Theory of Functions of a Real Variable
by Shlomo Sternberg
Number of pages: 393
I have taught the beginning graduate course in real variables and functional analysis three times in the last five years, and this book is the result. The course assumes that the student has seen the basics of real variable theory and point set topology. Contents: the topology of metric spaces, Hilbert spaces and compact operators, the Fourier transform, measure theory, the Lebesgue integral, the Daniell integral, Wiener measure, Brownian motion and white noise, Haar measure, Banach algebras and the spectral theorem, Stone’s theorem, scattering theory.
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by Marcel B. Finan - Arkansas Tech University
The text is designed for an introductory course in real analysis suitable to upper sophomore or junior level students who already had the calculus sequel and a course in discrete mathematics. The content is considered a moderate level of difficulty.
by Joseph L. Taylor
The goal is to develop in students the mathematical maturity they will need when they move on to senior level mathematics courses, and to present a rigorous development of the calculus, beginning with the properties of the real number system.
by Shanti Narayan - S.Chand And Company
Contents: Dedekind's theory of Real Numbers; Bounds and Limiting Points; Sequences; Real Valued Functions of a Real Variable; The derivative; Riemann Theory of Integration; Uniform Convergence; Improper Integrals; Fourier Series; and more.
by Henry Parker Manning - J. Wiley & sons
This book is intended to explain the nature of irrational numbers, and those parts of Algebra which depend on the theory of limits. We have endeavored to show how the fundamental operations are to be performed in the case of irrational numbers.