Advanced Analysis Ii
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Author | : A.K. Sharma |
Publisher | : Discovery Publishing House |
Total Pages | : 444 |
Release | : 2004 |
Genre | : |
ISBN | : 9788171418305 |
Contents: Power Series, Fourier Series, The Riemann-Stieltjes Integral, Integral on R3, Series of Arbitrary Terms and Double Series, The Lebesgue Integral, Functions of Two and Three Variable.
Author | : Patrick Fitzpatrick |
Publisher | : American Mathematical Soc. |
Total Pages | : 610 |
Release | : 2009 |
Genre | : 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 | : Terence Tao |
Publisher | : Springer |
Total Pages | : 235 |
Release | : 2016-08-22 |
Genre | : Mathematics |
ISBN | : 9811018049 |
This is part two 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 | : Vladimir A. Zorich |
Publisher | : Krishna Prakashan Media |
Total Pages | : 792 |
Release | : 2010-11-16 |
Genre | : 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 | : Terence Tao |
Publisher | : |
Total Pages | : 284 |
Release | : 2006 |
Genre | : Mathematical analysis |
ISBN | : |
Providing an introduction to real analysis, this text is suitable for honours undergraduates. It starts at the very beginning - the construction of the number systems and set theory, then to the basics of analysis, through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral.
Author | : Vladimir A. Zorich |
Publisher | : Springer Science & Business Media |
Total Pages | : 610 |
Release | : 2004-01-22 |
Genre | : 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 |
Total Pages | : 366 |
Release | : 2016-08-29 |
Genre | : 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 | : M Victoria Velasco |
Publisher | : World Scientific |
Total Pages | : 227 |
Release | : 2007-03-22 |
Genre | : Mathematics |
ISBN | : 9814478636 |
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 | : Steven G. Krantz |
Publisher | : CRC Press |
Total Pages | : 322 |
Release | : 1992-07-02 |
Genre | : Mathematics |
ISBN | : 9780849371554 |
Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.
Author | : Michael E. Taylor |
Publisher | : American Mathematical Soc. |
Total Pages | : 445 |
Release | : 2020-07-27 |
Genre | : 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.