Advanced Calculus And Vector Field Theory

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Advanced Calculus and Vector Field Theory

Author : Kathleen M. Urwin
Publisher : Elsevier
ISBN 13 : 1483195333
Total Pages : 279 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Advanced Calculus and Vector Field Theory by : Kathleen M. Urwin

Download or read book Advanced Calculus and Vector Field Theory written by Kathleen M. Urwin and published by Elsevier. This book was released on 2014-06-05 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: THIS book falls naturally into two parts. In Chapters 1-5 the basic ideas and techniques of partial differentiation, and of line, multiple and surface integrals are discussed. Chapters 6 and 7 give the elements of vector field theory, taking the integral definitions of the divergence and curl of a vector field as their starting points; the last chapter surveys very briefly some of the immediate applications of vector field theory to five branches of applied mathematics. Throughout I have given numerous worked examples. In these I have paid particular attention to those points which in my own experience I have found to give most difficulty to students. In the text I have denoted spherical polar coordinates by (/-, 0, ?)9 and cylindrical polar coordinates by (p, ?, ?), so that ? measures the same angle in both systems. Since there is no one standard notation for these systems, the reader will meet different notations in the course of his reading, and in quoting examination questions in the exercises I have kept to the notation of the originals. The Exercises at the end of each section are intended to give practice in the basic techniques just discussed. The Miscellaneous Exercises are more varied, and contain many examination questions.

Advanced Calculus (Revised Edition)

Author : Lynn Harold Loomis
Publisher : World Scientific Publishing Company
ISBN 13 : 9814583952
Total Pages : 595 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Advanced Calculus (Revised Edition) by : Lynn Harold Loomis

Download or read book Advanced Calculus (Revised Edition) written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 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.

Advanced Calculus

Author : Wilfred Kaplan
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 744 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Advanced Calculus by : Wilfred Kaplan

Download or read book Advanced Calculus written by Wilfred Kaplan and published by Addison Wesley Publishing Company. This book was released on 1984 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fifth Edition of this leading text offers substantial training in vectors and matrices, vector analysis, and partial differential equations. Vectors are introduced at the outset and serve at many points to indicate geometrical and physical significance of mathematical relations. Numerical methods are touched upon at various points, because of their practical value and the insights they give about theory. Vectors and Matrices; Differential Calculus of Functions of Several Variables; Vector Differential Calculus; Integral Calculus of Functions of Several Variables; Vector Integral Calculus; Two-Dimensional Theory; Three-Dimensional Theory and Applications; Infinite Series; Fourier Series and Orthogonal Functions; Functions of a Complex Variable; Ordinary Differential Equations; Partial Differential Equations For all readers interested in advanced calculus.

Calculus Using Mathematica

Author : K.D. Stroyan
Publisher : Academic Press
ISBN 13 : 1483214346
Total Pages : 366 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Calculus Using Mathematica by : K.D. Stroyan

Download or read book Calculus Using Mathematica written by K.D. Stroyan and published by Academic Press. This book was released on 2014-05-10 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus Using Mathematica: Scientific Projects and Mathematical Background is a companion to the core text, Calculus Using Mathematica. The book contains projects that illustrate applications of calculus to a variety of practical situations. The text consists of 14 chapters of various projects on how to apply the concepts and methodologies of calculus. Chapters are devoted to epidemiological applications; log and exponential functions in science; applications to mechanics, optics, economics, and ecology. Applications of linear differential equations; forced linear equations; differential equations from vector geometry; and to chemical reactions are presented as well. College students of calculus will find this book very helpful.

Multivariable Mathematics

Author : Theodore Shifrin
Publisher : John Wiley & Sons
ISBN 13 : 047152638X
Total Pages : 514 pages
Book Rating : 4.4/5 (715 download)

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Book Synopsis Multivariable Mathematics by : Theodore Shifrin

Download or read book Multivariable Mathematics written by Theodore Shifrin and published by John Wiley & Sons. This book was released on 2004-01-26 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Student Solution Manual to Accompany the 4th Edition of Vector Calculus, Linear Algebra, and Differential Forms, a Unified Approach

Author : John Hamal Hubbard
Publisher :
ISBN 13 : 9780971576674
Total Pages : 284 pages
Book Rating : 4.5/5 (766 download)

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Book Synopsis Student Solution Manual to Accompany the 4th Edition of Vector Calculus, Linear Algebra, and Differential Forms, a Unified Approach by : John Hamal Hubbard

Download or read book Student Solution Manual to Accompany the 4th Edition of Vector Calculus, Linear Algebra, and Differential Forms, a Unified Approach written by John Hamal Hubbard and published by . This book was released on 2009 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 : Tomá¿ Kisela
Publisher :
ISBN 13 : 9781681178998
Total Pages : 346 pages
Book Rating : 4.1/5 (789 download)

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Book Synopsis Advanced Calculus by : Tomá¿ Kisela

Download or read book Advanced Calculus written by Tomá¿ Kisela and published by . This book was released on 2018-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus is a very multipurpose and valuable tool. It is one of the greatest inventions of modern science. There is just so much it can offer. The success of calculus has been extended over time into various other important topics in mathematics. Some are: differential equations, vector calculus, calculus of variations, complex analysis and differential topology. Calculus is intensely integrated in every branch of the physical sciences, such as physics and biology. It is found in computer science, statistics, and engineering; in economics, business, and medicine. Modern developments such as architecture, aviation, and other technologies all make use of what calculus can offer. This book "Advanced Calculus" is intended to present coverage on harmonic analysis, integral transforms and equations, ordinary and partial differential equations, measure and integration, sequences and series, functional analysis, functions of real and complex variables, approximation and expansions. It gives an exposition of methods for approximating integrals, including those that are multidimensional. Applications of some of these methods in statistics are discussed. This subject area has recently gained prominence in several fields of science and engineering, and, in particular, Bayesian statistics. The material should be helpful to readers who may be interested in pursuing further studies in this area. Advanced calculus has had a fundamental and seminal role in the development of the basic theory underlying statistical methodology. With the rapid growth of statistics as a discipline, particularly in the last three decades, knowledge of advanced calculus has become imperative for understanding the recent advances in this field. Students as well as research workers in statistics are expected to have a certain level of mathematical sophistication in order to cope with the intricacies necessitated by the emerging of new statistical methodologies. This book is unique also in its special attention to the needs of applications and due to its unusually elaborate motivations coming from the history of mathematics and applications. This book is designed for advanced graduate students, practitioners as well as for those who are novice researchers in this field.

Advanced Calculus

Author : H.K Nickerson
Publisher : Courier Corporation
ISBN 13 : 0486173747
Total Pages : 561 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Advanced Calculus by : H.K Nickerson

Download or read book Advanced Calculus written by H.K Nickerson and published by Courier Corporation. This book was released on 2013-02-28 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with an abstract treatment of vector spaces and linear transforms, this introduction presents a corresponding theory of integration and concludes with applications to analytic functions of complex variables. 1959 edition.

Calculus On Manifolds

Author : Michael Spivak
Publisher : CRC Press
ISBN 13 : 0429981538
Total Pages : 162 pages
Book Rating : 4.4/5 (299 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 CRC Press. This book was released on 2018-05-04 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This little book is especially concerned with those portions of ?advanced calculus? in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.

Schaums Outline of Advanced Calculus, Second Edition

Author : Robert C. Wrede
Publisher : McGraw Hill Professional
ISBN 13 : 9780071375672
Total Pages : 460 pages
Book Rating : 4.3/5 (756 download)

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Book Synopsis Schaums Outline of Advanced Calculus, Second Edition by : Robert C. Wrede

Download or read book Schaums Outline of Advanced Calculus, Second Edition written by Robert C. Wrede and published by McGraw Hill Professional. This book was released on 2002-02-20 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Confusing Textbooks? Missed Lectures? Not Enough Time? Fortunately for you, theres Schaums Outlines. More than 40 million students have trusted Schaums to help them succeed in the classroom and on exams. Schaums is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaums Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaums highlights all the important facts you need to know. Use Schaums to shorten your study time-and get your best test scores! Schaums Outlines-Problem Solved.

Catalog of Copyright Entries. Third Series

Author : Library of Congress. Copyright Office
Publisher : Copyright Office, Library of Congress
ISBN 13 :
Total Pages : 548 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Catalog of Copyright Entries. Third Series by : Library of Congress. Copyright Office

Download or read book Catalog of Copyright Entries. Third Series written by Library of Congress. Copyright Office and published by Copyright Office, Library of Congress. This book was released on 1968 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamentals of Advanced Mathematics V2

Author : Henri Bourles
Publisher : Elsevier
ISBN 13 : 0081023855
Total Pages : 362 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Fundamentals of Advanced Mathematics V2 by : Henri Bourles

Download or read book Fundamentals of Advanced Mathematics V2 written by Henri Bourles and published by Elsevier. This book was released on 2018-02-03 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. Whereas the first volume focused on the formal conditions for systems of linear equations (in particular of linear differential equations) to have solutions, this book presents the approaches to finding solutions to polynomial equations and to systems of linear differential equations with varying coefficients. Fundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves begins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known). In addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems. Present Galois Theory, transcendental field extensions, and Picard Includes sections on Vessiot theory, differentially transcendental field extensions, topology, topological vector spaces, Radon measure, differential calculus in Banach spaces, sheaves, distributions, hyperfunctions, algebraic analysis, and local analysis of systems of linear differential equations

Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding

Author : Terrance J Quinn
Publisher : World Scientific
ISBN 13 : 9811222584
Total Pages : 250 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding by : Terrance J Quinn

Download or read book Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding written by Terrance J Quinn and published by World Scientific. This book was released on 2020-07-24 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.

Advanced Calculus

Author : Hans Sagan
Publisher : Houghton Mifflin
ISBN 13 :
Total Pages : 700 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Advanced Calculus by : Hans Sagan

Download or read book Advanced Calculus written by Hans Sagan and published by Houghton Mifflin. This book was released on 1974 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Classical Field Theory

Author : G. Giachetta
Publisher : World Scientific
ISBN 13 : 9812838961
Total Pages : 393 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Advanced Classical Field Theory by : G. Giachetta

Download or read book Advanced Classical Field Theory written by G. Giachetta and published by World Scientific. This book was released on 2009 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo are presented in a complete way. This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.