﻿ 微積分統一教學網-模01-02班課程大綱

# 微積分統一教學網

## 模01-02班課程大綱

### 手機版選單

#### 字級

 微積分 1 第一週 2.1 The Tangent and Velocity Problems 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 第二週 2.4 The Precise Definition of a Limit 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 第三週 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function 第四週 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 第五週 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions 第六週 11/2(二)微積分1停修截止 3.9 Related Rates 3.10 Linear Approximations and Differentials 4.1 Maximum and Minimum Values 第七週 4.2 The Mean Value Theorem 4.3 What Derivatives Tell Us about the Shape of a Graph 4.4 Indeterminate Forms and l'Hospital's Rule 第八週 4.5 Summary of Curve Sketching 4.7 Optimization Problems 4.9 Antiderivatives 期考 11/13(六)  考試以英文命題 微積分 2 第九週 11/23(二) 微積分2退選截止 5.1 The Area and Distance Problems 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule 第十週 6.1 Areas Between Curves 6.2 Volume 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function 第十一週 12/7(二) 微積分2停修截止 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 第十二週 7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration 7.8 Improper Integrals 第十三週 8.1 Arc Length 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 第十四週 10.3 Polar Coordinates 10.4 Calculus in Polar Coordinates 9.1 Modeling with Differential Equations 第十五週 9.3 Separable Equations 9.5 Linear Equations 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 第十六週 Laplace Transform Laplace Transform 期考1/9(日) 考試以英文命題
 微積分 3 第一週 12.6 Cylinders and Quadric Surfaces 14.1 Functions of Several Variables 14.2 Limits and Continuity 第二週 14.3 Partial Derivatives 14.4 Tangent Planes and Linear Approximations 第三週 14.5 The Chain Rule 14.6 Directional Derivatives and the Gradient Vector 14.7 Maximum and Minimum Values 第四週 14.8 Lagrange Multipliers 15.1 Double Integrals over Rectangles 15.2 Double Integrals over General Regions 第五週 15.3 Double Integrals in Polar Coordinates 15.4 Applications of Double Integrals   (教到 Moments and Center of Mass) 第六週 3/25(五)微積分3停修截止 15.5 Surface Area 15.6 Triple Integrals 15.7 Triple Integrals in Cylindrical Coordinates 第七週 15.8 Triple Integrals in Spherical Coordinates 15.9 Change of Variables in Multiple Integrals 第八週 緩衝時間 期考 4/9(六) 考試以英文命題 微積分 4 第九週 4/15(五) 微積分4退選截止 16.1 Vector Fields 16.2 Line Integrals 16.3 The Fundamental Theorem for Line Integrals 第十週 16.4 Green's Theorem 16.5 Curl and Divergence 16.6 Parametric Surfaces and Their Areas 第十一週 4/29(五) 微積分4停修截止 16.7 Surface Integrals 16.8 Stokes' Theorem 16.9 The Divergence Theorem 第十二週 16.10 Summary 11.1 Sequences 11.2 Series 第十三週 11.3 The Integral Test and Estimates of Sums 11.4 The Comparison Tests 11.5 Alternating Series and Absolute Convergence 第十四週 11.6 The Ratio and Root Tests 11.7 Strategy for Testing Series 11.8 Power Series 第十五週 11.9 Representations of Functions as Power Series 11.10 Taylor and Maclaurin Series 11.11 Applications of Taylor Polynomials 第十六週 緩衝時間 期考 6/4(六) 考試以英文命題