Math 151 syllabus and suggested textbook homework problems for Fall 2008
- Textbook Calculus, Early Transcendentals by Jon Rogawski, published by W. H. Freeman. Some background material, linked here, is included in the "Rutgers edition" of the book. This material should be the only difference between the generally available book and the Rutgers version.
- Students should have a graphing calculator available in class and while doing homework. Calculators may not be used during examinations.
- 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 may vary from section to section. The exact timing and coverage of exams during the semester will be announced by each lecturer, as will homework assignments. The problems listed below are suggestions. There will also be workshop writeups.
- The final exam for the course will be given on Monday, December 15 from 4 to 7 PM. All sections normally take the same final examination. Earlier in-class exams are usually written by each lecturer.
| 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 |