A Handbook of Real Variables: With Applications to Differential Equations and Fourier Analysis

ISBN-13: 9781461264095 / Angielski / Miękka / 2012 / 201 str.

Steven G. Krantz

Opis

This concise, well-written handbook provides a distillation of real variable theory with a particular focus on the subject's significant applications to differential equations and Fourier analysis. Ample examples and brief explanations---with very few proofs and little axiomatic machinery---are used to highlight all the major results of real analysis, from the basics of sequences and series to the more advanced concepts of Taylor and Fourier series, Baire Category, and the Weierstrass Approximation Theorem. Replete with realistic, meaningful applications to differential equations, boundary value problems, and Fourier analysis, this unique work is a practical, hands-on manual of real analysis that is ideal for physicists, engineers, economists, and others who wish to use the fruits of real analysis but who do not necessarily have the time to appreciate all of the theory. Valuable as a comprehensive reference, a study guide for students, or a quick review, "A Handbook of Real Variables" will benefit a wide audience.

Recenzje

"In eleven chapters, Krantz's book succeeds in providing a reference work for 'the working engineer or scientist' encompassing the essence of real analysis...Krantz's book suceeds in providing a reference work for "the working engineer or scientist" encompassing the essence of real analysis. ... True to the idea of a handbook, there are good, but brief, explanations, well-chosen examples, and only a few proofs. In addition to the book's principal audience, students preparing for exams at either the undergraduate or master's level will find this a valuable resource." (MAA Reviews)

"The purpose of this book is to acknowledge that there is a large audience of scientists and others who wish to use the fruits of real analysis, and who are not equipped to stop and appreciate all the theory.  This handbook uses ample examples and brief explanations and must give an opportunity to users of real analysis quickly to look up ideas, without axiomatic machinery and without becoming bogged down in long explanations and proofs. . . This very good written book can be highly recommended to everyone who are teaching or researching in the field of applied mathematics. The book is also of interest to graduate students, researchers in physics, engineering, economics, and other applied sciences." (ZAA)

Spis treści

Preface * Basics * Sequences * Series * The Topology of the Real Line * Limits and the Continuity of Functions * The Derivative * The Integral * Sequences and Series of Functions * Some Special Functions * Advanced Topics * Differential Equations * Glossary of Terms from Real Variable Theory * List of Notation * A Guide to the Literature * Bibliography * Index

O autorze

Steven Krantz, Ph.D., is Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 45 books on mathematics, including Calculus Demystified, another popular title in this series. He lives in St. Louis, Missouri.