Winter 2003–2004

Ma 108b - Classical Analysis
MWF 11:00 // 151 Sloan
M. Goldberg

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Final  (due March 17 @ 5pm):  [tex]  [pdf]   [ps]

Midterm  (due Feb. 10 @ 4pm):  [tex]  [pdf]   [ps]

Homework:

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The second term of Ma 108 covers a wide assortment of topics in real analysis. Chief among them are Lebesgue measure and integration, which enable us to interpret expressions like ∫ f(x) dx in many cases when the Riemann integral is undefined. Definitions will generally be presented in one dimension, with the details of extending them to Rn left to the imagination.

In order of appearance, the main topics are:

  • Inverse function theorem, implicit function theorem
  • Ordinary differential equations
  • Construction of Lebesgue measure
  • Properties of the Lebesgue integral
  • The Lp function spaces
  • Introduction to Fourier series (as much as time permits)

Text:  Robert Strichartz, The Way of Analysis, revised edition (2000)

Prerequisite:  Calculus of one variable, Ma108a or its equivalent

Grading:  Weekly homework 50%, midterm exam 20%, final exam 30%.

Collaboration Policy:  You may discuss homework problems with other students, but solutions should be written up individually in your own words. Take-home exams must be your own work, with outside references properly attributed.