﻿ 微積分統一教學網-模組15-17班

# 微積分統一教學網

## 模組15-17班

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 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