[PDF] Advanced Calculus eBook

Author : Lynn Harold Loomis
Publisher : World Scientific Publishing Company
Page : 595 pages
File Size : 49,74 MB
Release : 2014-02-26
Category : Mathematics
ISBN : 9814583952

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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 : Patrick Fitzpatrick
Publisher : American Mathematical Soc.
Page : 610 pages
File Size : 11,29 MB
Release : 2009
Category : Mathematics
ISBN : 0821847910

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"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.

Author : James J. Callahan
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 24,28 MB
Release : 2010-09-09
Category : Mathematics
ISBN : 144197332X

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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 : Robert S. Borden
Publisher : Courier Corporation
Page : 421 pages
File Size : 25,7 MB
Release : 2012-09-11
Category : Mathematics
ISBN : 0486150380

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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.

Author : David V. Widder
Publisher : Courier Corporation
Page : 548 pages
File Size : 13,19 MB
Release : 2012-05-23
Category : Mathematics
ISBN : 0486134660

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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.

Author : John Srdjan Petrovic
Publisher : CRC Press
Page : 574 pages
File Size : 10,1 MB
Release : 2013-11-01
Category : Mathematics
ISBN : 1466565632

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Suitable for a one- or two-semester course, Advanced Calculus: Theory and Practice expands on the material covered in elementary calculus and presents this material in a rigorous manner. 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 takes a motivating approach that makes ideas less abstract to students. It explains how various topics in calculus may seem unrelated but in reality 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 as well as help students develop the necessary skills to closely examine the theorems. Proofs are also presented in an accessible way to students. By strengthening skills gained through elementary calculus, this textbook leads students toward mastering calculus techniques. It will help them succeed in their future mathematical or engineering studies.

Author : B. R. THAKUR
Publisher : Ram Prasad Publications(R.P.H.)
Page : 656 pages
File Size : 42,55 MB
Release :
Category : Mathematics
ISBN : 9385630024

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MATHEMATICS, GANIT, RAM PRASAD, RPP UNFIED RP HARI KISHAN, THAKUR

Author : R. Creighton Buck
Publisher : Waveland Press
Page : 633 pages
File Size : 23,61 MB
Release : 2003-12-30
Category : Mathematics
ISBN : 147860820X

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Demonstrating analytical and numerical techniques for attacking problems in the application of mathematics, this well-organized, clearly written text presents the logical relationship and fundamental notations of analysis. Buck discusses analysis not solely as a tool, but as a subject in its own right. This skill-building volume familiarizes students with the language, concepts, and standard theorems of analysis, preparing them to read the mathematical literature on their own. The text revisits certain portions of elementary calculus and gives a systematic, modern approach to the differential and integral calculus of functions and transformations in several variables, including an introduction to the theory of differential forms. The material is structured to benefit those students whose interests lean toward either research in mathematics or its applications.