Handbook of Real Variables

With Applications to Differential Equations and Fourier Analysis

AvSteven G. Krantz

Inbunden, Engelska, 2003

1 073 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

Häftad

1 073 kr

Beskrivning

This concise, well-written handbook provides a distillation of the theory of real variables with a particular focus on the subject�s significant applications to differential equations and Fourier analysis. Ideal for the working engineer or scientist, the book uses ample examples and brief explanations---without a lot of proofs or axiomatic machinery---to give the reader quick, easy access to all of the key concepts and touchstone results of real analysis. Topics are systematically developed, beginning with sequences and series, and proceeding to topology, limits, continuity, derivatives, and Riemann integration. In the second half of the work, Taylor series, the Weierstrass Approximation Theorem, Fourier series, the Baire Category Theorem, and the Ascoli--Arzela Theorem are carefully discussed. Picard iteration and differential equations are treated in detail in the final chapter.Key features: * Completely self-contained, methodical exposition for the mathematically-inclined researcher; also valuable as a study guide for students * Realistic, meaningful connections to ordinary differential equations, boundary value problems, and Fourier analysis * Example-driven, incisive explanations of every important idea, with suitable cross-references for ease of use * Illuminating applications of many theorems, along with specific how-to hints and suggestions* Extensive bibliography and index This unique handbook is a compilation of the major results, techniques, and applications of real analysis; it is a practical manual for physicists, engineers, economists, and others who use the fruits of real analysis but who do not necessarily have the time to appreciate all of the theory. Appropriate as a comprehensive reference or for a quick review, the "Handbook of Real Variables" will benefit a wide audience.

Produktinformation

Utgivningsdatum:2003-11-18
Mått:155 x 235 x 17 mm
Vikt:500 g
Format:Inbunden
Språk:Engelska
Antal sidor:201
Upplaga:2004
Förlag:Birkhauser Boston Inc
ISBN:9780817643294

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

"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)

Innehållsförteckning

Basics.- Sets.- Operations on Sets.- Functions.- Operations on Functions.- Number Systems.- Countable and Uncountable Sets.- Sequences.- to Sequences.- Limsup and Liminf.- Some Special Sequences.- Series.- to Series.- Elementary Convergence Tests.- Advanced Convergence Tests.- Some Particular Series.- Operations on Series.- The Topology of the Real Line.- Open and Closed Sets.- Other Distinguished Points.- Bounded Sets.- Compact Sets.- The Cantor Set.- Connected and Disconnected Sets.- Perfect Sets.- Limits and the Continuity of Functions.- Definitions and Basic Properties.- Continuous Functions.- Topological Properties and Continuity.- Classifying Discontinuities and Monotonicity.- The Derivative.- The Concept of Derivative.- The Mean Value Theorem and Applications.- Further Results on the Theory of Differentiation.- The Integral.- The Concept of Integral.- Properties of the Riemann Integral.- Further Results on the Riemann Integral.- Advanced Results on Integration Theory.- Sequences and Series of Functions.- Partial Sums and Pointwise Convergence.- More on Uniform Convergence.- Series of Functions.- The Weierstrass Approximation Theorem.- Some Special Functions.- Power Series.- More on Power Series: Convergence Issues.- The Exponential and Trigonometric Functions.- Logarithms and Powers of Real Numbers.- The Gamma Function and Stirling’s Formula.- An Introduction to Fourier Series.- Advanced Topics.- Metric Spaces.- Topology in a Metric Space.- The Baire Category Theorem.- The Ascoli-Arzela Theorem.- Differential Equations.- Picard’s Existence and Uniqueness Theorem.- The Method of Characteristics.- Power Series Methods.- Fourier Analytic Methods.- Glossary of Terms from Real Variable Theory.- List of Notation.- Guide to the Literature.