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Calculus II (English)

微積分(二) (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.
為求學習成效完美，請購買課本！

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
Chapter11 Functions and Model
11-1 Sequences		線上觀看MP4下載
11-2 Series
11-3 The Integral Test and Estimates of Sums
11-4 The Comparison Tests		線上觀看MP4下載
11-4 The Comparison Tests
11-5 Alternating Series		線上觀看MP4下載
11-6 Absolute Convergence and the Ratio and Root Tests
11-8 Power Series		線上觀看MP4下載
11-9 Representations of Functions as Power Series
11-10 Taylor and Maclaurin Series		線上觀看MP4下載
11-10 Taylor and Maclaurin Series線上觀看MP4下載
11-11 The Binomial Series
11-12 Applications of Taylor Polynomials
Chapter12 Vectors and the Geometry of Space
12-1 Three-Dimensional Coordinate Systems
12-2 Vectors
12-3 The Dot Product		線上觀看MP4下載
12-4 The Cross Product
12-5 Equations of Lines and Planes
12-6 Cylinders and Quadric Surface		線上觀看MP4下載
12-6 Cylinders and Quadric Surface
12-7 Cylindrical and Spherical Coordinates
Chapter13 Vector Functions
13-1 Vector Functions and Space Curves		線上觀看MP4下載
13-1 Vector Functions and Space Curves
13-2 Derivatives and Integrals of Vector Functions		線上觀看MP4下載
13-2 Derivatives and Integrals of Vector Functions
13-3 Arc Length and Curvature
13-4 Motion in Space:Velocity and Acceleration		線上觀看MP4下載
Chapter14 Partial Derivatives
14-1 Functions of Several Variables
14-2 Limits and Continuity		線上觀看MP4下載
14-3 Partial Derivatives線上觀看MP4下載
14-4 Tangent Lanes and Linear Approximations線上觀看MP4下載
14-5 The Chain Rule
14-6 Directional Derivatives and the Gradient Vector		線上觀看MP4下載
14-6 Directional Derivatives and the Gradient Vector
14-7 Maximum and Minimum Values		線上觀看MP4下載
14-7 Maximum and Minimum Values
14-8 Lagrange Multipliers		線上觀看MP4下載
14-8 Lagrange Multipliers線上觀看MP4下載
Chapter15 Multiple Integrals
15-1 Double Integrals over Rectangles
15-2 Iterated Integrals		線上觀看MP4下載
15-3 Double Integrals over General Regions
15-4 Double Integrals in Polar Coordinates		線上觀看MP4下載
15-6 Surface Area
15-7 Triple Integrals		線上觀看MP4下載
15-7 Triple Integrals
15-8 Triple Integrals in Cylindrical and Spherical Coordinates		線上觀看MP4下載
15-9 Change of Variables in Multiple Integrals
Chapter16 Vector Calculus
16-1 Vector Fields		線上觀看MP4下載
16-2 Line Integrals
16-3 The Fundanental Theorem for Line Integrals		線上觀看MP4下載
16-3 The Fundanental Theorem for Line Integrals
16-5 Curl and Divergence		線上觀看MP4下載
16-6 Parametric Surface and Their Areas
16-7 Surface Area
16-8 Stokes Theorem
16-9 The Divergence Theorem		線上觀看MP4下載

課程目標

The lecture will closely follow the textbook.

課程章節

章節 主題內容
第十一章Infinite Sequences and Series
第十二章Vectors and the Geometry of Space
第十三章Vector Functions
第十四章Partial Derivatives
第十五章Multiple Integrals
第十六章Vector Calculus


課程書目

James Stewart, Calculus, Early Transcendentals, 5th Edition.

評分標準

評分描述
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 3 problems from our textbook and 5 additional exercises announced at this webpage. Only the 5 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 3 problems will make up 2% of the score; the additional 5 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 ?nal score.
Handling homework papers in late is possible, but you must handle them in before the solutions have been discussed! The score for homework papers handled in late is calculated 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, April 17th, 2008 and will make up another 15% of your final score.
The final test will take place on Thursday, June 5th, 2008 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.

  • Monday, February 25th, 2008: first assignment online.
  • Monday, March 3rd, 2008: start of weekly tutorial.
  • Thursday, March 6th, 2008: first inclass homework.
  • Monday, April 14th, 2008: review and questions.
  • Thursday, April 17th, 2008: midterm exam; no homework.
  • Monday, April 21st, 2008: results of midterm exam.
  • Thursday, June 5th, 2008: final exam; no homework.
  • Thursday, June 12th, 2008: final homework.
  • Monday, June 16th, 2008: preparation for 會考 (optional).
學期週次
上課日期
參考課程進度

第一週

2008/02/18
  • Introduction
  • Chapter11 Infinite Sequences and Series
  • Section11.1
第二週2008/02/25
  • Section11.2-11.4
第三週2008/03/03
  • Section11.4-11.5
2008/03/06
  • Section11.6 & 11.8
第四週2008/03/10
  • Section11.9-10
2008/03/13
  • Section11.10
第五週2008/03/17
  • Section11.11-12
2008/03/20
  • Chapter12 Vectors and the Geometry of Space
  • Section12.1-12.3
  • Section12.4-12.6
第六週2008/03/24
  • Section12.6-12.7
2008/03/27
  • Chapter13 Vector Functions
  • Section13.1 Section
  • 13.1-13.2
第七週2008/03/31
  • Section13.2-13.4
第八週2008/04/07
  • Chapter14 Partial Derivative
  • Section14.1-14.2
2008/04/10
  • Section14.3
第九週2008/04/14
  • Review Midterm Exam
2008/04/17
第十週2008/04/21
  • Section14.4
2008/04/24
第十一週2008/04/28
  • Section14.5-14.6
2008/05/01
  • Section14.6-14.7
第十二週2008/05/05
  • Section14.7-14.8
2008/05/08
  • Section14.8
第十三週2008/05/12
  • Chapter15 Multiple Integrals
  • Section15.1-15.2
2008/05/15
  • Section15.3-15.4
第十四週2008/05/19
  • Section15.6-15.7
2008/05/22
  • Section15.7-15.8
第十五週2008/05/26
  • Section15.9
  • Chapter16 Vector Calculus
  • Section16.1
2008/05/29
  • Section16.2-16.3
第十六週2008/06/02
  • Section16.3&16.5
2008/06/05
  • Section16.6-16.9
第十七週2008/06/09
  • Prepare for the Final Exam
2008/06/12

課程作業 Course Homework

 
Problems
Additional Examples
Inclass Homework
Answers
Homework 1Chapter 11.1：52；
Chapter 11.2：24；
Chapter 11.3：34；		HomeworkTestpaperAnswer
Homework 2Chapter 11.4：37；
Chapter 11.5：28；
Chapter 11.6：28；		Homework Answer
Homework 3Chapter 11.8：22；
Chapter 11.9：37；
Chapter 11.10：48；		Homework Answer
Homework 4Chapter 11.12：17；
Chapter 12.4：39；
Chapter 12.5：43；		HomeworkTestpaperAnswer
Homework 5Chapter 12.6：36；
Chapter 13.2：49；
Chapter 13.4：21；		Homework Answer
Homework 6Chapter 14.1：30；
Chapter 14.2：29；
Chapter 14.3：66；		HomeworkTestpaperAnswer
Homework 7Chapter 14.3：89；
Chapter 14.4：41,42；		Homework Answer
Homework 8Chapter 14.5：52；
Chapter 14.6：36,49；		HomeworkTestpaperAnswer
Homework 9Chapter 14.7：42；
Chapter 14.8：1,44；		Homework Answer
Homework 10Chapter 15.1：10；
Chapter 15.2：25；
Chapter 15.3：32；		HomeworkTestpaperAnswer
Homework 11Chapter 15.6：23；
Chapter 15.7：28；
Chapter 15.8：21；		HomeworkTestpaperAnswer
Homework 12Chapter 15.9：24；
Chapter 16.2：44；
Chapter 16.3：26；		HomeworkTestpaperAnswer
課程專區
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