Real Analysis

Series, Functions of Several Variables, and Applications

Author: Miklós Laczkovich,Vera T. Sós

Publisher: Springer

ISBN: 149397369X

Category: Mathematics

Page: 392

View: 3167

This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes form the first English edition of the popular Hungarian original, Valós Analízis I & II, based on courses taught by the authors at Eötvös Loránd University, Hungary, for more than 30 years. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems. Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading. Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics. Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. By developing the student’s intuition throughout, many definitions and results become motivated by insights from their context.

Problems and Solutions in Real Analysis

Author: Masayoshi Hata

Publisher: World Scientific

ISBN: 981277601X

Category: Mathematics

Page: 292

View: 5581

This unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamental definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis together with useful references.Problems and Solutions in Real Analysis may be used as advanced exercises by undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the prime number theorem through several exercises. The book is also suitable for non-experts who wish to understand mathematical analysis.

A Course in Calculus and Real Analysis

Author: Sudhir R. Ghorpade,Balmohan V. Limaye

Publisher: Springer Science & Business Media

ISBN: 0387364250

Category: Mathematics

Page: 432

View: 4848

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.

Advanced Calculus

An Introduction to Classical Analysis

Author: Louis Brand

Publisher: Courier Corporation

ISBN: 0486157997

Category: Mathematics

Page: 608

View: 6742

A course in analysis that focuses on the functions of a real variable, this text introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, theorems, and proofs. 1955 edition.

Real Analysis and Applications

Theory in Practice

Author: Kenneth R. Davidson,Allan P. Donsig

Publisher: Springer Science & Business Media

ISBN: 0387980989

Category: Mathematics

Page: 513

View: 4171

This new approach to real analysis stresses the use of the subject with respect to applications, i.e., how the principles and theory of real analysis can be applied in a variety of settings in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization. Users will be prepared for more intensive work in each topic through these applications and their accompanying exercises. This book is appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra.

Advanced Calculus of Several Variables

Author: C. H. Edwards

Publisher: Courier Corporation

ISBN: 0486131955

Category: Mathematics

Page: 480

View: 5437

Modern conceptual treatment of multivariable calculus, emphasizing interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. Over 400 well-chosen problems. 1973 edition.

Advanced Calculus

An Introduction to Modern Analysis

Author: Voxman

Publisher: CRC Press

ISBN: 9780824769499

Category: Mathematics

Page: 696

View: 5546

Introduction to linear algebra and ordinary differential equations; Limits and metric spaces; Continuity, compactness and connectedness; The derivative: theory and elementary applications; A first look at integration; Differentiation of functions of several variables; An introduction to fourier analysis; An introduction to modern integration theory; An introduction to complex integration.

Real Mathematical Analysis

Author: Charles Chapman Pugh

Publisher: Springer Science & Business Media

ISBN: 0387216847

Category: Mathematics

Page: 440

View: 4863

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.

A First Course in Sobolev Spaces: Second Edition

Author: Giovanni Leoni

Publisher: American Mathematical Soc.

ISBN: 1470429217

Category: Sobolev spaces

Page: 734

View: 6841

This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue–Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincaré's inequalities and traces. A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.

Inequalities from Complex Analysis

Author: John P. D'Angelo

Publisher: MAA

ISBN: 9780883850336

Category: Mathematics

Page: 264

View: 2694

Inequalities from Complex Analysis is a careful, friendly exposition of inequalities and positivity conditions for various mathematical objects arising in complex analysis. The author begins by defining the complex number field, and then discusses enough mathematical analysis to reach recently published research on positivity conditions for functions of several complex variables. The development culminates in complete proofs of a stabilization theorem relating two natural positivity conditions for real-valued polynomials of several complex variables. The reader will also encounter the Bergman kernel function, Fourier series, Hermitian linear algebra, the spectral theorem for compact Hermitian operators, plurisubharmonic functions, and some delightful inequalities. Numerous examples, exercises, and discussions of geometric reasoning appear along the way. Undergraduate mathematics majors who have seen elementary real analysis can easily read the first five chapters of this book, and second year graduate students in mathematics can read the entire text. Some physicists and engineers may also find the topics and discussions useful. The inequalities and positivity conditions herein form the foundation for a small but beautiful part of complex analysis. ohn P. D'Angelo was the 1999 winner of the Bergman Prize; he was cited for several important contributions to complex analysis, including his work on degenerate Levi forms and points of finite type, as well as work, some joint with David Catlin, on positivity conditions in complex analysis.

Measure and Integral

An Introduction to Real Analysis, Second Edition

Author: Richard L. Wheeden

Publisher: CRC Press

ISBN: 1498702902

Category: Mathematics

Page: 532

View: 4486

Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content. Published nearly forty years after the first edition, this long-awaited Second Edition also: Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 p Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of Hölder continuous functions and the space of functions of bounded mean oscillation Derives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension Extends the subrepresentation formula derived for smooth functions to functions with a weak gradient Applies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincaré–Sobolev inequalities, including endpoint cases Proves the existence of a tangent plane to the graph of a Lipschitz function of several variables Includes many new exercises not present in the first edition This widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.

Elements of the Theory of Functions

Author: Konrad Knopp

Publisher: Courier Dover Publications

ISBN: 0486165604

Category: Mathematics

Page: 160

View: 3364

Well-known book provides a clear, concise review of complex numbers and their geometric representation; linear functions and circular transformations; sets, sequences, and power series; analytic functions and conformal mapping; and elementary functions. 1952 edition.

Fourier Series and Orthogonal Functions

Author: Harry F. Davis

Publisher: Courier Corporation

ISBN: 0486140733

Category: Mathematics

Page: 432

View: 9842

An incisive text combining theory and practical example to introduce Fourier series, orthogonal functions and applications of the Fourier method to boundary-value problems. Includes 570 exercises. Answers and notes.

Lineare Algebra

Author: Gilbert Strang

Publisher: Springer-Verlag

ISBN: 3642556310

Category: Mathematics

Page: 656

View: 5729

Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

Complex Variables and the Laplace Transform for Engineers

Author: Wilbur R. LePage

Publisher: Courier Corporation

ISBN: 0486136442

Category: Technology & Engineering

Page: 512

View: 7141

Acclaimed text on engineering math for graduate students covers theory of complex variables, Cauchy-Riemann equations, Fourier and Laplace transform theory, Z-transform, and much more. Many excellent problems.

A Treatise on Advanced Calculus

Author: Philip Franklin

Publisher: Courier Dover Publications

ISBN: 048680707X

Category: Mathematics

Page: 608

View: 8926

This classic offers a comprehensive logical treatment that concentrates on theory rather than on techniques and applications, providing students with a substantial base for graduate work in physics. 1940 edition.

Mathematical Analysis

Author: S. C. Malik

Publisher: N.A

ISBN: 9781781831045


Page: 882

View: 7599

Key Features:Y New edition in multi-colour with improvised figuresY New version of outstanding textbook catering to international segmentsY Well developed, rigorous and not too pedantic subject matterY Application of modern methods to smooth out and shorten classical techniquesY Special effort has been made to include most of the lecture notes based on authors' decadal teachingexperience.About the Book:The book is intended to serve as a text in Mathematical Analysis for the undergraduate and postgraduatestudents of various universities. Professionals will also find this book useful.The book has theory from its very beginning. The foundations have been laid very carefully and thetreatment is rigorous based on modern lines. It opens with a brief outline of the essential properties ofrational numbers and using Dedekind's cut, the properties of real numbers are also established. Thisfoundation supports the subsequent chapters: Topological Framework Real Sequences and Series,Continuity, Differentiation, Functions of Several Variables, Elementary and Implicit Functions, Riemannand Riemann-Stieltjes Integrals, Lebesgue Integrals, Surface, Double and Triple Integrals are discussedin detail. Uniform Convergence, Power Series, Fourier Series, Improper Integrals have been presented inas simple and lucid manner as possible. Number of solved examples to illustrate various types have alsobeen included.As per need, in the present atmosphere, a chapter on Metric Spaces discussing completeness,compactness and connectedness of the spaces has been added. Finally, two appendices discussing Beta-Gamma functions, and Cantor's theory of real numbers, add glory to the contents of the book.

Von Fermat bis Minkowski

Eine Vorlesung über Zahlentheorie und ihre Entwicklung

Author: W. Scharlau,H. Opolka

Publisher: Springer-Verlag

ISBN: 3642618499

Category: Mathematics

Page: 226

View: 5085


Author: Reinhold Remmert

Publisher: N.A

ISBN: 9783540553847

Category: Functions of complex variables

Page: 299

View: 9335

Diese dritte Auflage wurde zusammen mit dem zweitgenannten Autor kritisch durchgesehen, ergnzt und verbessert. Ein weiteres Kapitel ber geometrische Funktionentheorie und schlichte Funktionen enthlt einen Beweis der Bieberbachschen Vermutung. Der ... vorliegende zweite Band der Funktionentheorie erfllt voll die Erwartungen, die der erste Band geweckt hat. Wieder beeindrucken vor allem die hochinteressanten historischen Bemerkungen zu den einzelnen Themenkreisen, als besonderer Leckerbissen wird das Gutachten von Gau ber Riemanns Dissertation vorgestellt... Jedes einzelne Kapitel enthlt ausfhrliche Literaturangaben. Ferner werden oft sehr aufschlussreiche Hinweise auf die Funktionentheorie mehrerer Vernderlicher gegeben. Die vielen Beispiele und bungsaufgaben bilden eine wertvolle Ergnzung der brillant dargelegten Theorie. Der Rezensent bedauert, dass ihm nicht schon als Student ein derartig umfassendes, qualitativ hochstehendes Lehrbuch zur Verfgung stand." Monatshefte fr Mathematik