Calculus I - 95 Academic Year
本課程是由 國立陽明交通大學應用數學系提供。
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。
Textbook：
Calculus (Early Transcendental), James Stewart, 5th EditionPublisher: Cengage Learning
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| Instructor(s) | Department of Applied Mathematics Prof. Jonq Juang |
|---|---|
| Course Credits | 4 Credits |
| Academic Year | 95 Academic Year |
| Level | Freshman |
| Prior Knowledge | High School Math |
| Related Resources | Course Video Course Syllabus Course Calendar Course Test |
| Week | Course Content | Course Video |
|---|---|---|
| 第一章 Functions and Model 1.5 Exponential Functions | Watch Online | |
| 1.6 Inverse Functions and Logarithms | Watch Online | |
| 第二章 Limits and derivatives 2.2 The Limit of a Function | Watch Online | |
| 2.3 Calculating Limits Using the Limit Laws | Watch Online | |
| 2.4 The Precise Definition of a Limit | Watch Online | |
| 2.5 Continuity | Watch Online | |
| 2.6 Limits at Infinity, Horizontal Asymptotes | Watch Online | |
| 2.8 Derivatives | Watch Online | |
| 2.9 The Derivative as a Function | Watch Online | |
| 第三章 Differentiation Rules 3.1 Derivatives of Polynomials and Exponential Functions | Watch Online | |
| 3.2 The Product and Quotient Rules | Watch Online | |
| 3.4 Derivatives of Trigonometric Functions | Watch Online | |
| 3.5 The Chain Rule | Watch Online | |
| 3.6 Implicit Differentiation | Watch Online | |
| 3.7 Higher Derivatives | Watch Online | |
| 3.8 Derivatives of Logarithmic Functions | Watch Online | |
| 3.10 Related Rates | Watch Online | |
| 3.11 Linear Approximations and Differentials | Watch Online | |
| 第四章 The Properties of Gases 4.1 Maximum and Minimum Values | Watch Online | |
| 4.2 The Mean Value Theorem | Watch Online | |
| 4.3 How Derivatives Affect the Shape of a Graph 4.5 Summary of Curve Sketching | Watch Online | |
| 4.4 Indeterminate Forms a nd L’Hospital’s Rule | Watch Online | |
| 4.7 Optimization Problems | Watch Online | |
| 4.10 Antiderivatives | Watch Online | |
| 第五章 Integrals 5.1 Areas and Distances | Watch Online | |
| 5.2 The Definite Integral | Watch Online | |
| 5.3 The Fundamental Theorem of Calculus | Watch Online | |
| 5.4 Indefinite Integrals and the Total Change Theorem | Watch Online | |
| 5.5 The Substitution Rule | Watch Online | |
| 5.6 The Logarithm Defined as an Integral | Watch Online | |
| 第六章 Applications of Integration 6.1 Areas between Curves | Watch Online | |
| 6.2 Volumes | Watch Online | |
| 第七章 Techniques of Integration 7.1 Integration by Parts | Watch Online | |
| 7.2 Trigonometric Integrals | Watch Online | |
| 7.3 Trigonometric Substitution | Watch Online | |
| 7.4 Integration of Rational Functions by Partial Fractions | Watch Online | |
| 7.7 Approximate Integration | Watch Online | |
| 7.8 Improper Integrals | Watch Online | |
| 第八章 Further Applications of Integration 8.1 Arc Length | Watch Online | |
| 8.2 Area of a Surface of Revolution | Watch Online | |
| 8.3 Applications to Physics and Engineering | Watch Online | |
| 第十章 Parametric Equations and Polar Coordinates 10.1 Curves Defined by Parametric Equations | Watch Online | |
| 10.2 Calculus with Parametric Curves | Watch Online | |
| 10.3 Polar Coordinates | Watch Online | |
| 10.4 Areas and Lengths in Polar Coordinates | Watch Online | |
| 重點回顧 | 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 | 章節內容 |
| 第一章 | Functions and Model |
| 第二章 | Limits and derivatives |
| 第三章 | Differentiation Rules |
| 第四章 | The Properties of Gases |
| 第五章 | Integrals |
| 第六章 | Applications of Integration |
| 第七章 | Techniques of Integration |
| 第八章 | Further Applications of Integration |
| 第十章 | Parametric Equations and Polar Coordinates |
課程書目
Calculus (Early Transcendental), James Stewart, 5th Edition.
評分標準
| 項目 | 百分比 |
| 期中考 | 20% |
| 期末考 | 30% |
| 小考 | 50% |
本課程行事曆提供課程進度與考試資訊參考。
學期週次 | 上課日期 | 參考課程進度 |
第一週 | 09/18, 09/24 |
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| 第二週 | 09/18, 09/24 |
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| 第三週 | 09/25, 10/01 |
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| 第四週 | 10/02, 10/08 |
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| 第五週 | 10/09, 10/15 |
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| 第六週 | 10/16, 10/22 |
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| 第七週 | 10/23, 10/29 |
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| 第八週 | 10/30, 11/05 |
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| 第九週 | 11/06, 11/12 |
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| 第十週 | 11/13, 11/19 |
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| 第十一週 | 11/20, 11/26 |
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| 第十二週 | 11/27, 12/03 |
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| 第十三週 | 12/04, 12/10 |
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| 第十四週 | 12/11, 12/17 |
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| 第十五週 | 12/18, 12/24 |
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| 第十六週 | 12/25, 12/31 |
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| 第十七週 | 01/01, 01/07 |
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| 第十八週 | 01/08, 01/14 |
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COURSE
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