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Math 4516: Topics in Analysis

Topics covered: Taylor series and approximation, Measure theory, Lebesque integral, Metric spaces; additional topics as appropriate for the particular class.

This class is a continuation of Math 3515, Analysis 1. Hence, I will frequently refer to it as "Analysis 2".

Prerequisite: Math 3515 (Analysis 1)

Textbook: We will be using the online resource Interactive Real Analysis, as well as the cheap and useful Dover(*) text book Introductory Real Analysis by Kolmogorov and Fomin. Additional resources will be made available as needed.

Lebesque Integral Illustration(*) Dover text books for Math are classic text books in mathematics, reprinted in paperback format, available for an incredibly low price - get as many Dover books as you can get, they are (almost) all good to have and for the price you can't go wrong..

Software: We will make use of the DyKnow client software. Please download and install that software.



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General Information


Final Exam



05: Metric Spaces

04: Lebesgue Integration

03: Sounds and Fourier Transform

02: Fourier Series

  • Part 1: Introduction and Basic Formulas
  • Part 2: Convergence Theorems
  • Part 3: Changing the Scale

01: Power and Taylor Series

  • Part 1: Power series
  • Part 2: Basic Algebra
  • Part 3: Multiplying and Dividing
  • Part 4: Taylor series
  • Part 5: Taylor's Theorem, Lagrange Reminder, & "most beautiful formula in mathematics"




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Bert G. Wachsmuth