Math 555, Spring 1998

University of South Carolina

To view an Acrobat version of each lecture, click on the symbol . Free reader here.

**Lectures**

Lectures developed during Spring 98. These typically state
definitions, theorems, and examples, in a such a way that the steps to
fill in the details are suitable for the student to perform.

- Special Functions
**Metric Spaces**- Introduction
- Open and Closed Sets
- Limits and Continuity
- Completeness
**Compactness and its applications**- Connectedness
**Riemann-Stieltjes Integration**- Introduction
- Conditions for Existence
- Properties of the Riemann- Stieltjes integral
- Additional Properties of the Riemann- Stieltjes integral
**Infinite Series: both in the Scalars and Normed Linear Spaces****Sequences and Series of Functions**- Power Series and their Radius of Convergence
- Interchange of Limit Operations
- Taylor's Approximation
- Exponential and Trigonmetric Functions in C
- Weierstrass Approximation Theorem
- Ascoli's Theorem
**Existence and Uniqueness of ODE****Fourier Series and Solutions to Partial Differential Equations**

If you have any questions, please send e-mail to