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Real Analysis and Applications: Theory in Practice by Kenneth R. Davidson, Allan P. Donsig (Hardcover, 2009)
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ISBN-13: 9780387980973, 978-0387980973. This new approach to real analysis stresses the use of the subject with respect to applications, [url] 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.