**國立清華大學數學系**

高等微積分一

**QF 2149-00 (Spring 2022) Advanced Calculus (I) **** **

Instructor: 陳國璋 Kuo-Chang Chen Hours and days: R1R2R3 Classroom: 綜三 203 Teaching assistant: 史昀玉, 梁睿燊 |
Office: 綜三 609 Phone Number: (03) 5715131 Ext: 33067 Office Hours: T7T8 or by appointments Email: kchen@math.nthu.edu.tw |

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**Course Description**:

This year-long, 6-credits course is an introduction to mathematical analysis intended for students who have received a standard training on single-variable calculus. We will study analytical tools, topological and geometric concepts needed for multi-variable calculus in a rigorous manner. The first semester will be focusing on series, uniform convergence, topology of R^n and metric spaces (Chapters 2, 6-10). The second semester will be focusing on differential calculus, optimization, integral calculus, and Fourier series (Chapters 11-14). Those who planning on taking more advanced courses of mathematical analysis, such as real and functional analysis, should seriously consider taking the other 8-credits advanced calculus offered by the math department.

**Textbook**:

William R. Wade: Introduction to Analysis, fourth edition, 2014.

**References**:

Elementary Classical Analysis 2nd Edition by J. E. Marsden and M. J. Hoffman

Principles of Mathematical Analysis by W. Rudin

**Some Lecture Notes**:

Due to the pandemic some lectures were
delivered online. Here are some lecture notes for these classes:
**5/5**,
**5/12**,
**5/19**,
**5/26**,
**6/2**,
**6/9**.

**Grading**:

Homework and Quizzes: 20%.
**Click Here**

Midterm Exam: 40% -- April 21 (Thursday) from 8:00-11:00am.

Final exam: 40% -- June 16 (Thursday) from 8:00-11:00am.