微積分(二) Calculus II (English) | 應用數學系符麥克老師

Calculus II (English)

微積分(二) (英語授課)

課程首頁
課程影音
課程綱要
課程行事曆
課程作業

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

每頁顯示個資料列

搜尋:

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

目前顯示第 1 至第 26 個資料列，總計 26 個資料列

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
第三週	2008/03/06	Section11.6 & 11.8
第四週	2008/03/10	Section11.9-10
第四週	2008/03/13	Section11.10
第五週	2008/03/17	Section11.11-12
第五週	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
第六週	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
第八週	2008/04/10	Section14.3
第九週	2008/04/14	Review Midterm Exam
第九週	2008/04/17	Review Midterm Exam
第十週	2008/04/21	Section14.4
第十週	2008/04/24	Section14.4
第十一週	2008/04/28	Section14.5-14.6
第十一週	2008/05/01	Section14.6-14.7
第十二週	2008/05/05	Section14.7-14.8
第十二週	2008/05/08	Section14.8
第十三週	2008/05/12	Chapter15 Multiple Integrals Section15.1-15.2
第十三週	2008/05/15	Section15.3-15.4
第十四週	2008/05/19	Section15.6-15.7
第十四週	2008/05/22	Section15.7-15.8
第十五週	2008/05/26	Section15.9 Chapter16 Vector Calculus Section16.1
第十五週	2008/05/29	Section16.2-16.3
第十六週	2008/06/02	Section16.3&16.5
第十六週	2008/06/05	Section16.6-16.9
第十七週	2008/06/09	Prepare for the Final Exam
第十七週	2008/06/12	Prepare for the Final Exam

課程作業 Course Homework

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