Calculus I (English)
微積分(一) (英語授課)
This course is offered by the Department of Applied Mathematicsand provides a first introduction into the theory of differentiation and integration.
The course mainly serves as a bridge between highschool mathematics and university mathematics. Its main goal is to make students acquainted with rigorous mathematical thinking. This is done via learning basic concepts such as limits, continuity, differentiability, etc. on the one hand and fundamental theorems such as the intermediate value theorem, the extreme value theorem, the mean value theorem, etc. on the other hand.
Moreover, the course is intended to train students problem solving skills as well as writing and oral skills. Finally, the course equips students with the basic tools needed in the more applied sciences and is the entrance door to more advanced courses on mathematics.
(This course is taught in English.)
課程用書：Calculus (Early Transcendental), James Stewart, 6th EditionPublisher: Cengage Learning.
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| 授課教師 | 應用數學系 符麥克老師 |
|---|---|
| 課程學分 | 4學分 |
| 授課年度 | 96學年度 |
| 授課對象 | 大學一年級學生 |
| 預備知識 | 基礎數學 |
| 課程提供 | 課程影音 課程綱要 課程行事曆 課程作業 |
| 週次 | 課程內容 | 課程影音 | 課程下載 |
|---|---|---|---|
| Chapter1 Functions and Model 1-5 Exponential Functions 1-6 Inverse Functions and Logarithms | 線上觀看 | MP4下載 | |
| Chapter2 Limits and Derivatives 2-2 The Limit of a Function 2-4 The Precise Definition of a Limit | 線上觀看 | MP4下載 | |
| 2-3 Calculating Limits Using the Limit Laws 2-6 Limits at Infinity: Horizontal Asymptotes | 線上觀看 | MP4下載 | |
| 2-5 Continuity 2-6 Limits at Infinity; Horizontal Asymptotes | 線上觀看 | MP4下載 | |
| 2-8 Derivatives 2-9 The Derivative as a Function | 線上觀看 | MP4下載 | |
| Chapter3 Differentiation Rules 3-1 Derivatives of Polynomials and Exponential Functions 3-2 The Product and Quotient Rules | 線上觀看 | MP4下載 | |
| 3-4 Derivatives of Trigonometric Functions 3-5 The Chain Rule 3-6 Implicit Differentiation | 線上觀看 | MP4下載 | |
| 3-6 Implicit Differentiation | 線上觀看 | MP4下載 | |
| 3-8 Derivatives of Logarithmic Functions 3-10 Related Rates | 線上觀看 | MP4下載 | |
| 3-7 Higher Derivatives 3-11 Linear Approximations and Differentials Chapter4 Applications of Differation 4-1 Maximum and Minimum Values | 線上觀看 | MP4下載 | |
| 4-1 Maximum and Minimum Values | 線上觀看 | MP4下載 | |
| 4-2 The Mean Value Theorem 4-3 How Derivatives Affect the Shape of a Graph | 線上觀看 | MP4下載 | |
| 4-4 Indeterminate Forms a nd L’Hospital’s Rule | 線上觀看 | MP4下載 | |
| 4-7 Optimization Problems | 線上觀看 | MP4下載 | |
| 4-5 Summary of Curve Sketching 4-7 Optimization Problems | 線上觀看 | MP4下載 | |
| 4-7 Optimization Problems 4-10 Antiderivatives | 線上觀看 | MP4下載 | |
| Chapter5 Integrals 5-1 Areas and Distances 5-2 The Definite Integral | 線上觀看 | MP4下載 | |
| 5-2 The Definite Integral 5-3 The Fundamental Theorem of Calculus | 線上觀看 | MP4下載 | |
| 5-4 Indefinite Integrals and the Total Change Theorem 5-5 The Substitution Rule | 線上觀看 | MP4下載 | |
| 5-5 The Substitution Rule 5-6 The Logarithm Defined as an Integral Chapter6 Applications of Integration 6-1 Areas between Curves | 線上觀看 | MP4下載 | |
| 6-1 Areas between Curves 6-2 Volumes | 線上觀看 | MP4下載 | |
| 6-3 Volumes be Cylindrical Shells Chapter7 Techniques of Integration 7-1 Integration by Parts 7-2 Trigonometric Integrals | 線上觀看 | MP4下載 | |
| 7-2 Trigonometric Integrals 7-3 Trigonometric Substitution | 線上觀看 | MP4下載 | |
| 7-4 Integration of Rational Functions by Partial Fractions 7-8 Improper Integrals | 線上觀看 | MP4下載 | |
| 7-8 Improper Integrals | 線上觀看 | MP4下載 | |
| 7-7 Approximate Integration Chapter8 Further Applications of Integration 8-1 Arc Length | 線上觀看 | MP4下載 | |
| 8-1 Arc Length 8-2 Area of a Surface of Revolution | 線上觀看 | MP4下載 | |
| Chapter10 Parametric Equations and Polar Coordinates 10-1 Curves Defined by Parametric Equations 10-2 Calculus with Parametric Curves | 線上觀看 | MP4下載 | |
| 10-2 Calculus with Parametric Curves 10-3 Polar Coordinates 10-4 Areas and Lengths in Polar Coordinates | 線上觀看 | MP4下載 | |
| 10-3 Polar Coordinates 10-4 Areas and Lengths in Polar Coordinates | 線上觀看 | MP4下載 |
課程目標/概述
The lecture will closely follow the textbook.
課程章節/概述
| 章節 | 主題內容 |
| 第一章 | Functions and Model |
| 第二章 | Limits and Derivatives |
| 第三章 | Differentiation Rules |
| 第四章 | Applications of Differation |
| 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
W. Rudin: Principles of Mathematical Analysis.
評分標準
| Inclass homeworks are compulsory. Attendence at tutorials will not be checked. As to the regular class times, in case you do not attend send me an email prior to the class (no reason has to be provided). I will occassionally check attendence and students not attending for more than three times without informing me will automatically fail the course. |
| We will have assignments every week consisting of 4 problems from our textbook and 6 additional exercises announced at this webpage. Only the 6 additional exercises will be thoroughly graded. Exercises can either be solved individually or in a team. If you have formed a study group (maximum 5 people), handle the homework papers of all members in together in order to help us speeding up the correction work. Assignments must be handled in every Thursday before the inclass homework takes place (concerning handling in assignments late see below). The 4 problems will make up 2% of the score; the additional 6 problems will make up 18% of the score. |
| The weekly assignments will be completed by 2 exercises which have to be solved individually, in class, every Thursday from 10:10 - 10:40. You are allowed to use the textbook and other materials but not the homework paper. These problem classes are compulsory; if you are late you will only get the remaining time and in case you do not attend, the 2 additional exercises as well as the homework paper of the same week will be graded 0 (unless you have provided a very strong reason that apologies your absence). Every inclass homework will consist of one standard and one more complicated problem. 1/4th of the more complicated problems will not count. The inclass homework will make up 20% of your final score. |
| The weekly assignments will be discussed every Monday from 17:00 - 18:00 (and aftwards published online on this webpage). Although this class will not be compulsory, I nevertheless strongly advice all students to attend it in order to be able to improve your performance. Apart from discussing assignments, this time can also be used for asking questions related to the material relevant for the next homework or midterm/final. |
| The weekly assignments will be discussed every Monday from 17:00 - 18:00 (and aftwards published online on this webpage). Although this class will not be compulsory, I nevertheless strongly advice all students to attend it in order to be able to improve your performance. Apart from discussing assignments, this time can also be used for asking questions related to the material relevant for the next homework or midterm/final. |
| Handling homework papers in late is possible ("late" here means within a reasonable time tolerance). However, scores will be reduced as follows: first two times: no effect on the score; 3rd time: only 50% of the score; 4th time: only 25% of the full score; From 5th time on: no score. |
| The midterm test will take place on Thursday, November 8th, 2007 and will make up another 15% of your final score. |
| The final test will take place on Thursday, December 27th, 2007 and will make up the final 15% (the remaining 30% are coming from our departments final exam which has to be taken by all calculus students). |
| The final test will take place on Thursday, December 27th, 2007 and will make up the final 15% (the remaining 30% are coming from our departments final exam which has to be taken by all calculus students). |
本課程行事曆提供課程進度與考試資訊參考。
Below a brief and detailed schedule of the course.
- Thursday, September 13th, 2007: start of weekly assignments.
- Monday, September 17th, 2007: start of weekly tutorial.
- Thursday, September 20th, 2007: start of weekly inclass homework.
- Thursday, September 27th, 2007: no homework.
- Thursday, November 8th, 2007: midterm exam; no homework.
- Thursday, December 27th, 2007: final exam of the course, no homework.
- Thursday, January 3rd, 2007: make up homework and end of the course.
- Monday, January 7th, 2007: preparation for final exam of the university (optional).
- Saturday, January 12th, 2007: final exam of the university.
學期週次 | 上課日期 | 參考課程進度 |
第一週 | 2007/09/13 |
|
| 第二週 | 2007/09/17 |
|
| 2007/09/20 | ||
| 第三週 | 2007/09/27 |
|
| 第四週 | 2007/10/01 |
|
| 2007/10/04 | ||
| 第五週 | 2007/10/08 |
|
| 2007/10/11 | ||
| 第六週 | 2007/10/15 |
|
| 2007/10/18 | ||
| 第七週 | 2007/10/22 |
|
| 2007/10/25 | ||
| 第八週 | 2007/10/29 |
|
| 2007/11/01 | ||
| 第九週 | 2007/11/05 |
|
| 2007/11/08 | ||
| 第十週 | 2007/11/12 |
|
| 2007/11/15 | ||
| 第十一週 | 2007/11/19 |
|
| 2007/11/22 | ||
| 第十二週 | 2007/11/26 |
|
| 2007/11/29 | ||
| 第十三週 | 2007/12/03 |
|
| 2007/12/06 | ||
| 第十四週 | 2007/12/10 |
|
| 2007/12/13 | ||
| 第十五週 | 2007/12/17 |
|
| 2007/12/20 | ||
| 第十六週 | 2007/12/24 |
|
| 2007/12/27 | ||
| 第十七週 | 2007/12/31 |
|
| 2008/01/03 | ||
| 第十八週 | 2008/01/08 |
|
| 2008/01/14 |
課程作業 Course Homework
Problems | Additional Examples | Inclass Homework | Answers | |
| Homework 1 | Chapter 1.5：20； | Homework | Testpaper | Answer |
| Homework 2 | Chapter 2.3：47； Chapter 2.4：13,42； Chapter 2.6：53； | Homework | Testpaper | Answer |
| Homework 3 | Chapter 2.5：48； Chapter 2.8：29； Chapter 2.9：15,37； | Homework | Testpaper | Answer |
| Homework 4 | Chapter 3.1：48； Chapter 3.2：32,40； Chapter 3.4：10； | Homework | Testpaper | Answer |
| Homework 5 | Chapter 3.5：40； Chapter 3.8：37； Chapter 3.10：32； | Homework | Testpaper | Answer |
| Homework 6 | Chapter 3.1：43； Chapter 4.1：37； Chapter 4.2：20； | Homework | Answer | |
| Homework 7 | Chapter 4.4 ：62,77； Chapter 4.5：52； | Homework | Testpaper | Answer |
| Homework 8 | Chapter 4.7：42； Chapter 4.10：55； Chapter 5.1：14； | Homework | Testpaper | Answer |
| Homework 9 | Chapter 5.2：16； Chapter 5.3：62； Chapter 5.4：61； | Homework | Testpaper | Answer |
| Homework 10 | Chapter 5.6：3； Chapter 6.1：30； Chapter 6.2：61； | Homework | Testpaper | Answer |
| Homework 11 | Chapter 6.3：38； Chapter 7.1：33； Chapter 7.2：66； | Homework | Testpaper | Answer |
| Homework 12 | Chapter 7.3：13； Chapter 7.4：55,56； | Homework | Testpaper | Answer |
| Homework 13 | Chapter 8.1：34； Chapter 8.2：25； Chapter 10.1：24； | Homework |
課程專區
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