After each lecture, you are expected to complete the problems associated with the lecture. You should:
|
Lesson number |
Topic | Section | Problems |
| 1 | Vectors in the Plane | 13.1: Vectors in the Plane | 17, 19, 20, 26, 28, 30, 44, 57, 61, 63 |
| 2 | Vectors in three dimensions | 13.2: Vectors in Three Dimensions | 9, 15, 19, 21, 23, 27, 32, 35, 41, 47, 51, 63, 73, 74 |
| 3 | Dot products | 13.3: Dot Products | 3, 15, 19, 25, 31, 37, 41, 55, 56, 65, 77, 83 |
| 4 | Cross products | 13.4: Cross Products | 2, 15, 23, 30, 35, 41, 52, 53, 59, 63 |
| 5 | Regions between curves | 6.2: Regions Between Curves | 1, 3, 4, 10, 15, 19, 27, 32, 39, 43, 63 |
| 6 | Volumes by slicing | 6.3: Volume by Slicing | 3, 13, 15, 19, 23, 37, 45, 49, 55, 66, 70 |
| 7 | Volumes by shells | 6.4: Volume by Shells | 1, 2, 3, 13, 15, 18, 21, 39, 43, 45, 55, 63 |
| 8 | Arc length and surface area |
6.5: Length of Curves 6.6: Surface Area |
(6.5) 1, 13, 17, 35, 36, 39 (6.6) 2, 3, 9, 11, 18, 20, 33, 39 |
| 9 | Physical applications, Part I | 6.7: Physical Applications | 1, 3, 13, 19, 22, 23, 25, 29, 31 |
| 10 | Physical applications, Part II | 6.7: Physical Applications | 5, 8, 36, 39, 43, 45, 47, 52, 55 |
| 11 | Integration techniques and integration by parts |
5.5: Substitution Rule 8.1: Basic Approaches 8.2: Integration by Parts |
(5.5) 55 (8.1) 1, 7 , 11, 12 (8.2) 1, 6, 10, 13, 24, 26, 27, 34, 36, 59, 63 |
| 12 | Trigonometric integrals, Part I |
8.1: Basic Approaches 8.3: Trigonometric Integrals |
(8.1) 56 (8.3) 1, 9, 13, 15, 20, 22, 24, 58 |
| 13 | Trigonometric integrals, Part II | 8.3: Trigonometric Integrals | 30, 35, 39, 42, 53, 56 |
| 14 | Trigonometric substitution, Part I | 8.4: Trigonometric Substitutions | 1, 2, 3, 7, 11, 16, 25, 27, 41, 58 |
| 15 | Trigonometric substitution, Part II | 8.4: Trigonometric Substitutions | 19, 22, 26, 29, 32, 54, 57, 63, 67, 68, 83 |
| 16 | Partial fractions decompositions, Part I | 8.5: Partial Fractions | 1, 5, 17, 20, 25, 29, 35, 39, 45, 46, 67 |
| 17 | Partial fractions decompositions, Part II |
8.5: Partial Fractions 8.6: Integration Strategies |
(8.5) 3, 10, 12, 34, 49, 50, 51, 52, 56, 58, 61, 77, 84 No problems are assigned from Section 8.6, but you should read this section because it summarizes all of the techniques we have learned. If you need extra practice with integration and help deciding which technique you should use to approach an integral, trying some of the problems at the end of this section would give you good practice. |
| 18 | Improper Integrals | 8.9: Improper Integrals | 1, 6, 7, 9, 12, 15, 19, 21, 28, 41, 53, 64, 94 |
| 19 | Sequences and series overview | 10.1: An Overview | 1, 2, 3, 10, 12, 13, 19, 24, 28, 31, 35, 41,61, 67, 69 |
| 20 | Sequences | 10.2: Sequences | 5, 10, 13, 22, 33, 35, 39, 43, 51, 54, 61, 70, 76, 82, 108 |
| 21 | Infinite series | 10.3: Infinite Series | 5, 6, 7, 32, 39, 50, 57, 65, 69, 83, 87, 111 |
| 22 | Divergence Test and Integral Test | 10.4: The Divergence and Integral Tests | 3, 4, 10, 12, 13, 17, 21, 22, 26, 28, 33, 53, 55, 69 |
| 23 | Comparison Tests | 10.5: Comparison Tests | 1, 3, 5, 9, 11, 13, 14, 22, 29, 51, 54, 59, 64 |
| 24 | Alternating series | 10.6: Alternating Series | 7, 11, 15, 16, 23, 34, 36, 37, 39, 45, 64 |
| 25 | Ratio Test and Root Test | 10.7: The Ratio and Root Tests | 8, 10, 18, 23, 28, 34, 36, 43, 46, 54, 60, 61 |
| 26 | Choosing a convergence test | 10.8: Choosing a Convergence Test | 11, 18, 23, 25, 27, 33, 37, 41, 43, 47, 53, 59, 79, 83, 88 (The next two problems are only available in the e-book at the end of the section. They are not available as randomized problems in MyLab) 56, 62 |
| 27 | Approximating functions with polynomials, Part I |
4.6: Linear Approximation and Differentials 11.1: Approximating Functions with Polynomials |
(4.6) 3, 19 (11.1) 1, 3, 5, 14, 18, 19, 25, 29, 31, 83 |
| 28 | Approximating functions with polynomials, Part II | 11.1: Approximating Functions with Polynomials | 41, 43, 45, 46, 48, 50, 51, 52, 57, 61 |
| 29 | Power series, Part I | 11.2: Properties of Power Series | 3, 7, 9, 11, 13, 29, 37, 41, 44, 59 |
| 30 | Power series, Part II | 11.2: Properties of Power Series | 5, 47, 49, 51, 54, 55, 61, 63, 64, 66, 70, 72, 74 |
| 31 | Taylor series | 11.3: Taylor Series | 1, 2, 3, 7, 11, 16, 27, 29, 31, 39, 65, 66 |
| 32 | Working with Taylor series | 11.4: Working with Taylor Series | 7, 17, 22, 25, 28, 37, 38, 49, 52, 56, 59, 61, 75, 78 |
| 33 | Polar coordinates, Part I |
1.4: Trigonometric Functions and Their Inverses 12.2: Polar Coordinates |
(1.4) 19, 20 (12.2) 1, 11, 14, 27, 29, 33, 37, 41, 48, 51, 53 |
| 34 | Polar coordinates, Part II | 12.2: Polar Coordinates | 7, 15, 19, 54, 56, 61, 63, 65, 67, 91, 96, 99, 109 |
| 35 | Area and length in polar coordinates | 12.3: Calculus in Polar Coordinates | 7, 45, 47, 49, 56, 65, 67, 74 |