Real Analysis

Author: John M. Howie

Publisher: Springer Science & Business Media

ISBN: 1447103416

Category: Mathematics

Page: 276

View: 6860

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Real Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, the book covers all the key topics with fully worked examples and exercises with solutions. All the concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject. This book offers a fresh approach to a core subject and manages to provide a gentle and clear introduction without sacrificing rigour or accuracy.

Essential Real Analysis

Author: Michael Field

Publisher: Springer

ISBN: 331967546X

Category: Mathematics

Page: 450

View: 7946

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This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.

Mathematische Modellierung

Author: Christof Eck,Harald Garcke,Peter Knabner

Publisher: Springer-Verlag

ISBN: 3662543354

Category: Mathematics

Page: 515

View: 3252

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Das Lehrbuch bietet eine lebendige und anschauliche Einführung in die mathematische Modellierung von Phänomenen aus den Natur- und Ingenieurwissenschaften. Leser lernen, mathematische Modelle zu verstehen und selbst herzuleiten und finden eine Fülle von Beispielen, u. a. aus den Bereichen chemische Reaktionskinetik, Populationsdynamik, Strömungsdynamik, Elastizitätstheorie und Kristallwachstum. Die Methoden der Linearen Algebra, der Analysis und der Theorie der gewöhnlichen und partiellen Differentialgleichungen werden sorgfältig eingeführt.

Differentialgleichungen für Dummies

Author: Steven Holzner

Publisher: John Wiley & Sons

ISBN: 3527658041

Category: Mathematics

Page: 327

View: 6370

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Als die Gute Fee H?nschen fragte: "was w?nschst Du dir?", antwortete er: "Keine Differentialgleichungen mehr in der Schule": Hans im Gl?ck! Jetzt k?nnen Sie auch auf eine Gute Fee warten, oder sich dieses Buch kaufen. Sie finden hier Hilfe sollten Sie mit linearen und nichtlinearen gew?hnlichen Differentialgleichungen ihre liebe M?he haben, seien sie nun erster, zweiter oder h?herer Ordnung. Sie lernen auch, was Sie zu Laplace Transformation, Potenzreihen und vielen anderen vertrackten Problemen wissen sollten. Sehen Sie der Realit?t ins Auge, mit diesem Buch.

The Real Numbers and Real Analysis

Author: Ethan D. Bloch

Publisher: Springer Science & Business Media

ISBN: 0387721762

Category: Mathematics

Page: 554

View: 6123

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This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.

Geschichte der Analysis

Author: Hans Niels Jahnke

Publisher: Spektrum Akademischer Verlag

ISBN: 9783827403926

Category: Mathematics

Page: 564

View: 7574

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"Geschichte der Analysis" ist von einem internationalen Expertenteam geschrieben und stellt die gegenwärtig umfassendste Darstellung der Herausbildung und Entwicklung dieser mathematischen Kerndisziplin dar. Der tiefgreifende begriffliche Wandel, den die Analysis im Laufe der Zeit durchgemacht hat, wird ebenso dargestellt, wie auch der Einfluß, den vor allem physikalische Probleme gehabt haben. Biographische und philosophische Hintergründe werden ausgeleuchtet und ihre Relevanz für die Theorieentwicklung gezeigt. Neben der eigentlichen Geschichte der Analysis bis ungefähr 1900 enthält das Buch Spezialkapitel über die Entwicklung der analytischen Mechanik im 18. Jahrhundert, Randwertprobleme der mathematischen Physik im 19. Jahrhundert, die Theorie der komplexen Funktionen, die Grundlagenkrise sowie historische Überblicke über die Variationsrechnung, Differentialgleichungen und Funktionalanalysis.

Analysis I

Author: Martin Barner,Friedrich Flohr

Publisher: Walter de Gruyter

ISBN: 3110854775

Category: Mathematics

Page: 554

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From Real to Complex Analysis

Author: R. H. Dyer,D. E. Edmunds

Publisher: Springer

ISBN: 3319062093

Category: Mathematics

Page: 332

View: 8222

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The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology. Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectedness and various forms of homotopy. The final chapter develops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using the approach due to Dixon. Special features are the inclusion of proofs of Montel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included in each of the chapters, detailed solutions of the majority of which are given at the end. From Real to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding in analysis; in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be made.

Real Mathematical Analysis

Author: Charles Chapman Pugh

Publisher: Springer Science & Business Media

ISBN: 0387216847

Category: Mathematics

Page: 440

View: 2827

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Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Introductory Mathematics: Algebra and Analysis

Author: Geoffrey C. Smith

Publisher: Springer Science & Business Media

ISBN: 1447106199

Category: Mathematics

Page: 215

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This text provides a lively introduction to pure mathematics. It begins with sets, functions and relations, proof by induction and contradiction, complex numbers, vectors and matrices, and provides a brief introduction to group theory. It moves onto analysis, providing a gentle introduction to epsilon-delta technology and finishes with continuity and functions. The book features numerous exercises of varying difficulty throughout the text.

Real Analysis

Foundations and Functions of One Variable

Author: Miklós Laczkovich,Vera T. Sós

Publisher: Springer

ISBN: 1493927663

Category: Mathematics

Page: 483

View: 4771

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Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.

Complex Analysis

Author: John M. Howie

Publisher: Springer Science & Business Media

ISBN: 1447100271

Category: Mathematics

Page: 260

View: 390

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Complex analysis can be a difficult subject and many introductory texts are just too ambitious for today’s students. This book takes a lower starting point than is traditional and concentrates on explaining the key ideas through worked examples and informal explanations, rather than through "dry" theory.

Real Analysis via Sequences and Series

Author: Charles H.C. Little,Kee L. Teo,Bruce van Brunt

Publisher: Springer

ISBN: 1493926519

Category: Mathematics

Page: 476

View: 2903

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This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

Real Analysis for the Undergraduate

With an Invitation to Functional Analysis

Author: Matthew A. Pons

Publisher: Springer Science & Business Media

ISBN: 1461496381

Category: Mathematics

Page: 409

View: 2077

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This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.

Analysis I

Author: Christiane Tretter

Publisher: Springer-Verlag

ISBN: 3034803494

Category: Mathematics

Page: 157

View: 5589

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Das Lehrbuch ist der erste von zwei einführenden Bänden in die Analysis. Es zeichnet sich dadurch aus, dass alle klassischen Themen der Analysis des ersten Semesters kompakt zusammengefasst sind und dennoch auf typische Anfängerprobleme eingegangen wird. Neben einer Einführung in die formale Sprache und die wichtigsten Beweistechniken der Mathematik bietet der Band eingängige Erläuterungen zu abstrakten Begriffen. Alle prüfungsrelevanten Inhalte sind abgedeckt und können anhand von Beispielen, Gegenbeispielen und Aufgaben nachvollzogen werden.

Foundations of Mathematical Analysis

Author: Saminathan Ponnusamy

Publisher: Springer Science & Business Media

ISBN: 0817682929

Category: Mathematics

Page: 570

View: 3971

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Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.

Distributionen Und Hilbertraumoperatoren

Mathematische Methoden Der Physik

Author: Philippe Blanchard,Erwin Brüning

Publisher: Springer

ISBN: 9783211825075

Category: Science

Page: 375

View: 6905

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Das Buch bietet eine Einführung in die zum Studium der Theoretischen Physik notwendigen mathematischen Grundlagen. Der erste Teil des Buches beschäftigt sich mit der Theorie der Distributionen und vermittelt daneben einige Grundbegriffe der linearen Funktionalanalysis. Der zweite Teil baut darauf auf und gibt eine auf das Wesentliche beschränkte Einführung in die Theorie der linearen Operatoren in Hilbert-Räumen. Beide Teile werden von je einer Übersicht begleitet, die die zentralen Ideen und Begriffe knapp erläutert und den Inhalt kurz beschreibt. In den Anhängen werden einige grundlegende Konstruktionen und Konzepte der Funktionalanalysis dargestellt und wichtige Konsequenzen entwickelt.