2024 Autumn - Mathematical Analysis B1(MATH1006.04)

Lecturer: Wang Huting

Time and Classroom: 1(3,4) 3(3,4) 5(1,2) at 5201

Textbook: Mathematical Analysis Vol.1 - Cheng Yi, Chen Qing and Li Ping

This page is for extended content of the course for the ones who are interested in deeper and broader knowledge of this course.

For the basic information of this course, check the course website here.

Chapter 1 (Limit)

• 1.1 Real Numbers
  • The conception of countability and uncountability, cardinality of a set
  • Three ways to construct real numbers: the equivalence class of rational Cauchy sequence, infinite decimal, dedekind cut
  • Basic definitions about topology on the real line, the sixth axiom on completeness of the real number system: finite covering condition
• 1.2 Limit of a Sequence
  • Toeplitz’s Theorem (generalized Stolz’s theorem): try to use this to solve Example 1.2.20 from Page 25 and exercise 11 from page 53 in the textbook.
  • Wallis’ Formula
  • Stirling’s Formula: exercise 1(4) from Page 25 and exercise 10(2) from Page 53 are direct results from this.
• 1.3 Limit of a Function

1st Recitation Class: Note here

Chapter 2 (Continuity)

• 2.1 Basic Concepts *