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Mathematics Department • University of Louisiana at Lafayette • 217 Maxim Doucet Hall • P.O. Box 41010 • Lafayette, LA 70504-1010 USA
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Calculus is a branch of mathematics which for over three centuries has served as the basis for the analysis of continuous change. Applying calculus to real-life problems in science, engineering, or other fields requires both an understanding of how the mathematics can be used to model problems, and the capability of performing the calculations and computations necessary to obtain solutions. The textbook concentrates on the most important topics of calculus (limits, derivatives, integrals, etc.), but with emphasis on the graphical and numerical representation of functions and other relations as well as the traditional use of symbolic formulas. The materials in our text are meant to be read thoroughly and carefully. The writing is plain and straight-forward. While the text does contain some routine "drill" exercises, the authors have included other types of in-depth problems designed to develop conceptual understanding. A number of the problems are intended to be discussed by students working together in small groups. This new approach to calculus is enhanced by the availability of new technology, which can heighten our understanding of mathematical relationships. In this course, the graphing calculator will be the standard tool for visualization and numerical computation.
This syllabus is an outline for 46 class periods of Calculus II. An additional 10 class periods are available during the semester for presentations, group activities, quizzes, and reviews.
| Lesson | Section/Topic | Suggested Homework Problems |
| 1 | 6.1 Antiderivatives Graphically and Numerically | 1, 2, 4, 5, 7, 8, 9, 11, 13, 14, 16, 18, 22, 23, 24, 26 |
| 2 | 6.2 Constructing Antiderivatives Analytically | 1-52 |
| 3 | 6.2 (continued) | 53-63, 65, 66, 68, 69, 71, 72, 73, 76, 77, 84, 85 |
| 4 | 6.3 Differential Equations | 2, 4, 5, 6, 8, 9, 10, 11, 12, 14, 18, 19, 20, 21, 22, 24, 25, 27 |
| 5 | 6.4 Second Fundamental Theorem of Calculus | 1, 3, 5, 8, 9, 10, 13, 15, 16, 18, 19, 20, 21, 24 |
| 6 |
6.4 (continued) 6.5 The Equations of Motion |
26, 29, 33, 34, 36, 44 1, 2, 3, 4, 5, 6, 7, 11 |
| 7 | 7.1 Integration by Substitution | 2, 3, 5, 6, 10, 11, 14, 16, 17, 18, 19, 20, 22, 24, 26, 28, 31, 33 |
| 8 | 7.1 (continued) | 34, 36, 38, 39, 41, 45, 46, 48, 51, 53, 54, 56, 58, 60, 61 |
| 9 | 7.1 (continued) | 63, 65, 66, 67, 69, 70, 74, 75, 77, 83, 90, 92, 97, 100, 101, 102, 108, 109 |
| 10 | Exam 1 | Sections 6.1 - 6.5, 7.1 |
| 11 | 7.2 Integration by Parts | 2, 3, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 23, 24, 26, 30 |
| 12 | 7.2 (continued) | 31, 32, 33, 34, 37, 39, 41, 42, 46, 48, 49, 53, 54, 60, 61, 62 |
| 13 | 7.3 Tables of Integrals | 2, 4, 7, 8, 9, 10, 14, 19, 20, 23, 26, 29, 31, 32, 33, 34, 37, 38, 41, 42, 45, 47, 48, 53 |
| 14 | 7.4 Algebraic Identities and Trig. Substitutions | 2, 3, 5, 6, 9, 10, 13, 14, 15, 17, 19, 21, 23, 25, 27, 28, 32, 35, 36, 42, 43, 44, 46, |
| 15 | 7.4 (continued) | 47, 50, 53, 55, 56, 59, 61 |
| 16 | 7.5 Approximating Definite Integrals | 1, 2, 5, 6, 7, 9, 10, 12, 13, 15, 18, 20, 22, 23 |
| 17 | 7.6 Simpson's Rule | 1, 2, 4, 5 |
| 18 | 7.7 Improper Integrals | 1, 2, 4, 5, 6, 9, 10, 13, 15, 18, 21, 27, 33, 36, 38, 50 |
| 19 | 7.8 Comparison of Improper Integrals | 1, 4, 5, 8, 10, 11, 13, 14, 17 |
| 20 | 7.8 (continued) | 18, 22, 23, 29 |
| 21 | Exam 2 | Sections 7.2 - 7.8 |
| 22 | 8.1 Areas and Volumes | 1, 2, 4, 5, 7, 9, 10, 11, 12, 13, 15, 16, 19, 20, 21, 22, 27 |
| 23 | 8.2 Applications to Geometry | 2, 3, 5, 6, 9, 12, 14, 15, 16, 18, 19, 21, 23 |
| 24 | 8.2 (continued) | 25, 26, 29, 31, 32, 33, 34, 35, 39, 41, 54 |
| 25 | 8.3 Area and Arc Length in Polar Coordinates | 1-8, 11, 12, 13, 15, 17, 18, 21, 23, 24, 25, 28, 29, 39, 42 |
| 26 | 8.4 Density and Center of Mass | 1-5, 8, 9, 10, 19 |
| 27 | 8.4 (continued) | 12, 13, 20, 23, 25, 29 |
| 28 | 8.5 Applications to Physics | 1, 2, 3, 6, 7, 12 |
| 29 | 8.5 (continued) | 16, 17, 18, 22, 23, 24, 26, 28 |
| 30 | Exam 3 | Section 8.1 - 8.5 |
| 31 | 9.1 Sequences | 1, 2, 3, 5, 8, 10, 11, 14, 15, 17, 18, 19, 22, 25, 26, 27, 29, 30, 33 |
| 32 | 9.2 Geometric Series | 1, 2, 5, 7, 8, 10, 11, 13, 14, 16, 18, 21, 26, 27 |
| 33 | 9.3 Convergence of Series | 1, 2, 4, 5, 9, 10, 14, 19, 21, 23 |
| 34 |
9.3 (continued) 9.4 Tests for Convergence |
26, 27, 30, 33, 39, 44, 46 1, 3, 4, 5, 7, 10, 12, 14, 18, 19, 20, 21 |
| 35 | 9.4 (continued) | 24, 25, 28, 29, 30, 36, 38, 41, 43 |
| 36 | 9.4 (continued) | 54, 55, 58, 59, 60, 62, 64, 66, 73, 74 |
| 37 | 9.5 Power Series and Interval of Convergence | 1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 15, 18, 21, 22, 23 |
| 38 | 9.5 (continued) | 24, 25, 28, 29, 36, 38, 41 |
| 39 | Exam 4 | Sections 9.1 - 9.5 |
| 40 | 10.1 Taylor Polynomials | 1, 3, 8, 9, 11, 14, 16, 17, 19, 22, 25, 26, 32, 33 |
| 41 | 10.2 Taylor Series | 1, 3, 4, 5, 7, 9, 16, 18, 21, 24, 25, 30, 31 |
| 42 | 10.2 (continued) | 34, 35, 37, 39, 43 |
| 43 | 10.3 Finding and Using Taylor Series | 1, 2, 6, 7, 10, 11 |
| 44 | 10.3 (continued) | 14, 15, 16, 17, 28, 29 |
| 45 | 10.4 The Error in Taylor Polynomial Approx. | 1, 2, 3, 5, 7, 8, 10, 15, 16 |
| 46 | Exam 5 | Sections 10.1 - 10.4 |
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