Ma 108a (Fall 2002-03)

Fall 2002–2003

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

Final Exam (due 5:00 pm on 12/12): [dvi] [pdf] [ps]

Midterm Exam (due 11/5): [dvi] [pdf] [ps]

Homework:

#1 (due 10/9): [dvi] [pdf] [ps]
#2 (due 10/23): [dvi] [pdf] [ps]
#3 (due 10/30): [dvi] [pdf] [ps]
#4 (due 11/13): [dvi] [pdf] [ps]
#5 (due 11/20): [dvi] [pdf] [ps]

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This course covers the basic tools and techniques of real analysis. While our primary focus is the calculus of functions on R^ⁿ, we will occasionally work in more abstract settings, keeping the real numbers in mind as a convenient example. Topics are likely to include:

Sequences and limits in the real line, metrics space, and normed linear spaces.

Open and closed sets in R^ⁿ, continuous functions

Compactness and its many consequences

Convergence of sequences of functions, Weierstrass Approximation Theorem

Differentiation of functions from R^ⁿ to R^{^m}. Taylor polynomials

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

Prerequisite: Calculus in one variable, familiarity with "epsilon-delta'' proofs

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

Late work will only be accepted with a valid and well-documented explanation.

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.