Introduction To Analysis In Several Variables Advanced Calculus

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Introduction to Analysis in Several Variables: Advanced Calculus

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
ISBN 13 : 1470456699
Total Pages : 445 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to Analysis in Several Variables: Advanced Calculus by : Michael E. Taylor

Download or read book Introduction to Analysis in Several Variables: Advanced Calculus written by Michael E. Taylor and published by American Mathematical Soc.. This book was released on 2020-07-27 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advanced Calculus of Several Variables

Author : C. H. Edwards
Publisher : Academic Press
ISBN 13 : 1483268055
Total Pages : 470 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Advanced Calculus of Several Variables by : C. H. Edwards

Download or read book Advanced Calculus of Several Variables written by C. H. Edwards and published by Academic Press. This book was released on 2014-05-10 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advanced Calculus

Author : Lynn Harold Loomis
Publisher : World Scientific Publishing Company
ISBN 13 : 9814583952
Total Pages : 596 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Advanced Calculus by : Lynn Harold Loomis

Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Calculus of Several Variables

Author : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1461210682
Total Pages : 624 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Calculus of Several Variables by : Serge Lang

Download or read book Calculus of Several Variables written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advanced Calculus

Author : G. B. Folland
Publisher : Pearson
ISBN 13 : 9780130652652
Total Pages : 0 pages
Book Rating : 4.6/5 (526 download)

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Book Synopsis Advanced Calculus by : G. B. Folland

Download or read book Advanced Calculus written by G. B. Folland and published by Pearson. This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For undergraduate courses in Advanced Calculus and Real Analysis. This text presents a unified view of calculus in which theory and practice reinforce each other. It covers the theory and applications of derivatives (mostly partial), integrals, (mostly multiple or improper), and infinite series (mostly of functions rather than of numbers), at a deeper level than is found in the standard advanced calculus books.

Introduction to Analysis in One Variable

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
ISBN 13 : 1470456680
Total Pages : 247 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to Analysis in One Variable by : Michael E. Taylor

Download or read book Introduction to Analysis in One Variable written by Michael E. Taylor and published by American Mathematical Soc.. This book was released on 2020-08-11 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit) (expit), for real t t, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone–Weierstrass theorem, and Fourier series.

Mathematical Analysis

Author : Mariano Giaquinta
Publisher : Springer Science & Business Media
ISBN 13 : 0817644148
Total Pages : 399 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Mathematical Analysis by : Mariano Giaquinta

Download or read book Mathematical Analysis written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2012-08-31 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Embraces a broad range of topics in analysis requiring only a sound knowledge of calculus and the functions of one variable. * Filled with beautiful illustrations, examples, exercises at the end of each chapter, and a comprehensive index.

Mathematical Analysis

Author : Mariano Giaquinta
Publisher : Springer Science & Business Media
ISBN 13 : 0817646124
Total Pages : 348 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Mathematical Analysis by : Mariano Giaquinta

Download or read book Mathematical Analysis written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2010-07-25 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This superb and self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include the differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This text motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Advanced Calculus

Author : Voxman
Publisher : Routledge
ISBN 13 : 1351468677
Total Pages : 428 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Advanced Calculus by : Voxman

Download or read book Advanced Calculus written by Voxman and published by Routledge. This book was released on 2017-10-19 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Calculus: An Introduction to Modem Analysis, an advanced undergraduate textbook,provides mathematics majors, as well as students who need mathematics in their field of study,with an introduction to the theory and applications of elementary analysis. The text presents, inan accessible form, a carefully maintained balance between abstract concepts and applied results ofsignificance that serves to bridge the gap between the two- or three-cemester calculus sequence andsenior/graduate level courses in the theory and appplications of ordinary and partial differentialequations, complex variables, numerical methods, and measure and integration theory.The book focuses on topological concepts, such as compactness, connectedness, and metric spaces,and topics from analysis including Fourier series, numerical analysis, complex integration, generalizedfunctions, and Fourier and Laplace transforms. Applications from genetics, spring systems,enzyme transfer, and a thorough introduction to the classical vibrating string, heat transfer, andbrachistochrone problems illustrate this book's usefulness to the non-mathematics major. Extensiveproblem sets found throughout the book test the student's understanding of the topics andhelp develop the student's ability to handle more abstract mathematical ideas.Advanced Calculus: An Introduction to Modem Analysis is intended for junior- and senior-levelundergraduate students in mathematics, biology, engineering, physics, and other related disciplines.An excellent textbook for a one-year course in advanced calculus, the methods employed in thistext will increase students' mathematical maturity and prepare them solidly for senior/graduatelevel topics. The wealth of materials in the text allows the instructor to select topics that are ofspecial interest to the student. A two- or three ll?lester calculus sequence is required for successfuluse of this book.

Advanced Calculus

Author : James J. Callahan
Publisher : Springer Science & Business Media
ISBN 13 : 144197332X
Total Pages : 526 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Advanced Calculus by : James J. Callahan

Download or read book Advanced Calculus written by James J. Callahan and published by Springer Science & Business Media. This book was released on 2010-09-09 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advanced Calculus

Author : Louis Brand
Publisher : Courier Corporation
ISBN 13 : 0486445488
Total Pages : 610 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Advanced Calculus by : Louis Brand

Download or read book Advanced Calculus written by Louis Brand and published by Courier Corporation. This book was released on 2006-01-30 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: A course in analysis that focuses on the functions of a real variable, this text is geared toward upper-level undergraduate students. It introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, practical theorems, and coherent proofs. Starting with the structure of the system of real and complex numbers, the text deals at length with the convergence of sequences and series and explores the functions of a real variable and of several variables. Subsequent chapters offer a brief and self-contained introduction to vectors that covers important aspects, including gradients, divergence, and rotation. An entire chapter is devoted to the reversal of order in limiting processes, and the treatment concludes with an examination of Fourier series.

Advanced Calculus

Author : Louis Brand
Publisher :
ISBN 13 :
Total Pages : 606 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Advanced Calculus by : Louis Brand

Download or read book Advanced Calculus written by Louis Brand and published by . This book was released on 1955 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Calculus

Author : Avner Friedman
Publisher : Courier Corporation
ISBN 13 : 0486137864
Total Pages : 434 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Advanced Calculus by : Avner Friedman

Download or read book Advanced Calculus written by Avner Friedman and published by Courier Corporation. This book was released on 2012-10-16 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advanced Calculus

Author : Patrick Fitzpatrick
Publisher : American Mathematical Soc.
ISBN 13 : 0821847910
Total Pages : 610 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advanced Calculus by : Patrick Fitzpatrick

Download or read book Advanced Calculus written by Patrick Fitzpatrick and published by American Mathematical Soc.. This book was released on 2009 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.

Calculus on Manifolds

Author : Michael Spivak
Publisher : Westview Press
ISBN 13 : 9780805390216
Total Pages : 164 pages
Book Rating : 4.3/5 (92 download)

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Book Synopsis Calculus on Manifolds by : Michael Spivak

Download or read book Calculus on Manifolds written by Michael Spivak and published by Westview Press. This book was released on 1965 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Analysis

Author : Edward Gaughan
Publisher : American Mathematical Soc.
ISBN 13 : 0821847872
Total Pages : 258 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Analysis by : Edward Gaughan

Download or read book Introduction to Analysis written by Edward Gaughan and published by American Mathematical Soc.. This book was released on 2009 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section."--pub. desc.

Mathematical Analysis

Author : Mariano Giaquinta
Publisher : Springer Science & Business Media
ISBN 13 : 0817683100
Total Pages : 405 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Mathematical Analysis by : Mariano Giaquinta

Download or read book Mathematical Analysis written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2011-11-04 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory – Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations.