政大教學大綱

課程簡介Course Description

This is a course in vector calculus. Tops include vector files, gradient divergence and curl, line and surface integrals, theorems of Green, Stokes and Gauss, conservative vecore fields and differential forms.

核心能力分析圖 Core Competence Analysis Chart

能力項目說明

課程目標與學習成效Course Objectives & Learning Outcomes

Upon completion of this course, students should be able to

Define and calculate the derivations of functions of several variables and vector-valued functions
Evaluate multiple integrals (double and triple integrals).
Define vector fields (gradient, divergence, curl).
Evaluate the integrals of functons and vector fields on lines and surfaces.
Express and Stokes's and Divergence Theorems.
Define differential forms on R^n and know basic properties of differential forms
Use Stokes's Theorem for integrals of differential forms.

每周課程進度與作業要求 Course Schedule & Requirements

Week	Course Theme	Content and Reading Assignment	Activity and Homework	Estimated time devoted to coursework per week
1	Introduction	Review of vectors	Selected exercises	5 hrs.
2	Calculus of vector-valued functions	Differentiation and arc length	Selected exercises	5 hrs.
3	Calculus of functions of several variables	Differentiation and Taylor’s theorem	Selected exercises	5 hrs.
4	Calculus of functions of several variables	Multivariate integrations	Selected exercises	5 hrs.
5	Vector fields	Scalar and vector fields, gradient, divergence and curl	Selected exercises	5 hrs.
6	Integration in vector fields	The path and line integrals	Selected exercises	5 hrs.
7	Integration in vector fields	Parametrized surfaces and areas of surfaces	Selected exercises	5 hrs.
8	Integration in vector fields	The integral of scalar functions over surfaces	Selected exercises	5 hrs.
9	Midterm Exam		Selected exercises	5 hrs.
10	Integration in vector fields	The surface integral	Selected exercises	5 hrs.
11	Integration in vector fields	Applications	Selected exercises	5 hrs.
12	The integral theorems of vector analysis	The Green’s theorem	Selected exercises	5 hrs.
13	The integral theorems of vector analysis	The stokes’ theorem	Selected exercises	5 hrs.
14	The integral theorems of vector analysis	Conservative fields	Selected exercises	5 hrs.
15	The integral theorems of vector analysis	The Gauss’ theorem	Selected exercises	5 hrs.
16	The integral theorems of vector analysis	Differential forms	Selected exercises	5 hrs.
17	The integral theorems of vector analysis	Catch up	Selected exercises	5 hrs.
18	Final Exam		Selected exercises	5 hrs.

授課方式Teaching Approach

90%

講述 Lecture

10%

討論 Discussion

小組活動 Group activity

數位學習 E-learning

其他： Others:

指定/參考書目Textbook & References

References

1. Vector Calculus by Marsden and Tromba

2. Vecore Calculus by W. Cox

3. Calculus by Stewart, Clegg and Watson

4. Thomas' Calculus by Thomas, Weir, Hass and Heil

5. 向量分析 by 林琦焜

6. Vecore Analysis Versus Vector Calculus by Galbis and Maestre

已申請之圖書館指定參考書目圖書館指定參考書查詢 |相關處理要點

書名 Book Title	作者 Author	出版年 Publish Year	出版者 Publisher	ISBN	館藏來源*	備註 Note

教學大綱 Syllabus

科目名稱：向量微積分

Course Name: vector calculus

修別：選

學分數

預收人數

課程簡介Course Description

核心能力分析圖 Core Competence Analysis Chart

課程目標與學習成效Course Objectives & Learning Outcomes

每周課程進度與作業要求 Course Schedule & Requirements

授課方式Teaching Approach

講述 Lecture

討論 Discussion

小組活動 Group activity

數位學習 E-learning

其他： Others:

評量工具與策略、評分標準成效Evaluation Criteria

指定/參考書目Textbook & References

已申請之圖書館指定參考書目圖書館指定參考書查詢 |相關處理要點

課程相關連結Course Related Links

課程附件Course Attachments

課程進行中，使用智慧型手機、平板等隨身設備 To Use Smart Devices During the Class

教學大綱 Syllabus

科目名稱：向量微積分

Course Name: vector calculus

修別：選

學分數

預收人數

課程簡介Course Description

核心能力分析圖 Core Competence Analysis Chart

課程目標與學習成效Course Objectives & Learning Outcomes

每周課程進度與作業要求 Course Schedule & Requirements

授課方式Teaching Approach

講述 Lecture

討論 Discussion

小組活動 Group activity

數位學習 E-learning

其他： Others:

評量工具與策略、評分標準成效Evaluation Criteria

指定/參考書目Textbook & References

已申請之圖書館指定參考書目 圖書館指定參考書查詢 |相關處理要點

課程相關連結Course Related Links

課程附件Course Attachments

課程進行中，使用智慧型手機、平板等隨身設備 To Use Smart Devices During the Class

已申請之圖書館指定參考書目圖書館指定參考書查詢 |相關處理要點