Advanced Calculus Of Several Variables PDF Download
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Author | : C. H. Edwards |
Publisher | : Academic Press |
Total Pages | : 470 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483268055 |
Download Advanced Calculus of Several Variables Book in PDF, ePub and Kindle
Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence.
Author | : Michael E. Taylor |
Publisher | : American Mathematical Soc. |
Total Pages | : 445 |
Release | : 2020-07-27 |
Genre | : Education |
ISBN | : 1470456699 |
Download Introduction to Analysis in Several Variables: Advanced Calculus Book in PDF, ePub and Kindle
This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory. The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss–Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.
Author | : Lynn Harold Loomis |
Publisher | : World Scientific Publishing Company |
Total Pages | : 595 |
Release | : 2014-02-26 |
Genre | : Mathematics |
ISBN | : 9814583952 |
Download Advanced Calculus (Revised Edition) Book in PDF, ePub and Kindle
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author | : Serge Lang |
Publisher | : Springer Science & Business Media |
Total Pages | : 624 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461210682 |
Download Calculus of Several Variables Book in PDF, ePub and Kindle
This new, revised edition covers all of the basic topics in calculus of several variables, 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. It includes many completely worked-out problems.
Author | : Devendra Kumar |
Publisher | : ALPHA SCIENCE INTERNATIONAL LIMITED |
Total Pages | : 222 |
Release | : 2014-06-09 |
Genre | : Mathematics |
ISBN | : 1783320273 |
Download Advanced Calculus of Several Variables Book in PDF, ePub and Kindle
ADVANCED CALCULUS OF SEVERAL VARIABLES covers important topics of Transformations and topology on Euclidean in n-space Rn Functions of several variables, Differentiation in Rn, Multiple integrals and Integration in Rn. The topics have been presented in a simple clear and coherent style with a number of examples and exercises. Proofs have been made direct and simple. Unsolved problems just after relevant articles in the form of exercises and typical problems followed by suggestions have been given. This book will help the reader work on the problems of Numerical Analysis, Operations Research, Differential Equations and Engineering applications.
Author | : Avner Friedman |
Publisher | : Courier Corporation |
Total Pages | : 434 |
Release | : 2012-10-16 |
Genre | : Mathematics |
ISBN | : 0486137864 |
Download Advanced Calculus Book in PDF, ePub and Kindle
Intended for students who have already completed a one-year course in elementary calculus, this two-part treatment advances from functions of one variable to those of several variables. Solutions. 1971 edition.
Author | : James J. Callahan |
Publisher | : Springer Science & Business Media |
Total Pages | : 542 |
Release | : 2010-09-09 |
Genre | : Mathematics |
ISBN | : 144197332X |
Download Advanced Calculus Book in PDF, ePub and Kindle
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 | : Wendell Fleming |
Publisher | : Springer Science & Business Media |
Total Pages | : 420 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468494619 |
Download Functions of Several Variables Book in PDF, ePub and Kindle
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 | : Theodore Shifrin |
Publisher | : John Wiley & Sons |
Total Pages | : 514 |
Release | : 2004-01-26 |
Genre | : Mathematics |
ISBN | : 047152638X |
Download Multivariable Mathematics Book in PDF, ePub and Kindle
Multivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs. * Contains plenty of examples, clear proofs, and significant motivation for the crucial concepts. * Numerous exercises of varying levels of difficulty, both computational and more proof-oriented. * Exercises are arranged in order of increasing difficulty.
Author | : Michael Spivak |
Publisher | : Westview Press |
Total Pages | : 164 |
Release | : 1965 |
Genre | : Science |
ISBN | : 9780805390216 |
Download Calculus on Manifolds Book in PDF, ePub and Kindle
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.