several real variables

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Functions Of Several Real Variables

Author : Martin A. Moskowitz
ISBN : 9789814299268
Genre : Mathematics
File Size : 82. 53 MB
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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
ISBN : 9783319279565
Genre : Mathematics
File Size : 51. 60 MB
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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.

Functions Of Several Real Variables

Author : J. R. L. Webb
ISBN : CORNELL:31924068834203
Genre : Mathematics
File Size : 86. 43 MB
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Investigations On The Theory Of Functions Of Several Real Variables And The Approximation Of Functions

Author : Sergej L. Sobolev
ISBN : LCCN:87031832
Genre : Approximation theory
File Size : 69. 33 MB
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Real Variable Methods In Harmonic Analysis

Author : Alberto Torchinsky
ISBN : 9781483268880
Genre : Mathematics
File Size : 28. 5 MB
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Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.

Investigations On The Theory Of Functions Of Several Real Variables And The Approximation Of Functions

Author : Sergej L. Sobolev
ISBN : LCCN:87031832
Genre : Approximation theory
File Size : 59. 21 MB
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Theory And Applications Of Differentiable Functions Of Several Variables

Author : Sergeĭ Mikhaĭlovich Nikolʹskiĭ
ISBN : 0821831178
Genre : Mathematics
File Size : 60. 83 MB
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A Comprehensive Textbook Of Classical Mathematics

Author : H.B. Griffiths
ISBN : 9781461263210
Genre : Mathematics
File Size : 46. 99 MB
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arithmetic of the integers, linear algebra, an introduction to group theory, the theory of polynomial functions and polynomial equations, and some Boolean algebra. It could be supplemented, of course, by material from other chapters. Again, Course 5 (Calculus) aiscusses the differential and integral calculus more or less from the beginnings of these theories, and proceeds through functions of several real variables, functions of a complex variable, and topics of real analysis such as the implicit function theorem. We would, however, like to make a further point with regard to the appropriateness of our text in course work. We emphasized in the Introduction to the original edition that, in the main, we had in mind the reader who had already met the topics once and wished to review them in the light of his (or her) increased knowledge and mathematical maturity. We therefore believe that our book could form a suitable basis for American graduate courses in the mathematical sciences, especially those prerequisites for a Master's degree.

Functions Of Several Variables

Author : Pramila Srivastava
ISBN : UCAL:B4036904
Genre : Mathematics
File Size : 67. 8 MB
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Elementary Theory Of Analytic Functions Of One Or Several Complex Variables

Author : Henri Cartan
ISBN : 9780486318677
Genre : Mathematics
File Size : 26. 21 MB
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Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.

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