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
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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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