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Introduction to the Theory of Functions II

766

A continuation of MATH 765.

Text: 

An Introduction to Analysis, Wade, Prentice Hall, 4th edition.

Prerequisite: 
Credit Hours: 
3

TOPICS

  1. Infinite series (continued). Uniform convergence of sequences and series of functions. Power series.
  2. Euclidean and Metric Spaces
    • Topology on Rn
    • Limits and continuity of functions on Rn
    • Metric spaces - topology and continuity of functions
  3. Differentiability on Rn
    • Partial derivatives and differentiability
    • Mean value theorem and Taylor's formula
    • Inverse and implicit function theorem
    • Extreme and tangent planes
  4. Integration on Rn (as time allows)
    • Iterated integrals and Fubini's theorem
    • Change of variables
    • Fundamental Theorem of Multivariable Calculus

       

(Stefanov 2010 )

Frequency: 
Every Spring Semester

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