applications. (Stewart 3.2–3) | 3.3: 4. 4.3: 6. 4.3: 6. 5.5: 30. |
| Mon 22 | Hyperbolic and inverse trig functions | 3.5: 14, 40. 3.6: 4, 12, 34. 6.1: 4. |
| Tue 23 | L'Hospital's rule | |
| Wed 24 | Further applications | — |
| Thu 25 | Review. | — |
| Fri 26 | Final exam. | — |