MATH2060C - Mathematical Analysis II - 2024/25
Announcement
- Jan 1: Welcome to the course. No tutorial in the 1st week.
- Jan 1: All homework and midterm will be graded online using the Gradescope system. The link of the Gradescope system can be found in the Blackboard system.
- Jan 1: The following arrangement at the end of the midterm will be implemented: 1. Stop writing when "pen-down" is announced by the instructor. 2. Use your "smartphone" to capture images of all the (non-empty) pages of your answers when instructed by the instructor. 3. Then convert the images of your answers into a pdf file. 4. Submit the pdf file of your answers into the "Midterm" in the Gradescope system. (You will have around 15 minutes for steps 3-5.) 5. Submit your answer book to the instructor.
- Feb 27: Midterm arrangement: Date: Mar 11, 2025 (Tuesday), Time: 7:00-8:30pm, Location: LSB LT1; Coverage: From the beginning of the term to Section 7.1 of the Textbook, including all material in the Textbook, lecture/tutorial notes and homework; Sick leave: Original copy of a medical certificate covering Mar 11, 2025 is needed for taking sick leave of the midterm, and it should be submitted on the day right after the period of sick leave specified on the medical certificate. (You are advised to send an email copy to your instructor as soon as possible, before submitting the original copy. So that a make-up midterm exam can be arranged sooner.) Calculator: Models approved by University are allowed.
General Information
Lecturer
-
Renjun DUAN
- Office: LSB 206
- Tel: 39437977
- Email:
- Office Hours: Freely visit the office or make an appointment by email
Teaching Assistant
-
Mr. Junhao ZHANG
- Office: LSB 232
- Tel: 5494 3956
- Email:
- Office Hours: Fri 14:00-15:00
-
Mr. Haowei QI
- Office: LSB 232
- Tel: 4470 7250
- Email:
- Office Hours: Thu 13:00-14:00
Time and Venue
- Lecture: Mo 4:30PM - 6:15PM Lady Shaw Bldg LT2; We 2:30PM - 3:15PM Science Centre L5
- Tutorial: We 3:30PM - 4:15PM Science Centre L5
Course Description
This is a continuation of MATH2050. Topics include: differentiability, Riemann integrals, series, sequences and series of functions, and uniform convergence.
Textbooks
- R.G. Bartle and D.R. Sherbert, Introduction to real analysis, 4th ed, Wiley, (Ch. 6-9)
References
- W. Rudin, Principles of Mathematical Analysis, McGraw Hill
Pre-class Notes
Lecture Notes
- Topic 01: Derivative
- Topic 02: Mean Value Theorem
- Topic 03: L'Hospital Rule
- Topic 04: Taylor's Theorem
- Topic 05: Riemann Integral
- Topic 06: Riemann Integrable Functions
- Topic 07: Fundamental Theorem
- Topic 08: Darboux Integral
- Topic 09: Pointwise and Uniform Convergence
- Topic 10: Interchange of Limits
- Topic 11: Exponential and Logarithmic Functions
- Topic 12: Trigonometric Functions (TBD)
- Topic 13: Absolute Convergence
- Topic 14: Tests for Absolute Convergence
- Topic 15: Tests for Non-absolute Convergence
- Topic 16: Series of Functions
- Revision
Tutorial Notes
Assignments
- Homework 1 (due on Jan 23, 2025 11:00am)
- Homework 2 (due on Feb 6, 2025 at 11:00am)
- Homework 3 (due on Feb 13, 2025 at 11:00am)
- Homework 4 (due on Feb 20, 2025 at 11:00am)
- Homework 5 (due on Feb 27, 2025 at 11:00am)
- Homework 6 (due on Mar 13, 2025 at 11:00am)
- Homework 7 (due on Mar 27, 2025 at 11:00am)
- Homework 8 (due on Apr 3, 2025 at 11:00am)
- Homework 9 (due on Apr 10, 2025 at 11:00am)
- Homework 10 (due on Apr 17, 2025 at 11:00am)
Solutions
- Suggested solution to Homework 1
- Suggested solution to Homework 2
- Suggested solution to Homework 3
- Suggested solution to Homework 4
- Suggested solution to Homework 5 (Updated 20250228)
- Suggested solution to Homework 6
- Suggested solution to Homework 7 (Updated 20250401)
- Suggested solution to Homework 8
- Suggested solution to Homework 9
- Suggested solution to Homework 10
Assessment Scheme
Homework | 10% | |
Mid-term (Mar 11, 2025, Tue, 7:00-8:30pm, LSB LT1. Common to both sections) | 40% | |
Final (TBA by university) | 50% |
Useful Links
Honesty in Academic Work
The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:
http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Assessment Policy Last updated: April 16, 2025 18:14:36