Fundamental Ideas of Analysis

The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.

Spis treści:
Preliminaries.
Sequences.
The Riemann Integral.
Differentiation.
Sequences of Functions.
Series of Functions.
Differential Equations.
Complex Analysis.
Fourier Series.
Probability Theory.
Bibliography.
Indexes.