Calculus I - 99 Academic Year
微積分(一) - 99學年度
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！
| 授課教師 | 應用數學系 白啟光老師 |
|---|---|
| 課程學分 | 4學分 |
| 授課年度 | 99學年度 |
| 授課對象 | 大學一年級學生 |
| 預備知識 | 高中數學 |
| 課程提供 | 課程影音 課程綱要 課程行事曆 Maple Worksheet |
| 週次 | 課程內容 | 課程影音 |
|---|---|---|
| 課程介紹 | 線上觀看 | |
| 第一週 | 1.5 Exponential Functions | 線上觀看 |
| 第一週 | 1.6 Inverse Functions and Logarithms | 線上觀看 |
| 第一週 | 2.2 The Limit of a Function | 線上觀看 |
| 第一週 | 2.3 Calculating Limits Using the Limit Laws | 線上觀看 |
| 第二週 | The Concept of limit --- revisit | 線上觀看 |
| 第二週 | 2.4 The Precise Definition of a Limit | 線上觀看 |
| 第三週 | 2.5.1 Continuity | 線上觀看 |
| 第三週 | 2.5.2 Concept on limit and continuity | 線上觀看 |
| 第三週 | 2.6 Limits at Infinity: Horizontal Asymptotes | 線上觀看 |
| 第四週 | 2.7 The Derivative of a Function | 線上觀看 |
| 第四週 | 2.7.1 Derivatives and the Tangent Lines | 線上觀看 |
| 第四週 | 3.10 Linear Approximations and Differentials | 線上觀看 |
| 第四週 | 3.2 The Product and Quotient Rules | 線上觀看 |
| 第四週 | 3.1 Derivatives of Polynomials and Exponential Functions 3.3 Derivatives of Trigonometric Functions | 線上觀看 |
| 第五週 | Revisit on differentiability | 線上觀看 |
| 第五週 | 3.4 The Chain Rule | 線上觀看 |
| 第六週 | 3.5 Implicit Differentiation | 線上觀看 |
| 第六週 | 3.5 (Continue) Derivatives of Inverse trigonometric Functions 3.6 Derivatives of Logarithmic Functions | 線上觀看 |
| 第六週 | 3.9 Related Rates | 線上觀看 |
| 第七週 | 4.1 Maximum and Minimum Values | 線上觀看 |
| 第七週 | 4.2 The Mean Value Theorem | 線上觀看 |
| 第八週 | 4.3 How Derivatives Affect the Shape of a Graph | 線上觀看 |
| 第八週 | 4.4-1 Indeterminate Forms and L’Hospital’s Rule | 線上觀看 |
| 第八週 | 4.4-2 Indeterminate Forms and L’Hospital’s Rule | 線上觀看 |
| 第九週 | 4.9 Antiderivatives | 線上觀看 |
| 第十週 | 5.1 Areas and Distances | 線上觀看 |
| 第十週 | 5.2 The Definite Integral | 線上觀看 |
| 第十週 | 5.3 The Fundamental Theorem of Calculus | 線上觀看 |
| 第十週 | 5.4 Indefinite Integrals and the Total Change Theorem | 線上觀看 |
| 第十一週 | 5.5 The Substitution Rule | 線上觀看 |
| 第十一週 | 6.1 Areas between Curves | 線上觀看 |
| 第十一週 | 補充 :Logarithm Defined as an integral | 線上觀看 |
| 第十二週 | 6.2 Volumes | 線上觀看 |
| 第十二週 | 6.3 Volumes by Cylindrical Shells | 線上觀看 |
| 第十二週 | 6.5 Average Value of a Function | 線上觀看 |
| 第十二週 | 7.1 Integration by Parts | 線上觀看 |
| 第十二週 | 7.2 Trigonometric Integrals | 線上觀看 |
| 第十三週 | 7.3 Trigonometric Substitution | 線上觀看 |
| 第十三週 | 7.4 Integration of Rational Functions by Partial Fractions | 線上觀看 |
| 第十四週 | 7.7 Approximate Integration | 線上觀看 |
| 第十四週 | 7.8 Improper Integrals | 線上觀看 |
| 第十四週 | 8.1 Arc Length | 線上觀看 |
| 第十四週 | 8.2 Area of a Surface of Revolution | 線上觀看 |
| 第十五週 | 10.3 Polar Coordinates | 線上觀看 |
| 第十五週 | 10.1 Curves Defined by Parametric Equations | 線上觀看 |
| 第十六週 | 10.2 Calculus with Parametric Curves | 線上觀看 |
| 第十六週 | 10.4 Areas and Lengths in Polar Coordinates (I) | 線上觀看 |
| 第十六週 | 10.4 Areas and Lengths in Polar Coordinates (II) | 線上觀看 |
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 |
課程專區
選單
