微積分（一）英文授課

Abstract

課程首頁 This course is offered by the Department of Applied Mathematics and 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.

課程目標/概述 The lecture will closely follow the textbook. 課程章節

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

評分標準

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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.

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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.

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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.

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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.

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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.

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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.

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The midterm test will take place on Thursday, November 8th, 2007 and will make up another 15% of your final score.

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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).

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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).

授課對象：Freshman

預備知識：Basic Mathematics