Calculus I - 99 Academic Year
本課程是由交通大學應用數學系提供。
本課程影片於99學年暑假課程錄製，配合99年上學期網路課程調整安排課程內容。
課程用書：Calculus (Early Transcendental), James Stewart, 6th EditionPublisher: Cengage Learning.
為求學習成效完美，請購買課本！
| Instructor(s) | Department of Applied Mathematics Prof. Chi-Kaung Pai |
|---|---|
| Course Credits | 4 Credits |
| Academic Year | 99 Academic Year |
| Level | First year university students |
| Prior Knowledge | High School Mathematics |
| Related Resources | Course Video Course Syllabus Course Calendar Maple Worksheet |
| Week | Course Content | Course Video |
|---|---|---|
| 課程介紹 | Watch Online | |
| Week 01 | 1.5 Exponential Functions | Watch Online |
| Week 01 | 1.6 Inverse Functions and Logarithms | Watch Online |
| Week 01 | 2.2 The Limit of a Function | Watch Online |
| Week 01 | 2.3 Calculating Limits Using the Limit Laws | Watch Online |
| Week 02 | The Concept of limit --- revisit | Watch Online |
| Week 02 | 2.4 The Precise Definition of a Limit | Watch Online |
| Week 03 | 2.5.1 Continuity | Watch Online |
| Week 03 | 2.5.2 Concept on limit and continuity | Watch Online |
| Week 03 | 2.6 Limits at Infinity: Horizontal Asymptotes | Watch Online |
| Week 04 | 2.7 The Derivative of a Function | Watch Online |
| Week 04 | 2.7.1 Derivatives and the Tangent Lines | Watch Online |
| Week 04 | 3.10 Linear Approximations and Differentials | Watch Online |
| Week 04 | 3.2 The Product and Quotient Rules | Watch Online |
| Week 04 | 3.1 Derivatives of Polynomials and Exponential Functions 3.3 Derivatives of Trigonometric Functions | Watch Online |
| Week 05 | Revisit on differentiability | Watch Online |
| Week 05 | 3.4 The Chain Rule | Watch Online |
| Week 06 | 3.5 Implicit Differentiation | Watch Online |
| Week 06 | 3.5 (Continue) Derivatives of Inverse trigonometric Functions 3.6 Derivatives of Logarithmic Functions | Watch Online |
| Week 06 | 3.9 Related Rates | Watch Online |
| Week 07 | 4.1 Maximum and Minimum Values | Watch Online |
| Week 07 | 4.2 The Mean Value Theorem | Watch Online |
| Week 08 | 4.3 How Derivatives Affect the Shape of a Graph | Watch Online |
| Week 08 | 4.4-1 Indeterminate Forms and L’Hospital’s Rule | Watch Online |
| Week 08 | 4.4-2 Indeterminate Forms and L’Hospital’s Rule | Watch Online |
| Week 09 | 4.9 Antiderivatives | Watch Online |
| Week 10 | 5.1 Areas and Distances | Watch Online |
| Week 10 | 5.2 The Definite Integral | Watch Online |
| Week 10 | 5.3 The Fundamental Theorem of Calculus | Watch Online |
| Week 10 | 5.4 Indefinite Integrals and the Total Change Theorem | Watch Online |
| Week 11 | 5.5 The Substitution Rule | Watch Online |
| Week 11 | 6.1 Areas between Curves | Watch Online |
| Week 11 | 補充 :Logarithm Defined as an integral | Watch Online |
| Week 12 | 6.2 Volumes | Watch Online |
| Week 12 | 6.3 Volumes by Cylindrical Shells | Watch Online |
| Week 12 | 6.5 Average Value of a Function | Watch Online |
| Week 12 | 7.1 Integration by Parts | Watch Online |
| Week 12 | 7.2 Trigonometric Integrals | Watch Online |
| Week 13 | 7.3 Trigonometric Substitution | Watch Online |
| Week 13 | 7.4 Integration of Rational Functions by Partial Fractions | Watch Online |
| Week 14 | 7.7 Approximate Integration | Watch Online |
| Week 14 | 7.8 Improper Integrals | Watch Online |
| Week 14 | 8.1 Arc Length | Watch Online |
| Week 14 | 8.2 Area of a Surface of Revolution | Watch Online |
| Week 15 | 10.3 Polar Coordinates | Watch Online |
| Week 15 | 10.1 Curves Defined by Parametric Equations | Watch Online |
| Week 16 | 10.2 Calculus with Parametric Curves | Watch Online |
| Week 16 | 10.4 Areas and Lengths in Polar Coordinates (I) | Watch Online |
| Week 16 | 10.4 Areas and Lengths in Polar Coordinates (II) | Watch Online |
課程目標
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 |
| 第一章 Functions and Model | 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms |
| 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 6.2 Volumes 6.3 Volumes be Cylindrical Shells 6.5 Average Value of a Function |
| 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.
評分標準
| 項目 | 百分比 |
| Practice Quizes | 5% |
| 學習歷程檔案 & 討論區 | 5% |
| 小考 | 40% |
| 期中考 | 20% |
| 期末考 | 30% |
本課程行事曆提供課程進度與考試資訊參考。
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學期週次 |
上課日期 |
參考課程進度 |
| 第一週 | 09/12-09/18 |
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| 第二週 | 09/19-09/25 |
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| 第三週 | 09/26-10/02 |
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| 第四週 | 10/03-10/09 |
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| 第五週 | 10/10-10/16 |
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| 第六週 | 10/17-10/23 |
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| 第七週 | 10/24-10/30 |
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| 第八週 | 10/31-11/06 |
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| 第九週 | 11/07-11/13 |
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| 第十週 | 11/14-11/20 |
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| 第十一週 | 11/21-11/27 |
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| 第十二週 | 11/28-12/04 |
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| 第十三週 | 12/05-12/11 |
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| 第十四週 | 12/12-12/18 |
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| 第十五週 | 12/19-12/25 |
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| 第十六週 | 12/26-01/01 |
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| 第十七週 | 01/02-01/08 |
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| 第十八週 | 01/09-01/15 |
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請依照您電腦的版本下載 Maple Player Download Maple Player
章節 | 章節內容 | Maple下載 |
| 1.5 | Exponential Functions | worksheet |
| What is √2 ? | worksheet | |
| 1.6 | Inverse Functions | worksheet |
| 2.2 | Limits | worksheet |
| 2.3 | Limit Laws | worksheet |
| 2.4 | The Precise Definition of a Limit | worksheet |
| 2.5 | Couninuity | worksheet |
| 2.6 | Asymptotes | worksheet |
| 2.8，2.9 | Tangent Lines and Definition of the Derivative | worksheet |
| The Derivatives and Tangent Lines | worksheet | |
| 3.1，3.2 | Continuous Functions that Fail to Be Differentiable | worksheet |
| 3.8，3.10 | Derivatives of Inverse Functions | worksheet |
| 4.1 | Maximum and Minimum Values | worksheet |
| 4.2 | The Mean Value Theorem | worksheet |
| 4.3 | How Derivatives Affect the Shape of a Graph? | worksheet |
| 4.4 | L’Hospital’s Rule | worksheet |
| 4.10 | Antiderivatives | worksheet |
| 6.2 | Volumes by Cross Sections? | worksheet |
| 6.3 | Volumes by Cylindrical Shells | worksheet |
| 10.1 | Graphic Design | worksheet |
| Bezier Curves | worksheet | |
| 10.3 | Polar Coordinates and Polar Curves | worksheet |
| 10.4 | Area in Polar Coordinates | worksheet |
COURSE
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