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Unified Mathematics Advanced Calculus
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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.
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.
Book Synopsis Advanced Calculus by : Harold M. Edwards
Download or read book Advanced Calculus written by Harold M. Edwards and published by Springer Science & Business Media. This book was released on 2013-11-10 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes’ theorem. The result is genuine mathematics, both in spirit and content, and an exciting choice for an honors or graduate course or indeed for any mathematician in need of a refreshingly informal and flexible reintroduction to the subject. For all these potential readers, the author has made the approach work in the best tradition of creative mathematics. This affordable softcover reprint of the 1994 edition presents the diverse set of topics from which advanced calculus courses are created in beautiful unifying generalization. The author emphasizes the use of differential forms in linear algebra, implicit differentiation in higher dimensions using the calculus of differential forms, and the method of Lagrange multipliers in a general but easy-to-use formulation. There are copious exercises to help guide the reader in testing understanding. The chapters can be read in almost any order, including beginning with the final chapter that contains some of the more traditional topics of advanced calculus courses. In addition, it is ideal for a course on vector analysis from the differential forms point of view. The professional mathematician will find here a delightful example of mathematical literature; the student fortunate enough to have gone through this book will have a firm grasp of the nature of modern mathematics and a solid framework to continue to more advanced studies. The most important feature...is that it is fun—it is fun to read the exercises, it is fun to read the comments printed in the margins, it is fun simply to pick a random spot in the book and begin reading. This is the way mathematics should be presented, with an excitement and liveliness that show why we are interested in the subject. —The American Mathematical Monthly (First Review) An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically rigorous, entertaining but serious. Remarkable diverse applications, physical and mathematical. —The American Mathematical Monthly (1994) Based on the Second Edition
Book Synopsis UNIFIED MATHEMATICS ADVANCED CALCULUS by : B. R. THAKUR
Download or read book UNIFIED MATHEMATICS ADVANCED CALCULUS written by B. R. THAKUR and published by Ram Prasad Publications(R.P.H.). This book was released on with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATHEMATICS, GANIT, RAM PRASAD, RPP UNFIED RP HARI KISHAN, THAKUR
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:
Book Synopsis A Course in Advanced Calculus by : Robert S. Borden
Download or read book A Course in Advanced Calculus written by Robert S. Borden and published by Courier Corporation. This book was released on 2012-09-11 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more. Carefully chosen problems appear at the end of each chapter, and this new edition features an additional appendix of tips and solutions for selected problems.
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.
Book Synopsis Old School Advanced Calculus by : William Fite
Download or read book Old School Advanced Calculus written by William Fite and published by Createspace Independent Publishing Platform. This book was released on 2018-03-11 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Old School Advanced Calculus is exactly what the title says it is: A full year course in advanced calculus the way it was offered at all American universities until the 1970's saw the sundering of the sequence into various "analysis for mathematicians" and "analysis for physical science students" courses. With the republication of this comprehensive, long-out-of-print text by Fite in a wonderfully inexpensive edition, the hope is to bring the advanced calculus course as it was taught for nearly half a century back into the consciousness of the 21st century mathematics and physical science students and educators. The main advantage of the original AC course, as exemplified by Fite, is a unified presentation of mathematical analysis comprised of virtually all the main topics of undergraduate analysis needed by both mathematics and physical science majors, covered using a uniform terminology and level of rigor. Even if each semester was taught by a different faculty member, they were both bound by more or less the same syllabus, which limited their ability to diverge from it drastically. When the subject selection, notation and rigor level is consistent throughout like it is with books like Fine's, then a balance that benefits all involved is achieved and maintained in the entire course. Pure mathematics students get exposed to important physical and geometric applications along with mathematical rigor. Physics and engineering students get exposed to pure mathematics and the abstract minimalist deductive skills it builds in them that will be invaluable when they begin research. Fite, in particular, does a terrific job of combining a careful "epsilon-delta' presentation of calculus of one and several variables with many applications to classical physics, differential equations and geometry. This book can be used for a number of different courses, either a standard classical advanced calculus course, an honors calculus course for strong freshman or independent reading by students or professors of analysis. Requiring only a year-long basic single variable calculus course as prerequisite, a course based on this book will give both the beginning mathematics major and serious physics or engineering major a thorough grounding in classical analysis and it's many applications in preparation for further research in either real variables or mathematical physics. A lengthy new preface has been added by Karo Maestro explaining the history of the advanced calculus course in America and where Fite's book was groundbreaking as one of the first standard such texts. He has also added a recommended reading section reviewing many of the other standard classical analysis texts for additional reading.
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.
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.
Book Synopsis Advanced Calculus by : David V. Widder
Download or read book Advanced Calculus written by David V. Widder and published by Courier Corporation. This book was released on 2012-05-23 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic text offers exceptionally precise coverage of partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Includes exercises and selected answers.
Book Synopsis Advanced Mathematics by : Leonard Keith Turner
Download or read book Advanced Mathematics written by Leonard Keith Turner and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advanced Calculus by : John Petrovic
Download or read book Advanced Calculus written by John Petrovic and published by CRC Press. This book was released on 2020-08-05 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Calculus: Theory and Practice, Second Edition offers a text for a one- or two-semester course on advanced calculus or analysis. The text improves students’ problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics. The book explains how various topics in calculus may seem unrelated but have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems. Features of the Second Edition: Improved Organization. Chapters are reorganized to address common preferences. Enhanced Coverage of Axiomatic Systems. A section is added to include Peano’s system of axioms for the set of natural numbers and their use in developing the well-known properties of the set N. Expanded and Organized Exercise Collection. There are close to 1,000 new exercises, many of them with solutions or hints. Exercises are classified based on the level of difficulty. Computation-oriented exercises are paired and solutions or hints provided for the odd-numbered questions. Enrichment Material. Historical facts and biographies of over 60 mathematicians. Illustrations. Thirty-five new illustrations are added in order to guide students through examples or proofs. About the Author: John Srdjan Petrovic is a professor at Western Michigan University.
Book Synopsis Advanced Calculus. Exercieses. Vol 2 by : Vladimir Zhivetin
Download or read book Advanced Calculus. Exercieses. Vol 2 written by Vladimir Zhivetin and published by Риски и безопасность. This book was released on 2007 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 542 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.
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.
Book Synopsis Clifford Algebra to Geometric Calculus by : David Hestenes
Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes and published by Springer Science & Business Media. This book was released on 1984 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
