交通大學開放式課程─微積分作業演算

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  

授課進度
第二章 Limits and derivatives
  2-4 The Precise Definition of a Limit
  2-5 Continuity
  2-6 Limits at Infinity; Horizontal Asymptotes
  2.7 Derivatives and Rates of Change
  2-8 Derivatives
第三章 Differentiation Rules
  3-1 Derivatives of Polynomials and Exponential Functions
  3-2 The Product and Quotient Rules
  3-3 Rates of Change in the Natural and Social Science
  3-4 Derivatives of Trigonometric Functions
  3-5 The Chain Rule
  3-6  Implicit Differentiation
  3-9  Related Rates
  3-10 Related Rates
第四章 The Properties of Gases
  4-1 Maximum and Minimum Values
  4-2 The Mean Value Theorem
  4-3  How Derivatives Affect the Shape of a Graph
  4-4  Indeterminate Forms a nd L’Hospital’s Rule
  4-5 Summary of Curve Sketching
  4-7 Optimization Problems
  4-9 Newtons Method
第五章 Integrals
  5-1 Areas and Distances
  5-2 The Definite Integral
  5-3 The Fundamental Theorem of Calculus
  5-4 Indefinite Integrals and the Total Change Theorem
  5-5 The Substitution Rule
第六章 Applications of Integration
  6-1 Areas between Curves
  6-2 Volumes
  6-3 Volumes be Cylindrical Shells
  6-5 Volumes be Cylindrical Shells
第七章 Techniques of Integration
  7-1 Integration by Parts
  7-2 Trigonometric Integrals
  7-3 Trigonometric Substitution
  7-4 Integration of Rational Functions by Partial Fractions
  7-8 Improper Integrals
第八章 Further Applications of Integration
  8-1 Arc Length
第十章 Parametric Equations and Polar Coordinates
  10-1 Curves Defined by Parametric Equations
  10-2 Calculus with Parametric Curves
  10-3 Polar Coordinates
  10-4 Areas and Lengths in Polar Coordinates

課程書目  

Calculus(Early Transendentals), James Stewart, 6th Edition

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