MA4542 Real Analysis


This course aims to provide an introduction of some fundamental topics on real analysis, for example, set theory, Lebesgue measure, Lebesgue integrals and Lp spaces. It will help students extend their knowledge about analysis taught in basic calculus courses and make them ready for further studies in advanced numerical analysis and functional analysis..

Lecture Notes:

  • Chapter 1: Preliminary.
  • Chapter 2: Lebesgue Measure.
  • Chapter 3: Lebesgue Measurable Functions.
  • Chapter 4: Lebesgue Integrations.
  • Chapter 5: Lp Spaces.

  • Exercises:

  • Chapter 1: Exercise 1 and Solution 1
  • Chapter 2: Exercise 2 and Solution 2
  • Take Home Assignments: Take Home Assignment #1. Solution
  • Midterm: Solution
  • Take Home Assignments: Take Home Assignment #2 Part I and Part II

  • Suggested reference books:

  • Real Analysis, H. Royden and P. Fitzpatrick, Publisher: Pearson.
  • Real and Complex Analysis, W. Rudin. Publisher: WCB/McGraw-Hill.
  • Real Analysis: Modern Techniques and Their Applications, G. Folland. Publisher: John Wiley & Sons, Inc..
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