﻿ 微積分統一教學網-模組01-09班

# 微積分統一教學網

## 模組01-09班

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 Stewart, Calculus: Early Transcendentals 第九版 章節 題號 1.5 Inverse Functions and Logarithms(✽WS) 74, 77, 78 2.1 The Tangent and Velocity Problems 3, 6 2.2 The Limit of a Function 4, 10, 16, 38,  42 2.3 Calculating Limits Using the Limit Laws 2,  34, 42, 54, 57 2.5 Continuity 30, 44, 48, 58, 74 2.6 Limits at Infinity; Horizontal Asymptotes 30, 48, 58 2.7 Derivatives and Rates of Change 34, 36, 58 2.8 The Derivative as a Function 40, 44, 52, 63 3.1 Derivatives of Polynomials and Exponential Functions 86, 88, 90 3.2 The Product and Quotient Rules 44, 50, 58 3.3 Derivatives of Trigonometric Functions 46, 60, 62, 66 3.4 The Chain Rule 46, 48, 69, 78, 99 3.5 Implicit Differentiation 44, 48, 65, 66, 67 3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions 36, 58, 78, 83, 85 3.9 Related Rates (✽WS) 23, 29, 30, 44, 53 3.10 Linear Approximations and Differentials 36, 48, 52 4.1 Maximum and Minimum Values 45, 60, 63, 66 4.2 The Mean Value Theorem 23, 28, 35, 39, 42 4.3 What Derivatives Tell Us about the Shape of a Graph 55, 62, 64, 84, 99 4.4 Indeterminate Forms and l'Hospital's Rule 60, 69, 76, 78, 90 4.5 Summary of Curve Sketching 11, 37, 54, 56, 75 4.7 Optimization Problems 47, 57, 77, 83 4.9 Antiderivatives 4, 12, 24, 52 5.1 The Area and Distance Problems 18, 22, 34 5.2 The Definite Integral 23, 57, 60, 68 5.3 The Fundamental Theorem of Calculus 68, 74, 76, 78, 93 5.4 Indefinite Integrals and the Net Change Theorem 22, 54, 72 5.5 The Substitution Rule 80, 83, 94, 98, 99 6.1 Areas Between Curves 18, 31, 42, 43 6.2 Volumes (✽WS) 44, 62, 74, 86 6.3 Volumes by Cylindrical Shells (✽WS) 47, 55, 56, 62 6.5 Average Value of a Function 13, 25, 26 7.1 Integration by Parts 2, 48, 60, 78 7.2 Trigonometric Integrals 32, 56, 63, 71 7.3 Trigonometric Substitution 30, 45, 47, 49 7.4 Integration of Rational Functions by Partial Fractions 27, 50, 58, 60 7.5 Strategy for Integration 8, 27, 44, 76, 93 7.8 Improper Integrals 68, 74, 75, 80 8.1 Arc Length(✽WS) 39, 40, 43, 46 9.1 Modeling with Differential Equations 21, 25, 29 9.3 Separable Equations 42, 44, 48, 54 9.4 Models for Population Growth (✽) 9, 18, 21 9.5 Linear Equations 30, 39, 41 10.1 Curves Defined by Parametric Equations 30, 49, 53 10.2 Calculus with Parametric Curves 18, 31, 38, 50 10.3 Polar Coordinates 36, 54, 58 10.4 Calculus in Polar Coordinates 10, 28, 45, 68 12.6 Cylinders and Quadric Surfaces 38, 48, 50 14.1 Functions of Several Variables 30, 32, 54 14.2 Limits and Continuity 17, 23, 33, 52 14.3 Partial Derivatives 32, 44, 62, 67 14.4 Tangent Planes and Linear Approximations 9, 20, 52, 54 14.5 The Chain Rule 14, 38, 49, 52, 59 14.6 Directional Derivatives and the Gradient Vector 17, 32, 51, 57, 60 14.7 Maximum and Minimum Values 21, 39, 55, 61 14.8 Lagrange Multipliers 10, 28, 57, 58(b) 15.1 Double Integrals over Rectangles 22, 34, 54 15.2 Double Integrals over General Regions 22, 28, 62, 64, 68 15.3 Double Integrals in Polar Coordinates 16, 20, 32, 41 15.4 Applications of Double Integrals(✽WS) 8, 13, 18 15.6 Triple Integrals 10, 26, 38, 42, 58 15.7 Triple Integrals in Cylindrical Coordinates 11, 16, 22, 30 15.8 Triple Integrals in Spherical Coordinates 10, 21, 28, 30 15.9 Change of Variables in Multiple Integrals 20, 24, 26, 31 16.1 Vector Fields 14, 21, 27 16.2 Line Integrals 12, 36, 49, 52 16.3 The Fundamental Theorem for Line Integrals 22, 41, 42 16.4 Green's Theorem 10, 18, 25, 31 16.5 Curl and Divergence 33, 35, 39, 40 16.6 Parametric Surfaces and Their Areas 42, 62, 63, 64(a)(c) 16.7 Surface Integrals 14, 30, 44 16.8 Stokes' Theorem 10, 14, 20, 22 16.9 The Divergence Theorem 12, 14, 20, 26 11.1 Sequences 85, 89, 97, 98 11.2 Series 52, 69, 92, 95 11.3 The Integral Test and Estimates of Sums 32, 42, 46 11.4 The Comparison Tests 46, 52, 53, 55 11.5 Alternating Series and Absolute Convergence 18, 49, 50, 53 11.6 The Ratio and Root Tests 34, 36, 38, 42 11.7 Strategy for Testing Series 45, 47, 48 11.8 Power Series 36, 38, 40, 44, 46 11.9 Representations of Functions as Power Series 12, 15, 28, 40 11.10 Taylor and Maclaurin Series 59, 71, 75, 97 11.11 Applications of Taylor Polynomials 33, 37, Review 60 (p.823) 17.1 Second-Order Linear Equations 4, 5, 10, 34 17.2 Nonhomogeneous Linear Equations Review 7, 8, 21 (pp.1221, 1222)