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Introductn to the Theory of Functions I

765

MATH 765 and MATH 766 are theoretical courses on the fundamental concepts of analysis and the methods of proof. These two courses include the concept of a real number; limits, continuity, and uniform convergence; derivatives and integrals of functions of one and of several real variables.

Text: 

Intro to Analysis, Wade, Prentice Hall, 4th edition.

Prerequisite: 

MATH 223 and MATH 290 or equivalent.

Credit Hours: 
3

TOPICS

  1. The Real Number System
    • Field properties, well-ordering and completeness
    • Sequences and Bolzano-Weierstrass theorem
    • Functions and countability
  2. Continuity and Differentiability on the Real Line
    • Limits, continuity and uniform continuity
    • Differentiability, mean value theorem and monotonicity
  3. The Riemann Integral
    • The Riemann integral and Riemann sums
    • The fundamental theorem of calculus, integration by parts and change of variables
    • Improper Riemann Integrals
  4. Infinite Series
    • Convergence, absolute convergence and tests of convergence

(Torres 2017 )

Frequency: 
Every Fall Semester

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