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微積分作業演算(二) Calculus Exercise II

課程綱要

  • 微積分作業演算(二) Calculus Exercise II

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.


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