Real analysis and applications : theory in practice
Author(s)
Bibliographic Information
Real analysis and applications : theory in practice
（Undergraduate texts in mathematics）
Springer, c2010
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Note
Includes bibliographical references (p. 505-506) and index
Description and Table of Contents
Description
This new approach to real analysis stresses the use of the subject with respect to applications, i.e., how the principles and theory of real analysis can be applied in a variety of settings in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization. Users will be prepared for more intensive work in each topic through these applications and their accompanying exercises. This book is appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra.
Table of Contents
Analysis.- Review.- The Real Numbers.- Series.- Topology of.- Functions.- Differentiation and Integration.- Norms and Inner Products.- Limits of Functions.- Metric Spaces.- Applications.- Approximation by Polynomials.- Discrete Dynamical Systems.- Differential Equations.- Fourier Series and Physics.- Fourier Series and Approximation.- Wavelets.- Convexity and Optimization.
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