## 核心能力 Competence

Ability to handle continuity phenomena and approximations.

Ability to operate with symbols and digits.

Ability to visualize space, shape, and images.

Ability of using computer to do mathematics.

Ability to apply stochastic mathematics.

Ability to handle large amount of data.

Ability to do mathematics relating to discrete models.

Ability to do independent studies of mathematics.

Abilities to use computer as a tool.

## 課程概述 Course Description

This course provides the mathematical foundations needed for understanding and working with the modern analysis. The main topics are complex number system, analytic functions, integrations, conformal mappings and some integral transformations. Some applications in physics and engineering will also be included.

## 課程學習目標 Course Objectives

• Properties of Analytic Functions
• Isolated Singularities of an Analytic Function and The Residue Theorem
• Conformal Mapping and the Riemann Mapping Theorem
• ## 課程進度 Progress Description

進度說明 Progress Description
1The Complex Numbers
2The Complex Numbers Function of the Complex Variable z
3Function of the Complex Variable z
4Analytic Functions
5Line Integrals and Entire Functions
6Properties of Entire Functions
7Properties of Analytic Functions
8Properties of Analytic Functions
9Simply Connected Domains
10Midterm (11/23 19:00-21:00 數學系 3174 教室)
11Isolated Singularities of an Analytic Function
12The Residue Theorem
13Applications of the Residue Theorem to the Evaluation of Integrals and Sums
14Applications of the Residue Theorem to the Evaluation of Integrals and Sums
15Applications of the Residue Theorem to the Evaluation of Integrals and Sums
16Introduction to Conformal Mapping
17Introduction to Conformal Mapping
18Final Exam
以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

## 有關課程其他調查 Other Surveys of Courses

1.本課程是否規劃業界教師參與教學或演講? 否
Is there any industry specialist invited in this course? How many times? No
2.本課程是否規劃含校外實習(並非參訪)? 否
Are there any internships involved in the course? How many hours? No
3.本課程是否可歸認為學術倫理課程? 否
Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics? No
4.本課程是否屬進入社區實踐課程? 否
Is this course recognized as a Community engagement and Service learning course? Which community will be engaged? No