Fundamental Ideas Of Analysis

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