Davidson K.R., Donsig A.P. Real Analysis and Applications: Theory in Practice

Springer, 2009. - 516 Pages.This new approach to real analysis stresses the use of the subject in applications, by showing 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.