微積分作業演算（二）

Abstract

課程首頁

本課程是由交通大學應用數學系、微積分教學小組提供。

課程目標/概述 本課程除了微分積分之方法與計算之外，學習重點在於基本數學觀念的理解。例如中間值定理、平均值定理、極值定理等。這些定理不僅本身有其基本應用的價值，背後也有它們數學的涵義與想法。瞭解這些想法，一方面可以推廣這些定理，另一方面當我們面臨更複雜的問題時，解決問題初步的試探可以以這些基本數學想法做為基礎或做為類比。這是數學做為一種科學思考的價值。 課程章節

章節

主題內容

第十一章 Infinite Sequences and Series

11.1 Sequences 11.2 Series 11.3 The Integral Test and Estimates of Sums 11.4 The Comparison Tests 11.5 Alternating Series 11.6 Absolute Convergence and the Ratio and Root Tests 11.8 Power Series 11.9 Representations of Functions as Power Series 11.10 Taylor and Maclaurin Series 11.11 Applications of Taylor Polynomials

第十二章 Vectors and the Geometry of Space

12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Equations of Lines and Planes

第十三章 Vector Functions

13.1 Vector Functions and Space Curves 13.2 Derivatives and Integrals of Vector Functions 13.3 Arc Length And Curvature

第十四章 Partial Derivatives

14.1 Functions of Several Variables 14.2 Limits and Continuity 14.3 Partial Derivatives 14.4 Tangent Plans and Differentials? 14.5 The Chain Rule 14.6 Directional Derivatives and the Gradient Vector 14.7 Maximum and Minimum Values 14.8 Lagrange Multipliers

第十五章 Multiple Integrals

15.1 Double Integrals over Rectangles 15.2 Iterated Integrals 15.3 Double Integrals over General Regions 15.4 Double Integrals in Polar Coordinates 15.5 Application of Double Integrals 15.6 Triple Integrals 15.7 Triple Integrals in Cylindrical Coordinates 15.8 Triple Integrals in Spherical Coordinates 15.9 Change of Variables in Multiple Integrals

課程書目 Calculus(Early Transcendental), James Stewart, 6th Edition.

授課對象：大學一年級學生

預備知識：高中數學 、微積分