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Author | Martin A. Moskowitz | |

ISBN-10 | 9789814299268 | |

Release | 2011 | |

Pages | 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. |

Author | J. R. L. Webb | |

ISBN-10 | CORNELL:31924068834203 | |

Release | 1991 | |

Pages | 289 | |

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Functions of several real variables has been writing in one form or another for most of life. You can find so many inspiration from Functions of several real variables also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Functions of several real variables book for free. |

Author | Shmuel Kantorovitz | |

ISBN-10 | 9783319279565 | |

Release | 2016-02-09 | |

Pages | 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. |

Author | Wendell H Fleming | |

ISBN-10 | 9781468494617 | |

Release | 2012-12-06 | |

Pages | 412 | |

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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. |

Author | Hubert Brian Griffiths | |

ISBN-10 | STANFORD:36105033141032 | |

Release | 1970 | |

Pages | 637 | |

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A comprehensive textbook of classical mathematics has been writing in one form or another for most of life. You can find so many inspiration from A comprehensive textbook of classical mathematics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full A comprehensive textbook of classical mathematics book for free. |

Author | Mariano Giaquinta | |

ISBN-10 | 9781461200079 | |

Release | 2012-12-06 | |

Pages | 353 | |

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For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today the traditional place of mathematics in education is in grave danger. Unfortunately, professional representatives of mathematics share in the reponsibiIity. The teaching of mathematics has sometimes degen erated into empty drill in problem solving, which may develop formal ability but does not lead to real understanding or to greater intellectual indepen dence. Mathematical research has shown a tendency toward overspecialization and over-emphasis on abstraction. Applications and connections with other fields have been neglected . . . But . . . understanding of mathematics cannot be transmitted by painless entertainment any more than education in music can be brought by the most brilliant journalism to those who never have lis tened intensively. Actual contact with the content of living mathematics is necessary. Nevertheless technicalities and detours should be avoided, and the presentation of mathematics should be just as free from emphasis on routine as from forbidding dogmatism which refuses to disclose motive or goal and which is an unfair obstacle to honest effort. (From the preface to the first edition of What is Mathematics? by Richard Courant and Herbert Robbins, 1941. |

Author | Pramila Srivastava | |

ISBN-10 | UCAL:B4036904 | |

Release | 1990 | |

Pages | 151 | |

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Functions of several variables has been writing in one form or another for most of life. You can find so many inspiration from Functions of several variables also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Functions of several variables book for free. |

Author | Henri Cartan | |

ISBN-10 | 9780486318677 | |

Release | 2013-04-22 | |

Pages | 228 | |

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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. |

Author | Serge Lang | |

ISBN-10 | UOM:39015016357652 | |

Release | 1973 | |

Pages | 376 | |

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Calculus of several variables has been writing in one form or another for most of life. You can find so many inspiration from Calculus of several variables also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Calculus of several variables book for free. |

Author | Masayoshi Hata | |

ISBN-10 | 9789812776013 | |

Release | 2007 | |

Pages | 292 | |

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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. |

Author | S. M. Nikolskii | |

ISBN-10 | 0821802763 | |

Release | 1994 | |

Pages | 260 | |

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This book explores various topical trends in the theory of differentiable functions of several real variables and its applications. Among the subjects covered are: imbedding of various spaces of differentiable functions defined on sets in Euclidean space, on a sphere, and in a polydisc; approximation of functions; estimates for the norms of various integral operators in weighted space; conditions for stabilization of a function to a polynomial; sufficient conditions for multipliers; construction of unconditional bases in anisotropic spaces; existence of entire solutions for quasilinear equations; and establishment of an asymptotic formula for the kernels of powers of the resolvent of elliptic operators. |

Author | S. M. Nikol | |

ISBN-10 | 0821831526 | |

Release | 1994-03-29 | |

Pages | 265 | |

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This colletion is the fourteenth in an ongoing series on differentiable functions of several variables, presenting recent contributions to a line of research begun by Sobolev in 1950. The papers study various spaces of differentiable functions of several real variables in Euclidean space, their imbeddings, equivalent normings, weighted estimates of derivatives, and traces on sets. Several questions of approximation in function spaces on the line, on a hyperboloid, and on Lobachevsky space are studied. Investigations of bilinear approximations are applied to estimates of the singular numbers of integral operators and widths. The authors also examine the asymptotics of the spectrum of elliptic systems, as well as the Dirichlet variational problem for a degenerate elliptic operator. Finally, a block method of solving Laplace's equation for nonanalytic boundary conditions is developed. |

Author | Sergeĭ Lʹvovich Sobolev | |

ISBN-10 | LCCN:87031832 | |

Release | 1987 | |

Pages | 378 | |

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Investigations on the Theory of Functions of Several Real Variables and the Approximation of Functions has been writing in one form or another for most of life. You can find so many inspiration from Investigations on the Theory of Functions of Several Real Variables and the Approximation of Functions also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Investigations on the Theory of Functions of Several Real Variables and the Approximation of Functions book for free. |

Author | Michael Spivak | |

ISBN-10 | 0805390219 | |

Release | 1965 | |

Pages | 144 | |

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This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. |

Author | Roman Sikorski | |

ISBN-10 | WISC:89041213455 | |

Release | 1969 | |

Pages | 460 | |

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Advanced calculus has been writing in one form or another for most of life. You can find so many inspiration from Advanced calculus also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Advanced calculus book for free. |

Author | James J. Callahan | |

ISBN-10 | 144197332X | |

Release | 2010-09-09 | |

Pages | 526 | |

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With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study. |

Author | Charles F. Dunkl | |

ISBN-10 | 0521800439 | |

Release | 2001-02-22 | |

Pages | 390 | |

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Orthogonal polynomials of several variables, approximation theory, symmetry-group methods. |