Functions of Several Real Variables

Author: Martin A. Moskowitz,Fotios Paliogiannis

Publisher: World Scientific

ISBN: 981429926X

Category: Mathematics

Page: 716

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This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one theorem upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify the theory and teach the reader how to apply it to solve problems in mathematics and other sciences and economics. Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Brouwer's fixed point theorem, Picard's theorem and the Weierstrass approximation theorem are discussed in stared sections.

Several Real Variables

Author: Shmuel Kantorovitz

Publisher: Springer

ISBN: 3319279564

Category: Mathematics

Page: 307

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This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as: •The p-norms on vector space and their equivalence •The Weierstrass and Stone-Weierstrass approximation theorems •The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables •The Implicit Function Theorem for a system of equations, proved via Banach’s Fixed Point Theorem •Applications to Ordinary Differential Equations •Line integrals and an introduction to surface integrals This book features numerous examples, detailed proofs, as well as exercises at the end of sections. Many of the exercises have detailed solutions, making the book suitable for self-study. Several Real Variables will be useful for undergraduate students in mathematics who have completed first courses in linear algebra and analysis of one real variable.

Advanced calculus

Functions of several variables

Author: Roman Sikorski

Publisher: N.A


Category: Mathematics

Page: 460

View: 6060

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Continuous Functions of Vector Variables

Author: Alberto Guzman

Publisher: Springer Science & Business Media

ISBN: 1461200830

Category: Mathematics

Page: 210

View: 5341

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This is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. The author covers boundedness, extreme values, and uniform continuity of functions, along with connections between continuity and topological concepts such as connectedness and compactness. The order of topics mimics the order of development in elementary calculus, with analogies and generalizations from such familiar ideas as the Pythagorean theorem.

Functions of Several Variables

Author: Wendell Fleming

Publisher: Springer Science & Business Media

ISBN: 1468494619

Category: Mathematics

Page: 412

View: 7149

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This new edition, like the first, presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. However, an additional chapter on elementary topology makes the book more complete as an advanced calculus text, and sections have been added introducing physical applications in thermodynamics, fluid dynamics, and classical rigid body mechanics.

A Course in Multivariable Calculus and Analysis

Author: Sudhir R. Ghorpade,Balmohan V. Limaye

Publisher: Springer Science & Business Media

ISBN: 1441916210

Category: Mathematics

Page: 475

View: 9734

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This self-contained textbook gives a thorough exposition of multivariable calculus. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike.

Elements of Mathematics Functions of a Real Variable

Elementary Theory

Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 9783540653400

Category: Mathematics

Page: 338

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This is an English translation of Bourbaki’s Fonctions d'une Variable Réelle. Coverage includes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.

Calculus of several variables

Author: Serge Lang

Publisher: Addison Wesley Publishing Company


Category: Mathematics

Page: 479

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This is a new, revised edition of this widely known text. All of the basic topics in calculus of several variables are covered, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green's theorem, multiple integrals, surface integrals, Stokes' theorem, and the inverse mapping theorem and its consequences. The presentation is self-contained, assuming only a knowledge of basic calculus in one variable. Many completely worked-out problems have been included.

Theory and Applications of Differentiable Functions of Several Variables

Collection of Papers : Dedicated to Academician Sergeĭ Mikhaĭlovich Nikolʹskiĭ on His Eighty-fifth Birthday

Author: Sergei Mikhailovich Nicol'skii,L. D. Kudryavtsev

Publisher: American Mathematical Soc.

ISBN: 9780821803387

Category: Differentiable functions

Page: 286

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This book is dedicated to Sergei Mikhailovich Nikolskii on the occasion of his eighty-fifth birthday. The collection contains new results on the following topics: approximation of functions, imbedding theory, interpolation of function spaces, convergence of series in trigonometric and general orthogonal systems, quasilinear elliptic problems, spectral theory of nonselfadjoint operators, asymptotic properties of pseudodifferential operators, and methods of approximate solution of Laplace's equation.

Functions of Two Variables

Author: Sean Dineen

Publisher: CRC Press

ISBN: 9781584881902

Category: Mathematics

Page: 208

View: 9297

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Multivariate calculus, as traditionally presented, can overwhelm students who approach it directly from a one-variable calculus background. There is another way-a highly engaging way that does not neglect readers' own intuition, experience, and excitement. One that presents the fundamentals of the subject in a two-variable context and was set forth in the popular first edition of Functions of Two Variables. The second edition goes even further toward a treatment that is at once gentle but rigorous, atypical yet logical, and ultimately an ideal introduction to a subject important to careers both within and outside of mathematics. The author's style remains informal and his approach problem-oriented. He takes care to motivate concepts prior to their introduction and to justify them afterwards, to explain the use and abuse of notation and the scope of the techniques developed. Functions of Two Variables, Second Edition includes a new section on tangent lines, more emphasis on the chain rule, a rearrangement of several chapters, refined examples, and more exercises. It maintains a balance between intuition, explanation, methodology, and justification, enhanced by diagrams, heuristic comments, examples, exercises, and proofs.