MATH 441 REAL ANALYSIS II

Course Outline:

I. Differentiation

A. The Derivative of a Function

B. Some Mean Value Theorems

II. Integration

A. The Riemann Integral

B. Some Properties and Application of the Riemann Integral

C. The Riemann Stieljes-Integral (optional)

D. Deficiencies of the Riemann Integral (optional)

E. The Generalized Riemann Integral (optional)

F. Introduction to the Lebesque Measure in R (optional)

III. Sequences and Series of Functions

A. Sequences of Functions

B. Series of Functions

C. Taylor Series

IV. Fourier Series (optional topic)

A. Fourier Coefficients

B. Representation by Fourier Series

V. Metric Spaces (optional topic)

A. Axioms and Examples, Normed Spaces, Innerproduct Spaces

B. Topology in Metric Spaces

Pre-requisite: Math 440

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