國立清華大學數學系

高等微積分一

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

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.