Mathematical Analysis I

Author: V. A. Zorich

Publisher: Springer

ISBN: 3662487926

Category: Mathematics

Page: 616

View: 9998

This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.

Mathematical Analysis II

Author: V. A. Zorich

Publisher: Springer

ISBN: 3662489937

Category: Mathematics

Page: 720

View: 322

This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

Analysis II

Author: Vladimir A. Zorich

Publisher: Springer

ISBN: 9783540462316

Category: Mathematics

Page: 708

View: 1343

Ausführlich, klar, exakt, solide: die Anfänge der Analysis in 2 Bänden. Von der Einführung der reellen Zahlen bis hin zu fortgeschrittenen Themen wie u.a. Differenzialformen auf Mannigfaltigkeiten, asymptotische Betrachtungen, Fourier-, Laplace- und Legendre-Transformationen, elliptische Funktionen und Distributionen. Deutlich auf naturwissenschaftliche Fragen ausgerichtet, erläutert dieses Werk detailliert Begriffe, Inhalte und Sätze der Integral- und Differenzialrechnung. Die Fülle hilfreicher Beispiele, Aufgaben und Anwendungen ist selten in Analysisbüchern zu finden. Band 2 beschreibt den heutigen Stand der klassischen Analysis.

Mathematical Analysis II

Author: Claudio Canuto,Anita Tabacco

Publisher: Springer

ISBN: 3319127578

Category: Mathematics

Page: 559

View: 1153

The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, familiarise with the corresponding key techniques and find the proofs of the main results. The second level enables the strongly motivated reader to explore further into the subject, by studying also the material contained in the appendices. Definitions are enriched by many examples, which illustrate the properties discussed. A host of solved exercises complete the text, at least half of which guide the reader to the solution. This new edition features additional material with the aim of matching the widest range of educational choices for a second course of Mathematical Analysis.

Advanced Courses of Mathematical Analysis II

Proceedings of the 2nd International School, Granada, Spain, 20-24 September 2004

Author: M. V. Velasco

Publisher: World Scientific

ISBN: 981256652X

Category: Mathematics

Page: 213

View: 9692

This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of new directions and advances in topics for current and future research in the field. Contents: Lineable and Spaceable Properties (R M Aron); Alexander Grothendieck's Work on Functional Analysis (F Bombal); Maximal Functions in Fourier Analysis (J Duoandikoetxea); Hypercyclic Operators: Some Recent Progress (G Godefroy); On the Hahn-Banach Theorem (L Narici); Lipschitz Quotient Maps Between Banach Spaces (W B Johnson); Approximation Algorithms in Banach Spaces (N Kalton); Spectral Properties of Cesa'ro-Like Operators (M M Neumann); Some Ideas on Mathematical Training Concerning Mathematical Analysis (B Rubio); Interpolation and Sampling (K Seip); Classes of Indefinitely Differentiable Functions (M Valdivia); Classical Potential Theory and Analytic Capacity (J Verdera); Best Approximations on Small Regions: A General Approach (F Zo & H H Cuenya). Readership: Mathematicians in analysis and differential equations and approximation theory.

Problems in Mathematical Analysis: Continuity and differentiation

Author: Wiesława J. Kaczor,Maria T. Nowak

Publisher: American Mathematical Soc.

ISBN: 0821820516

Category: Mathematics

Page: 398

View: 3530

We learn by doing. We learn mathematics by doing problems. And we learn more mathematics by doing more problems. This is the sequel to Problems in Mathematical Analysis I (Volume 4 in the Student Mathematical Library series). If you want to hone your understanding of continuous and differentiable functions, this book contains hundreds of problems to help you do so. The emphasis here is on real functions of a single variable. The book is mainly geared toward students studying the basic principles of analysis. However, given its selection of problems, organization, and level, it would be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. It is also suitable for self-study. The presentation of the material is designed to help student comprehension, to encourage them to ask their own questions, and to start research. The collection of problems will also help teachers who wish to incorporate problems into their lectures. The problems are grouped into sections according to the methods of solution. Solutions for the problems are provided.

Analysis 1

Author: V. A. Zorich

Publisher: Springer-Verlag

ISBN: 3540332782

Category: Mathematics

Page: 598

View: 1214

Ausführlicher Einblick in die Anfänge der Analysis: von der Einführung der reellen Zahlen bis hin zu fortgeschrittenen Themen wie Differentialformen auf Mannigfaltigkeiten, asymptotische Betrachtungen, Fourier-, Laplace- und Legendre-Transformationen, elliptische Funktionen und Distributionen. Ausgerichtet auf naturwissenschaftliche Fragestellungen und in detaillierter Herangehensweise an die Integral- und Differentialrechnung. Mit einer Fülle hilfreicher Beispiele, Aufgaben und Anwendungen. In Band 1: vollständige Übersicht zur Integral- und Differentialrechnung einer Variablen, erweitert um die Differentialrechnung mehrerer Variablen.

Analysis II

Author: Herbert Amann,Joachim Escher

Publisher: Springer Science & Business Media

ISBN: 3764371056

Category: Mathematics

Page: 415

View: 8755

Wie schon der erste, enthait auch dieser zweite Band wesentlich mehr Stoff, als in einer einsemestrigen Vorlesung behandelt werden kann. Wir hoffen, dadurch den Leser anzuregen, im Selbststudium weiter in die Mathem tik einzudringen und vie.-. Ie schone und tiefgriindige Anwend ungen der Analysis kennfmzulernen und groJ3ere Zusammenhange zu erfahren. Dem Dozenten mochten wir geeignetes Material fiir Proseminare und Seminare zur Verfiigung stellen. Fiir einen Uberblick iiber den dargebotenen Stoff verweisen wir auf das aus fiihrliche Inhaltsverzeichnis sowie auf die Einleitungen zu den einzelnen Kapiteln. Hervorheben mochten wir die zahlreichen Ubungsaufgaben, deren Bearbeitung fUr das Verstandnis der Materie unabdingbar ist. Dariiber hinaus haben wir viele niitzliche Erganzungen und Abrundungen des im Haupttext behandelten Materials in den Aufgabenteil verlegt. Auch beim Schreiben dieses Bandes konnten wir uns auf die Hilfe Ande rer verlassen. Ganz besonders danken wir unseren Freunden und Kollegen Pavol Quittner und Gieri Simonett. Sie haben nicht nur groJ3e Teile des Manuskripts sorgfaitig gelesen und uns geholfen, Fehler auszumerzen, sondern durch ihre wert vollen Verbesserungsvorschlage wesentlich zur endgiiltigen Darstellung beigetra gen. Zu groJ3em Dank sind wir auch unseren Mitarbeitern Georg Prokert, Frank Weber und Bea Wollenmann verpflichtet fiir die sehr genaue Lektiire des gesamten Manuskripts und das Aufspiiren von Druckfehlern und Ungenauigkeiten. Unser allerherzlichster Dank gilt wieder unserem "Satzperfektionisten," ohne l dessen unermiidliche Arbeit dieses Buch nie in der vorliegenden perfekten Gestalt zustandegekommen ware, sowie Andreas, der uns wieder bei Hard-und Software Problemen zur Seite stand."

Analysis II

Third Edition

Author: Terence Tao

Publisher: Springer

ISBN: 9811018049

Category: Mathematics

Page: 220

View: 2929

This is part two of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

Analysis II

Convex Analysis and Approximation Theory

Author: R.V. Gamkrelidze

Publisher: Springer Science & Business Media

ISBN: 3642612679

Category: Mathematics

Page: 255

View: 7415

Intended for a wide range of readers, this book covers the main ideas of convex analysis and approximation theory. The author discusses the sources of these two trends in mathematical analysis, develops the main concepts and results, and mentions some beautiful theorems. The relationship of convex analysis to optimization problems, to the calculus of variations, to optimal control and to geometry is considered, and the evolution of the ideas underlying approximation theory, from its origins to the present day, is discussed. The book is addressed both to students who want to acquaint themselves with these trends and to lecturers in mathematical analysis, optimization and numerical methods, as well as to researchers in these fields who would like to tackle the topic as a whole and seek inspiration for its further development.

Problems in Mathematical Analysis

Author: Biler

Publisher: CRC Press

ISBN: 9780824783129

Category: Mathematics

Page: 244

View: 2117

Chapter 1 poses 134 problems concerning real and complex numbers, chapter 2 poses 123 problems concerning sequences, and so it goes, until in chapter 9 one encounters 201 problems concerning functional analysis. The remainder of the book is given over to the presentation of hints, answers or referen

Introduction to Calculus and Analysis

Author: Richard Courant,Fritz John

Publisher: Springer Science & Business Media

ISBN: 9783540665694

Category: Mathematics

Page: 556

View: 2111

Biography of Richard Courant Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called "a reservoir of talent" to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence. For Courant mathematics was an adventure, with applications forming a vital part. This spirit is reflected in his books, in particular in his influential calculus text, revised in collaboration with his brilliant younger colleague, Fritz John. (P.D. Lax) Biography of Fritz John Fritz John was born on June 14, 1910, in Berlin. After his school years in Danzig (now Gdansk, Poland), he studied in Göttingen and received his doctorate in 1933, just when the Nazi regime came to power. As he was half-Jewish and his bride Aryan, he had to flee Germany in 1934. After a year in Cambridge, UK, he accepted a position at the University of Kentucky, and in 1946 joined Courant, Friedrichs and Stoker in building up New York University the institute that later became the Courant Institute of Mathematical Sciences. He remained there until his death in New Rochelle on February 10, 1994. John's research and the books he wrote had a strong impact on the development of many fields of mathematics, foremost in partial differential equations. He also worked on Radon transforms, illposed problems, convex geometry, numerical analysis, elasticity theory. In connection with his work in latter field, he and Nirenberg introduced the space of the BMO-functions (bounded mean oscillations). Fritz John's work exemplifies the unity of mathematics as well as its elegance and its beauty. (J. Moser)

Analysis II

Author: Wolfgang Walter

Publisher: Springer-Verlag

ISBN: 3642967922

Category: Mathematics

Page: 398

View: 4988

Dem erfolgreichen Konzept von Analysis I folgend, wird auch im zweiten Teil dieses zweibändigen Analysis-Werkes viel Wert auf historische Zusammenhänge, Ausblicke und die Entwicklung der Analysis gelegt. Zu den Besonderheiten, die über den kanonischen Stoff des zweiten und dritten Semesters einer Analysisvorlesung hinausgehen, gehört das Lemma von Marston Morse. Die Grundtatsachen über die verschiedenen Integralbegriffe werden allesamt aus Sätzen über verallgemeinerte Limites (Moore-Smith-Konvergenz) abgeleitet. Die C?-Approximation von Funktionen (Friedrich Mollifiers) wird ebenso behandelt, wie die Theorie der absolut stetigen Funktionen. Bei den Fourierreihen wird die klassische Theorie in Weiterführung einer von Chernoff und Redheffer entwickelten Methode behandelt. Zahlreiche Beispiele, Übungsaufgaben und Anwendungen, z.B. aus der Physik und Astronomie runden dieses Lehrbuch ab.

Analysis II.

Author: Serge Lang

Publisher: Addison-Wesley

ISBN: N.A

Category: Mathematics

Page: 476

View: 2823

Analysis II

Author: Martin Barner

Publisher: Walter de Gruyter

ISBN: 3110808897

Category: Mathematics

Page: 449

View: 5117

Analysis II für Dummies

Author: Mark Zegarelli

Publisher: John Wiley & Sons

ISBN: 3527657983

Category: Mathematics

Page: 358

View: 4064

Nach der Analysis ist vor der Analysis. Dies ist das richtige Buch f?r Sie, wenn es in der Analysis ein wenig mehr sein soll oder auch muss. Mark Zegarelli erkl?rt Ihnen, was Sie zur infiniten Integration und zu differential- und multivariablen Gleichungen wissen m?ssen. Er f?hrt mit Taylorreihe und Substitutionen fort und f?hrt Sie auch in die Dritte Dimension der Analysis; und das ist lange noch nicht alles! Im Ton verbindlich, in der Sache kompetent f?hrt er Ihre Analysiskenntnisse auf eine neue Stufe.