Math 151 - Suggested Problems and Syllabus
- TEXTBOOK: James Stewart, Calculus (Early Transcendentals) 5e., Brooks/Cole Publishing Co.
- This edition of the textbook differs in important ways from previous editions. Unfortunately the older editions won't always have the same problems, so they won't work for this course.
- CALCULATOR: A graphing calculator is required for this course. We have traditionally used the TI-82 or 83 and recommend either of them, but any calculator with equivalent capacities can be used, such as the popular TI-85 or 86. Calculators will not be permitted on final exams.
CAUTION: Your schedule
may vary. There are many sections of Math 151. The order in which topics are
covered, the rate at which they are covered, the precise times of examinations,
and the assigned exercises will vary from section to section. The
"schedule" below therefore may not be followed exactly in your
section. Your first exam, for example, might occur in the 10th or any other
lecture period, as announced by your instructor. Likewise the exercises listed
below are only suggestions. As a student in Math 151, your assignments and
obligations will be set and announced by your individual instructors, and you
will find them out only by attending your own class. Lectures are held twice
each week. There is an additional workshop each week, and certain sections have
an additional practicum session each week.
| Lecture | Sections | 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; derivatives 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 | |
| 12 | 3.6, 3.7, 3.8 | Derivatives of logs and inverse trig functions, higher derivatives | 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 | |
| 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 and review for final exam | |
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