| # | Date | Topics | Homework |
|---|---|---|---|
| 1 | F 9/8 | Introduction | - |
| 2 | M 9/11 | Basic rules for differentiation (3.1) | Practice problems: 3.1, p. 191: #1,3,5,6,7, 9,10,11 |
| 3 | W 9/13 | Review of exponents, exponential functions (1.5). | - |
| - | - | Lab 1: Zooming into a graph to estimate its slope at a point | - |
| 4 | F 9/15 | Derivative of e^x (3.1). Find equation of tangent line (p. 159-160) | Practice problems: p. 191: 12, 13, 17, 22. |
| - | - | - | HW 1: p. 191 (3.1): 2bc, 23, 32, 33 (use the interval -20 < x < 20), 36, 39, 41, 45 (due 9/20) |
| 5 | M 9/18 | Product rule (3.2) | Challenge problem #1 (optional): p. 191: 49 (hand in by 9/25) |
| 6 | W 9/20 | Quiz #1. Product and quotient rules (3.2) | Practice problems: p. 197: 3, 5, 7, 9 (in two ways), 11 |
| - | - | Demonstration of why e is a special number | - |
| 7 | F 9/22 | Tangent and secant lines (pp. 4, 87-89, 149-152) | - |
| 8 | M 9/25 | Three ways of defining the derivative (see above pages) | Practice problems: p. 91: 4ab, 7ab |
| 9 | W 9/27 | Quiz #2. | - |
| - | - | The derivative as rate of change in various situations (3.3). | Lab 2: UBC slope and velocity applet |
| - | - | - | HW 2: p. 197: 13, 14, 16, 27, 31, 35. P. 208: 13, 28a (due 10/4) |
| 10 | F 9/29 | Review of trigonometry (Appendix D); Derivatives of trigonometric functions (for now we'll just do sine and cosine) (3.4) | Practice problems: p. 216: 1, 2, 5, 13. Also p. A32: 1, 4, 7, 10, 35, 36. |
| 11 | M 10/2 | Chain rule (3.5) | HW 3: p. 216 (3.4): 9, 16, 23, 25, 31 (since the answer to the last question is in the back of the book, your job is to explain how you get it.) |
| - | - | - | Practice problems (3.5) p. 224: 5, 7, 9, 11. |
| 12 | W 10/4 | Chain rule (con't) | HW 4: p. 224 (3.5): 13, 15, 17, 21, 23, 25, 48, 50, 53, 55 (due 10/17). |
| - | - | - | - |
| 14 | F 10/6 | [no class] | - |
| 15 | W 10/11 | Implicit differentiation (3.6) | Practice problems: p. 233: 1a,3a |
| 16 | F 10/13 | Implicit differentiation (con't) | Practice problems: p. 233: 1bc, 2bc |
| - | - | - | HW 5 (3.6): p. 233: 7, 9, 25, 27, 38, 55 (due 10/23) |
| 17 | M 10/16 | Higher derivatives (3.7) | - |
| - | - | - | MHC velocity applet |
| 18 | W 10/18 | Orthogonal families (p. 231-2) | - |
| - | - | Recognizing f, f', f'' from shape of graphs (p. 240) | - |
| 19 | F 10/20 | Logarithms (only the natural logarithm) (3.8). Practice problems p. 249: 2, 3, 4. | HW 6: p. 235: 59; p. 249 (3.8): 7, 9, 10, 16, 21, 31 (due 10/27) |
| - | - | - | Test 1 |
| 20 | M 10/23 | Related rates (3.10) | Practice problem: A stone is dropped into a pond. The radius of the resulting wave is increasing at 0.5 m/sec. (a) How fast is the area increasing when the radius is 2m? (b) How fast is the circumference increasing when the radius is 2m? |
| 21 | W 10/25 | Maximum and minimum values (4.1). | Practice problems: p. 287: 31, 33 |
| 22 | F 10/27 | Second derivative test (4.3) | For 10/30: Write a careful presentation of the solution to problem (b) above. |
| - | - | - | HW 7: p. 240 (3.7): 2, 3, 5, 7, 11, 23, 25. p. 260 (3.10): 8. Due 11/1 |
| - | - | - | Challenge problem 2: p. 242: 66 (Do as much of parts a, b and c as you can.) Due 11/3 |
| 23 | M 10/30 | Maxima and minima (4.1) | HW 8: p. 285 (4.1): 35, 47, 49, 52, 53, 60 (due 11/3) |
| 24 | W 11/1 | How derivatives affect the shape of a graph (4.3) | HW 9: p. 304 (4.3): 2, 6, 8, 9, 11 (due 11/6) |
| - | - | - | Quiz 4 on 3.6, 3.7, 3.8 |
| 25 | F 11/3 | Curve sketching (4.5, 4.6) | - |
| 26 | M 11/6 | Curve sketching | Practice problem p. 336 #3 |
| 27 | W 11/8 | Asymptotes (p. 317-318) | Practice problem: p. 337: #7. |
| - | - | - | Quiz 5 on 4.1, 4.3 |
| 28 | F 11/10 | First and second derivative tests (encore) | HW 10 p. 360 (3.10): 7, 9; p. 336 (4.7): 11 (due 11/20) |
| 29 | M 11/13 | Optimization (4.7) | - |
| 30 | W 11/15 | - | - |
| - | - | - | Test II handed out |
| 31 | F 11/17 | The derivative of the tangent function is the secant squared (p. 214) | HW 11 p. 224 (3.4): 2, 12, 32 (due 11/29) |
| - | - | - | Test II due |
| 32 | M 11/20 | - | - |
| 33 | M 11/27 | Antiderivatives (4.10) | - |
| 34 | W 11/29 | Areas by rectangles (5.1) | Worksheet on numerical integration (due 12/1) |
| - | - | Practice problem: p. 378: 1 | HW 12: p. 358 (4.10): 4, 6, 8, 11, 37, 43, 46; p. 378 (5.1): 4, 6 (due 12/4) |
| 35 | F 12/1 | [go over test] | - |
| 36 | M 12/4 | Differentials (p. 265-267); Areas and the Fundamental Theorem of Calculus (5.3) | Practice problems: p. 268: 15; p. 402: 19, 21 |
| - | - | - | HW 14: p. 268: 16, 17, 18; p. 402: 20, 22, 23, 25, 28 (due 12/8) |
| - | - | - | HW 13: Find a definition of "tangent" in a dictionary. Is it correct? Other comments? (due 12/6) |
| 37 | W 12/6 | Practice exam handed out | - |
| 38 | F 12/8 | The definite integral counts area under the x-axis with a negative sign (p. 382) | - |
| 39 | M 12/11 | Handout from "Calculus made easy". Look at the discussion of limits and also of infintesimals (differentials). | - |
| 40 | W 12/13 | - | All homework is due at 5pm today |