Author : Vladimir A. Zorich
Publisher : Krishna Prakashan Media
Page : 792 pages
File Size : 49,39 MB
Release : 2010-11-16
Category : Mathematics
ISBN :
The second volume expounds classical analysis as it is today, as a part of unified mathematics, and its interactions with modern mathematical courses such as algebra, differential geometry, differential equations, complex and functional analysis. The book provides a firm foundation for advanced work in any of these directions.
Author : Patrick Fitzpatrick
Publisher : American Mathematical Soc.
Page : 610 pages
File Size : 42,69 MB
Release : 2009
Category : Mathematics
ISBN : 0821847910
"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 : Vladimir A. Zorich
Publisher : Springer Science & Business Media
Page : 610 pages
File Size : 10,11 MB
Release : 2004-01-22
Category : Mathematics
ISBN : 9783540403869
This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions.
Author : Terence Tao
Publisher : Springer
Page : 366 pages
File Size : 12,30 MB
Release : 2016-08-29
Category : Mathematics
ISBN : 9811017891
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
Author : A. Rodriguez-Palacios
Publisher : World Scientific
Page : 227 pages
File Size : 48,92 MB
Release : 2007
Category : Mathematics
ISBN : 9812708448
This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of new directions and advances in topics for current and future research in the field.
Author : R. Beals
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 25,15 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 146849886X
Once upon a time students of mathematics and students of science or engineering took the same courses in mathematical analysis beyond calculus. Now it is common to separate" advanced mathematics for science and engi neering" from what might be called "advanced mathematical analysis for mathematicians." It seems to me both useful and timely to attempt a reconciliation. The separation between kinds of courses has unhealthy effects. Mathe matics students reverse the historical development of analysis, learning the unifying abstractions first and the examples later (if ever). Science students learn the examples as taught generations ago, missing modern insights. A choice between encountering Fourier series as a minor instance of the repre sentation theory of Banach algebras, and encountering Fourier series in isolation and developed in an ad hoc manner, is no choice at all. It is easy to recognize these problems, but less easy to counter the legiti mate pressures which have led to a separation. Modern mathematics has broadened our perspectives by abstraction and bold generalization, while developing techniques which can treat classical theories in a definitive way. On the other hand, the applier of mathematics has continued to need a variety of definite tools and has not had the time to acquire the broadest and most definitive grasp-to learn necessary and sufficient conditions when simple sufficient conditions will serve, or to learn the general framework encompass ing different examples.
Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 41,77 MB
Release : 2008-07-11
Category : Mathematics
ISBN : 0817644423
* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
Author : Robert S. Borden
Publisher : Courier Corporation
Page : 421 pages
File Size : 46,46 MB
Release : 2012-09-11
Category : Mathematics
ISBN : 0486150380
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 : Lynn Harold Loomis
Publisher : World Scientific Publishing Company
Page : 595 pages
File Size : 24,48 MB
Release : 2014-02-26
Category : Mathematics
ISBN : 9814583952
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 : Wieslawa J. Kaczor
Publisher : American Mathematical Soc.
Page : 400 pages
File Size : 13,2 MB
Release : 2000
Category : Mathematical analysis
ISBN : 9780821884430
