Lecture | Reading | Topics |
---|---|---|
1 | 1.1, 1.2, 1.3 | Inequalities, intervals, functions. Types of functions. |
2 | 1.4, 1.5 | Trigonometric functions. Inverse functions. |
3 | 1.6, 1.7, 2.1 | Exponentials and logarithms. Use of graphing calculators. |
4 | 2.2, 2.3, 2.4 | Tangents. Limits, numerically and graphically. Continuity. Laws of limits. |
5 | 2.5, 2.6, 2.7 | Evaluating limits. Trigonometric limits. The Intermediate Value Theorem. |
6 | 2.8, 3.1, 3.2 | Definition of limit and derivative. Power rule. |
7 | 3.3, 3.4 | Product and quotient rule. Rates of change. |
8 | 3.5, 3.6 | Higher derivatives. Differentiation of trigonometric functions. |
9 | 3.7 | Chain rule. |
10 | First Hour Exam | (In the usual class time and place.) |
11 | 3.8 | Implicit differentiation. |
12 | 3.9, 3.10 | Differentiation of inverse functions, exponentials,
logarithms. Note: Hyperbolic functions may be omitted. |
13 | 3.11 | Related Rates. |
14 | 4.1, 4.8 | Linear approximations. Newton's method. |
15 | 4.2 | Maxima and minima. Critical points. |
16 | 4.3, 4.4 | Shape of a graph. Mean Value Theorem. First derivative test. Concavity. |
17 | 4.5 | Curve sketching. Asymptotes. |
18 | 4.6 | Maxima and minima problems. |
19 | 4.7 | Indeterminate forms. L'Hôpital's rule. |
20 | 4.9 | Antiderivatives. |
21 | 5.1 | Approximating and computing area. |
22 | Second Hour Exam | (In the usual class time and place.) |
23 | 5.2 | Definite integrals. |
24 | 5.3, 5.4 | Fundamental Theorem of Calculus. |
25 | 5.5, 5.6 | Net change. Integration by substitution. |
26 | 5.7, 5.8 | Transcendental functions. Exponential growth. |
27 | 6.1 | Area between two curves. |
28 | Review |
Suggested Homework Problems for Mathematics 151 | |
---|---|
Section 1.1: | 2, 7, 12, 15, 19, 26, 34(a), 35, 41, 43, 46, 49, 53, 61, 62, 70 |
Section 1.2: | 7, 9, 13, 14, 23, 29, 37, 38, 45 |
Section 1.3: | 1, 5, 9, 13, 14, 16, 17, 18, 27, 30 |
Section 1.4: | 1, 3(a), (b), 4(a), (b), 5, 8, 9, 10, 15, 20, 31, 38 |
Section 1.5: | 1, 2, 4, 9, 11, 16(a), (e), 23, 24, 27, 29, 30, 31, 40 |
Section 1.6: | 3, 4, 5, 6, 11, 12, 13, 24, 25, 29 |
Section 1.7: | 1, 2, 3, 13, 16 |
Section 2.1: | 5, 6, 7, 11, 22, 23, 33 |
Section 2.2: | 3, 5, 8, 14, 21, 23, 24, 38, 43, 53 |
Section 2.3: | 7, 11, 15, 16, 24, 25, 26 |
Section 2.4: | 1, 2, 3, 4, 7, 17, 27, 39, 40, 59, 61, 62, 65, 69, 70, 80 |
Section 2.5: | 1, 2, 5, 7, 11, 16, 18, 22, 29, 39, 48, 49 |
Section 2.6: | 3, 4, 6, 9, 10, 20, 21, 22, 28, 38 |
Section 2.7: | 2, 4, 7, 15, 19 |
Section 2.8: | 1, 2, 4, 6 |
Section 3.1: | 3, 7, 8, 10, 21, 23, 26, 27, 34, 44, 53, 54 |
Section 3.2: | 2, 7, 10, 21, 22, 23, 27, 34, 36, 47, 50, 77 |
Section 3.3: | 3, 7, 8, 21, 22, 23, 27, 34, 44, 50, 51, 52 |
Section 3.4: | 3, 6, 9, 10, 13, 30, 31 |
Section 3.5: | 1, 2, 7, 8, 20, 24, 25, 30, 34, 39, 44 |
Section 3.6: | 3, 5, 6, 7, 18, 20, 23, 29, 36, 39, 44 |
Section 3.7: | 2, 9, 11, 17, 21, 22, 25, 27, 37, 43, 44, 49, 57, 67, 70, 76, 85 |
Section 3.8: | 3, 9, 11, 16, 23, 25, 29, 30, 36, 43 |
Section 3.9: | 3, 7, 11, 15, 18, 19, 23, 27, 28, 31 |
Section 3.10: | 1, 3, 7, 10, 12, 20, 23, 30, 35, 36, 45 |
Section 3.11: | 3, 5, 7, 9, 14, 15, 19, 26 |
Section 4.1: | 3, 4, 9, 11, 17, 18, 33, 41, 44 |
Section 4.8: | 3, 7, 9, 13, 20 |
Section 4.2: | 1, 5, 7, 11, 12, 29, 31, 32, 33, 39, 48, 61 |
Section 4.3: | 5, 12, 13, 17, 27, 28, 43, 45, 63, 64 |
Section 4.4: | 7, 10, 17, 22, 25, 28, 37, 47 |
Section 4.5: | 1, 3, 4, 13, 18, 27, 31, 39, 44, 51, 52, 57, 58, 61, 62, 66, 77, 81, 86 |
Section 4.6: | 2, 3, 9, 10, 13, 18, 28, 39 |
Section 4.7: | 3, 5, 6, 9, 11, 12, 17, 19, 20, 27, 28, 32, 43, 48 |
Section 4.9: | 3, 13, 18, 20, 25, 29, 33, 35, 39, 41, 47, 64 |
Section 5.1: | 1, 7, 13, 15, 18, 20, 31(c), (d), 35, 37, 41, 60 |
Section 5.2: | 1, 7, 8, 13, 14, 15, 17, 31, 37, 61, 74 |
Section 5.3: | 7, 10, 11, 23, 31, 33, 36, 37, 44, 49 |
Section 5.4: | 7, 9, 11, 15, 21, 24, 29, 31, 32 |
Section 5.5: | 1, 4, 10, 13 |
Section 5.6: | 9, 10, 11, 18, 20, 25, 38, 39, 45, 51, 53, 56, 58, 82, 89 |
Section 5.7: | 7, 17, 22, 25, 27, 43, 50, 59, 61, 70 |
Section 5.8: | 2, 5, 7, 8, 12, 24, 31 |
Section 6.1: | 1, 5, 6, 8, 9, 11, 16, 30, 33, 36, 41 |