Author : S. M. Nikol'skii
Publisher : American Mathematical Soc.
Page : 348 pages
File Size : 10,35 MB
Release : 1982-12-31
Category : Mathematics
ISBN : 9780821830475
Author : Lev Dmitrievich Kudri︠a︡vt︠s︡ev
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 39,81 MB
Release : 1994
Category : Mathematics
ISBN : 9780821803387
This book is dedicated to Sergei Mikhailovich Nikol'skii on the occasion of his eighty-fifth birthday. The collection contains new results on the following topics: approximation of functions, imbedding theory, interpolation of function spaces, convergence of series in trigonometric and general orthogonal systems, quasilinear elliptic problems, spectral theory of nonselfadjoint operators, asymptotic properties of pseudodifferential operators, and methods of approximate solution of Laplace's equation.
Author : Michael E. Taylor
Publisher : American Mathematical Soc.
Page : 462 pages
File Size : 14,36 MB
Release : 2020-07-27
Category : Education
ISBN : 1470456699
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.
Author : C. H. Edwards
Publisher : Academic Press
Page : 470 pages
File Size : 15,38 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483268055
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.
Author :
Publisher :
Page : pages
File Size : 24,63 MB
Release : 1965
Category :
ISBN :
Author : Lynn Harold Loomis
Publisher : World Scientific Publishing Company
Page : 595 pages
File Size : 30,79 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 : Robert G. Mortimer
Publisher : Elsevier
Page : 406 pages
File Size : 11,61 MB
Release : 2005-06-10
Category : Science
ISBN : 0080492886
Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data. - Numerous examples and problems interspersed throughout the presentations - Each extensive chapter contains a preview, objectives, and summary - Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory - Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics
Author : S. M. Nikol'skii
Publisher :
Page : 0 pages
File Size : 14,14 MB
Release : 1979
Category :
ISBN :
Author : Hugo D. Junghenn
Publisher : CRC Press
Page : 613 pages
File Size : 33,48 MB
Release : 2015-02-13
Category : Mathematics
ISBN : 148221928X
A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The book's material has been extensively classroom tested in the author's two-semester undergraduate course on real analysis at The George Washington University.The first part of the text presents the
Author : Jan R. Magnus
Publisher : John Wiley & Sons
Page : 660 pages
File Size : 25,78 MB
Release : 2019-03-15
Category : Mathematics
ISBN : 1119541166
A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have mastered the technique. Jan Magnus, who, along with the late Heinz Neudecker, pioneered the theory, develops it further in this new edition and provides many examples along the way to support it. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics, Third Edition contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference. Fulfills the need for an updated and unified treatment of matrix differential calculus Contains many new examples and exercises based on questions asked of the author over the years Covers new developments in field and features new applications Written by a leading expert and pioneer of the theory Part of the Wiley Series in Probability and Statistics Matrix Differential Calculus With Applications in Statistics and Econometrics Third Edition is an ideal text for graduate students and academics studying the subject, as well as for postgraduates and specialists working in biosciences and psychology.
