| 章節 |
題號 |
| 1.1 |
Four Ways to Represent a Function |
4, 78 |
| 1.2 |
Mathematical Models: A Catalog of Essential Functions |
2, 4 |
| 1.3 |
New Functions from Old Functions |
4, 36, 54 |
| 1.4 |
Exponential Functions |
2, 20 |
| 1.5 |
Inverse Functions and Logarithms |
43, 56, 74, 77 |
| 2.2 |
The Limit of a Function |
4, 10, 16, 38, 42 |
| 2.3 |
Calculating Limits Using the Limit Laws |
2, 34, 42, 54 |
| 2.5 |
Continuity |
30, 44, 48, 58 |
| 2.6 |
Limits at Infinity; Horizontal Asymptotes |
30, 48, 58 |
| 3.1 |
Derivatives of Polynomials and Exponential Functions |
38, 86, 88 |
| 3.2 |
The Product and Quotient Rules |
44, 50, 54 |
| 3.3 |
Derivatives of Trigonometric Functions |
46, 60, 62 |
| 3.4 |
The Chain Rule |
46, 48, 69, 78 |
| 3.5 |
Implicit Differentiation |
44, 48, 65 |
| 3.6 |
Derivatives of Logarithmic and Inverse Trigonometric Functions |
36, 58, 78, 83, 85 |
| 3.10 |
Linear Approximations and Differentials |
34, 36, 52 |
| 4.1 |
Maximum and Minimum Values |
45, 60, 63, 66 |
| 4.2 |
The Mean Value Theorem |
23, 33 |
| 4.3 |
What Derivatives Tell Us about the Shape of a Graph |
55, 62, 64, 95 |
| 4.4 |
Indeterminate Forms and l'Hospital's Rule |
60, 69, 70, 76, 78 |
| 4.5 |
Summary of Curve Sketching |
11, 37, 54, 75 |
| 4.7 |
Optimization Problems |
47, 57, 79, 83 |
| 5.2 |
The Definite Integral |
57, 60, 61 |
| 5.3 |
The Fundamental Theorem of Calculus |
74, 76, 78, 93 |
| 5.4 |
Indefinite Integrals and the Net Change Theorem |
22, 54, 72 |
| 5.5 |
The Substitution Rule |
78, 80, 83, 94 |
| 7.1 |
Integration by Parts |
2, 42, 48, 60 |
| 7.2 |
Trigonometric Integrals |
14, 30, 56 |
| 7.3 |
Trigonometric Substitution |
20, 30, 45 |
| 7.4 |
Integration of Rational Functions by Partial Fractions |
27, 50, 58, 60 |
| 7.5 |
Strategy for Integration |
8, 27, 76 |
| 7.8 |
Improper Integrals |
68, 70, 92 |
| 9.1 |
Modeling with Differential Equations |
21, 25 |
| 9.3 |
Separable Equations |
16, 18, 54 |
| 9.5 |
Linear Equations |
24, 30, 41 |
| 11.2 |
Series |
15, 20, 48, 49 |
| 11.9 |
Representations of Functions as Power Series |
12, 15, 28 |
| 11.10 |
Taylor and Maclaurin Series |
8, 36, 59, 71, 92 |
| 12.5 |
Equations of Lines and Planes |
22, 36, 60, 64 |
| 12.6 |
Cylinders and Quadric Surfaces |
26, 30, 38, 48 |
| 14.1 |
Functions of Several Variables |
25, 32, 54 |
| 14.3 |
Partial Derivatives |
32, 44, 49, 62, 67 |
| 14.4 |
Tangent Planes and Linear Approximations |
9, 24 |
| 14.5 |
The Chain Rule |
3, 14, 38, 49 |
| 14.6 |
Directional Derivatives and the Gradient Vector |
12, 32, 51, 60 |
| 14.7 |
Maximum and Minimum Values |
20, 21, 39, 61 |
| 14.8 |
Lagrange Multipliers |
7, 10, 28, 57 |
| 6.1 |
Areas Between Curves |
18, 31, 42, 43 |
| 6.2 |
Volumes (✽WS) |
44, 62, 74, 86 |
| 15.1 |
Double Integrals over Rectangles |
22, 34, 54 |
| 15.2 |
Double Integrals over General Regions |
9, 21, 25, 64, 68 |
| 15.3 |
Double Integrals in Polar Coordinates |
13, 16, 32, 41 |
| 15.9 |
Change of Variables in Multiple Integrals |
20, 26, 28 |