﻿ 微積分統一教學網-模組11-14班

# 微積分統一教學網

## 模組11-14班

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 Stewart, Calculus: Early Transcendentals 第九版 章節 題號 1.5 Inverse Functions and Logarithms 74, 77, 78 2.1 The Tangent and Velocity Problems 3 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 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, 58 3.1 Derivatives of Polynomials and Exponential Functions 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, 66 3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions 36, 58, 78, 83, 85 3.8 Exponential Growth and Decay (✽) 22 3.1 Linear Approximations and Differentials 34, 36, 52 4.1 Maximum and Minimum Values 45, 60, 63, 66 4.2 The Mean Value Theorem 23, 35, 39 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 57, 65, 66 4.9 Antiderivatives 4, 12, 24, 52 5.1 The Area and Distance Problems 18, 22 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, 77 5.5 The Substitution Rule 78, 80, 83, 94 6.1 Areas Between Curves 18, 31, 43, 62 6.5 Average Value of a Function 13, 26 7.1 Integration by Parts 2, 42, 48, 60 7.2 Trigonometric Integrals 14, 32, 63 7.3 Trigonometric Substitution 30, 39, 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, 89 9.1 Modeling with Differential Equations 21, 25 9.3 Separable Equations 16, 18, 54 9.4 Models for Population Growth (✽) 9, 18, 21 9.5 Linear Equations 24, 30, 41 10.1 Curves Defined by Parametric Equations 15, 30, 49 10.2 Calculus with Parametric Curves 18, 31, 38, 40 10.3 Polar Coordinates 10, 18, 25 12.6 Cylinders and Quadric Surfaces 38, 48, 50 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 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 15.6 Triple Integrals 10, 26, 58 15.9 Change of Variables in Multiple Integrals 20, 26, 28 11.9 Representations of Functions as Power Series 12, 15, 28 11.1 Taylor and Maclaurin Series 36, 59, 71