Calculus Exercise I
本課程是由交通大學應用數學系、微積分教學小組提供。
課程用書：Calculus (Early Transcendental), James Stewart, 6th EditionPublisher: Cengage Learning.
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| Instructor(s) | 微積分教學小組 |
|---|---|
| Course Credits | None |
| Academic Year | 97 Academic Year |
| Level | First Year of University |
| Prior Knowledge | High School Mathematics、Calculus |
| Related Resources | Course Video Course Syllabus |
| Week | Course Content | Course Video |
|---|---|---|
| 2-4 The Precise Definition of a Limit 題號：43 2-5 Continuity 題號：6,18 | Watch Online | |
| 2-5 Continuity 題號：34,39,44,45 | Watch Online | |
| 2-5 Continuity 題號：50,60 | Watch Online | |
| 2-5 Continuity 題號：60 2-6 Limits at Infinity; Horizontal Asymptotes 題號：4,7 | Watch Online | |
| 2-6 Limits at Infinity; Horizontal Asymptotes 題號：21,25,47,53 | Watch Online | |
| 2-6 Limits at Infinity; Horizontal Asymptotes 題號：57,65 2-7Derivatives and Rates of Change 題號：17,19 | Watch Online | |
| 2-7 Derivatives and Rates of Change 題號：22,28,29,35,38,45 | Watch Online | |
| 2-7 Derivatives and Rates of Change 題號：51 2-8 The Derivative as a Function 題號：3,10,14,25 | Watch Online | |
| 2-8 The Derivative as a Function 題號：36,50(a)(b) | Watch Online | |
| 2-8 The Derivative as a Function 題號：50(c) 3-1 Derivatives of Polynomials and Exponential Functions 題號：2(b)(c), 11,23,35,53 | Watch Online | |
| 3-1 Derivatives of Polynomials and Exponential Functions 題號：57,67,75 | Watch Online | |
| 3-2 The Product and Quotient Rules 題號：2,5,11, 19, 33, 43, 45,50(d),52 | Watch Online | |
| 3-3 Derivatives of Trigonometric Functions 題號：14,22, 34, 37,39,43 | Watch Online | |
| 3-4 The Chain Rule 題號：3,13,23,31,37,42 | Watch Online | |
| 3-4 The Chain Rule 題號：69,94 | Watch Online | |
| 3-5 Implicit Differentiation 題號：3,15,21,24,27,49 | Watch Online | |
| 3-5 Implicit Differentiation 題號：53,58 | Watch Online | |
| 3-5 Implicit Differentiation 題號：68 | Watch Online | |
| 3-6 Derivatives of Logarithmic Functions 題號：11,17, 24, 30,39,41,50 | Watch Online | |
| 3-6 Derivatives of Logarithmic Functions 題號：54 3-9 Related Rates 題號：7,13 | Watch Online | |
| 3-9 Related Rates 題號：19,23,33 | Watch Online | |
| 3-9 Related Rates 題號：41 3-10 Linear Approximations and Differentials 題號：3,16,23 | Watch Online | |
| 3-10 Linear Approximations and Differentials 題號：35 4-1 Maximum and Minimum Values 題號：3,4 | Watch Online | |
| 4-1 Maximum and Minimum Values 題號：5,6,9,27,39 | Watch Online | |
| 4-1 Maximum and Minimum Values 題號：39,41,49,54,70 | Watch Online | |
| 4-1 Maximum and Minimum Values 題號：75 4-2 The Mean Value Theorem 題號：5,12 | Watch Online | |
| 4-2 The Mean Value Theorem 題號：17,21 | Watch Online | |
| 4-2 The Mean Value Theorem 題號：23,25,31,35 | Watch Online | |
| 4-3 How Derivatives Affect the Shape of a Graph 題號：2,3,8 | Watch Online | |
| 4-3 How Derivatives Affect the Shape of a Graph 題號：12,13,19,23 | Watch Online | |
| 4-3 How Derivatives Affect the Shape of a Graph 題號：31,33,39,43,45 | Watch Online | |
| 4-3 How Derivatives Affect the Shape of a Graph 題號：67 | Watch Online | |
| 4-4 Indeterminate Forms a nd L'Hospital's Rule 題號：4,7, 15,27,39 | Watch Online | |
| 4-4 Indeterminate Forms a nd L'Hospital's Rule 題號：53, 57,63,71,73 | Watch Online | |
| 4-4 Indeterminate Forms a nd L'Hospital's Rule 題號：79, 83(a) | Watch Online | |
| 4-4 Indeterminate Forms a nd L'Hospital's Rule 題號：83(b) | Watch Online | |
| 4-5 Summary of Curve Sketching 題號：15,27,35,38,57 | Watch Online | |
| 4-5 SummaryofCurveSketching 題號：70 | Watch Online | |
| 4-7 OptimizationProblems 題號：9,13,17,21,24 | Watch Online | |
| 4-7 Optimization Problems 題號：44,52 | Watch Online | |
| 4-7 Optimization Problems 題號：65,67 | Watch Online | |
| 4-9 Antiderivatives 題號：63,65 | Watch Online | |
| 5-1 Areas and Distances 題號：3,11,15,19 | Watch Online | |
| 5-1 Areas and Distances 題號：21 5-2 The Definite Integral 題號：23 | Watch Online | |
| 5-2 The Definite Integral 題號：37,42,45,48,53,67 | Watch Online | |
| 5-3 The Fundamental Theorem of Calculus 題號：67,69 | Watch Online | |
| 5-3 The Fundamental Theorem of Calculus 題號：5,9,13,17,25,29 | Watch Online | |
| 5-3 The Fundamental Theorem of Calculus 題號：29,37,46,55,59,73 | Watch Online | |
| 5-4 Indefinite Integrals and the Total Change Theorem 題號：15,23,25,35,39,43,47,57 | Watch Online | |
| 5-4 Indefinite Integrals and the Total Change Theorem 題號：65 5-5 The Substitution Rule 題號：3,5,13,21 | Watch Online | |
| 5-5 The Substitution Rule 題號：39,59,67,75 | Watch Online | |
| 5-5 The Substitution Rule 題號：75 6-1 Areas between Curves 題號：3,9 | Watch Online | |
| 6-1 Areas between Curves 題號：23,29,32,49 | Watch Online | |
| 6-1 Areas between Curves 題號：53 | Watch Online | |
| 6-2 Volumes 題號：2,11,16,25,28,44 | Watch Online | |
| 6-2 Volumes 題號：51,53,57 | Watch Online | |
| 6-2 Volumes 題號：66 | Watch Online | |
| 6-3 Volumes be Cylindrical Shells 題號：13,15,19,23,32 | Watch Online | |
| 6-3 Volumes be Cylindrical Shells 題號：39,43 6-5 Average Value of a Function 題號：3,5,9,14 | Watch Online | |
| 7-1 Integration by Parts 題號：5,17 | Watch Online | |
| 7-1 Integration by Parts 題號：54,57,59,65 | Watch Online | |
| 7-2 Trigonometric Integrals 題號：7,13,35,41 | Watch Online | |
| 7-2 Trigonometric Integrals 題號：45,55,61,70 | Watch Online | |
| 7-3 Trigonometric Substitution 題號：2,6 | Watch Online | |
| 7-3 Trigonometric Substitution 題號：13,19 | Watch Online | |
| 7-3 Trigonometric Substitution 題號：25,34,41 | Watch Online | |
| 7-4 Integration of Rational Functions by Partial Fractions 題號：3,9,17,19 | Watch Online | |
| 7-4 Integration of Rational Functions by Partial Fractions 題號：28,35,41,47,51 | Watch Online | |
| 7-4 Integration of Rational Functions by Partial Fractions 題號：64 7-8 Improper Integrals 題號：1,9 | Watch Online | |
| 7-8 Improper Integrals 題號：11,19 | Watch Online | |
| 7-8 Improper Integrals 題號：59,61,75,77 | Watch Online | |
| 8-1 Arc Length 題號：4,7,13,23 | Watch Online | |
| 10-1 Curves Defined by Parametric Equations 題號：3,9,15,21 | Watch Online | |
| 10-1 Curves Defined by Parametric Equations 題號：44 10-2 Calculus with Parametric Curves | Watch Online | |
| 10-2 Calculus with Parametric Curves 題號：25,29,33 | Watch Online | |
| 10-2 Calculus with Parametric Curves 題號：43,57 | Watch Online | |
| 10-3 Polar Coordinates 題號：13,27,31,49,59 | Watch Online | |
| 10-3 Polar Coordinates 題號：63 10-4 Areas and Lengths in Polar Coordinates 題號：7,11,17,27,29,41,47 | Watch Online |
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/概述
| 章節 | 主題內容 |
| 第二章 Limits and derivatives | 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function |
| 第三章 Stochastic Integrals | 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 3.7 Rates of Change in the Natural and Social Sciences 3.9 Related Rates 3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions |
| 第四章 Applications of Differentiation | 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 and L’Hospital’s Rule 4.5 Summary of Curve Sketching 4.7 Optimization Problems 4.8 Newtons Method 4.9 Antiderivatives |
| 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 |
| 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 7.7 Approximate Integration 7.8 Improper Integrals |
| 第八章 Further Applications of Integration | 8.1 Further Applications of Integration 8.2 Area of a Surface of Revolution 8.3 Applications to Physics and Engineering 8.4 Applications to Economics and Biology 8.5 Probability |
| 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.
COURSE
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