Type of Credit: Elective
Credit(s)
Number of Students
This course a continuation of the two-semester course in Advanced Calculus. It covers the fundamentals of mathematical analysis, shows the utility of abstract concepts and teaches an understanding and construction of proofs. Topics include definitions and properties of some special functions and differentation and integration of functions of several variables.
Prerequisite: Completion of two semesters of Advanced Calculus courses.
能力項目說明
By the end of the course, students should be able to
1. understand the definitions and properties of power series;
2. understand the definitions and properties of exponential, logarithmic and triganometric functions;
3. understand the definitions and properties of Fouries series and Gamma function;
4. better understand vector spaces and linear transformations;
5. understnad the differentiation of functions of several veriables and the related properties;
6. underdtand the integration of functions of several veriables and the related properties;
7. comprehend the stoke theorem;
8. read and write rigorous mathematical proofs in the context of analysis;
9. communicate mathematical ideas verbally and in writing.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
|
週次 Week |
課程主題 Topic
|
課程內容與指定閱讀
Content and Reading Assignment |
教學活動與作業
Teaching Activities and Homework |
學習投入時間 Student workload expectation |
|
|
課堂講授 In-class Hours |
課程前後 Outside-of-class Hours |
||||
|
1 |
Special functions |
Chapter 8 |
Selected Exercises |
3 |
8 |
|
2 |
中秋節放假 |
Chapter 8 |
Selected Exercises |
0 |
8 |
|
3 |
Special functions |
Chapter 8 |
Selected Exercises |
3 |
8 |
|
4 |
Special functions |
Chapter 8 |
Selected Exercises |
3 |
8 |
|
5 |
Special functions |
Chapter 8 |
Selected Exercises |
3 |
8 |
|
6 |
Differentation |
Chapter 9 |
Selected Exercises |
3 |
8 |
|
7 |
Differentation |
Chapter 9 |
Selected Exercises |
3 |
8 |
|
8 |
Differentation |
Chapter 9 |
Selected Exercises |
3 |
8 |
|
9 |
Midterm week |
Chapter 9 |
Selected Exercises |
3 |
8 |
|
10 |
Differentiation |
Chapter 9 |
Selected Exercises |
3 |
8 |
|
11 |
Differentiation |
Chapter 9 |
Selected Exercises |
3 |
8 |
|
12 |
Integration |
Chapter 10 |
Selected Exercises |
3 |
8 |
|
13 |
Integration |
Chapter 10 |
Selected Exercises |
3 |
8 |
|
14 |
Integration |
Chapter 10 |
Selected Exercises |
3 |
8 |
|
15 |
Integration |
Chapter 10 |
Selected Exercises |
3 |
8 |
|
16 |
Integration |
Chapter 10 |
Selected Exercises |
3 |
8 |
|
17 |
|
|
Selected Exercises |
0 |
8 |
|
18 |
Final week |
|
|
|
8 |
本課程無涉及 AI 使用。
Participation and Attendance: 50%
Final Exam: 50%
1. Principles of Mathematical Analysis by Walter Rudin, 3rd Edition.
2. An Introduction to Analysis by William R. Wade, 4th Edition.
3. Mathematical Analysis by Apostol, 2nd Edition.
Moodle教學平台: http://moodle.nccu.edu.tw