Author: Walter Rudin
Publisher: McGraw-Hill Publishing Company
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Author: Paul Sacks
Publisher: Academic Press
Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations, and especially partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and as PhD research preparation in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs are limited, and their sources precisely identifie d, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. Provides an introduction to the mathematical techniques widely used in applied mathematics and needed for advanced research Establishes the advanced background needed for sophisticated literature review and research in both differential and integral equations Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics
Author: Franck Boyer,Pierre Fabrie
Publisher: Springer Science & Business Media
The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .
With Problems and Solutions
Author: Michela Petrini,Gianfranco Pradisi,Alberto Zaffaroni
Publisher: World Scientific Publishing Company
Mathematics plays a fundamental role in the formulation of physical theories. This textbook provides a self-contained and rigorous presentation of the main mathematical tools needed in many fields of Physics, both classical and quantum. It covers topics treated in mathematics courses for final-year undergraduate and graduate physics programmes, including complex function: distributions, Fourier analysis, linear operators, Hilbert spaces and eigenvalue problems. The different topics are organised into two main parts — complex analysis and vector spaces — in order to stress how seemingly different mathematical tools, for instance the Fourier transform, eigenvalue problems or special functions, are all deeply interconnected. Also contained within each chapter are fully worked examples, problems and detailed solutions. A companion volume covering more advanced topics that enlarge and deepen those treated here is also available. Contents:Complex Analysis:Holomorphic FunctionsIntegrationTaylor and Laurent SeriesResiduesFunctional Spaces:Vector SpacesSpaces of FunctionsDistributionsFourier AnalysisLinear Operators in Hilbert Spaces I: The Finite-Dimensional CaseLinear Operators in Hilbert Spaces II: The Infinite-Dimensional CaseAppendices:Complex Numbers, Series and IntegralsSolutions of the Exercises Readership: Students of undergraduate mathematics and postgraduate students of physics or engineering.
Author: Paul J. Sally, Jr.
Publisher: American Mathematical Soc.
This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in ``AP Calculus'', possibly followed by a routine course in multivariable calculus and a computational course in linear algebra. There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread throughout the chapters and should be regarded as an essential component of the student's learning. Some of these exercises comprise a routine follow-up to the material, while others challenge the student's understanding more deeply. The second feature is the set of independent projects presented at the end of each chapter. These projects supplement the content studied in their respective chapters. They can be used to expand the student's knowledge and understanding or as an opportunity to conduct a seminar in Inquiry Based Learning in which the students present the material to their class. The third really important feature is a series of challenge problems that increase in impossibility as the chapters progress.
Author: Walter Rudin
Publisher: Walter de Gruyter
Category: Analysis - Lehrbuch
Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.
Author: International Atomic Energy Agency
Category: Nuclear energy
Author: Paulo Ney de Souza,Jorge-Nuno Silva
Publisher: Springer Science & Business Media
This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.
Author: Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans
This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, DaniellLebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?
Author: Environmental Science Information Center. Library and Information Services Division
Category: Book catalogs
Author: E. G. Phillips
International Series of Monographs in Pure and Applied Mathematics, Volume 86, Some Topics in Complex Analysis deals with a variety of topics related to complex analysis. This book discusses the method of comparison, periods of an integral, generalized Joukowski transformations, and Koebe's distortion theorems. The deductions from the maximum-modulus principle, canonical products and genus of an I.F., and Weierstrass's primary factors are also reviewed. This text likewise considers Mittag-Leffler's theorem, summation of series by the calculus of residues, definition of regular functions by integrals, and Riemann zeta function. This publication is a good reference for students and specialists researching in the field of applied and pure mathematics.
Author: Library of Congress
Category: Monographic series
Author: Walter Rudin
Publisher: Tata McGraw-Hill Education
Category: Functional analysis
Author: G. M. Fikhtengol'ts
The Fundamentals of Mathematical Analysis, Volume 1 is a textbook that provides a systematic and rigorous treatment of the fundamentals of mathematical analysis. Emphasis is placed on the concept of limit which plays a principal role in mathematical analysis. Examples of the application of mathematical analysis to geometry, mechanics, physics, and engineering are given. This volume is comprised of 14 chapters and begins with a discussion on real numbers, their properties and applications, and arithmetical operations over real numbers. The reader is then introduced to the concept of function, important classes of functions, and functions of one variable; the theory of limits and the limit of a function, monotonic functions, and the principle of convergence; and continuous functions of one variable. A systematic account of the differential and integral calculus is then presented, paying particular attention to differentiation of functions of one variable; investigation of the behavior of functions by means of derivatives; functions of several variables; and differentiation of functions of several variables. The remaining chapters focus on the concept of a primitive function (and of an indefinite integral); definite integral; geometric applications of integral and differential calculus. This book is intended for first- and second-year mathematics students.
Band 2: Integrale und Geometrie in IRn
Author: Kenneth Eriksson,Donald Estep,Claes Johnson
"Angewandte Mathematik: Body & Soul" ist ein neuer Grundkurs in der Mathematikausbildung für Studienanfänger in den Naturwissenschaften, der Technik, und der Mathematik, der an der Chalmers Tekniska Högskola in Göteborg entwickelt wurde. Er besteht aus drei Bänden sowie Computer-Software. Das Projekt ist begründet in der Computerrevolution, die ihrerseits völlig neue Möglichkeiten des wissenschaftlichen Rechnens in der Mathematik, den Naturwissenschaften und im Ingenieurwesen eröffnet hat. Es besteht aus einer Synthese der mathematischen Analysis (Soul) mit der numerischen Berechnung (Body) sowie den Anwendungen. Die Bände I-III geben eine moderne Version der Analysis und der linearen Algebra wieder, einschließlich konstruktiver numerischer Techniken und Anwendungen, zugeschnitten auf Anfängerprogramme im Maschinenbau und den Naturwissenschaften. Weitere Bände behandeln Themen wie z.B. dynamische Systeme, Strömungsdynamik, Festkörpermechanik und Elektromagnetismus. Dieser Band entwickelt das Riemann-Integral, um eine Funktion zu einer gegebenen Ableitung zu bestimmen. Darauf aufbauend werden Differentialgleichungen und Anfangswertprobleme mit einer Vielzahl anschaulicher Anwendungen behandelt. Die lineare Algebra wird auf n-dimensionale Räume verallgemeinert, wobei wiederum dem praktischen Umgang und numerischen Lösungstechniken besonderer Platz eingeräumt wird. Die Autoren sind führende Experten im Gebiet des wissenschaftlichen Rechnens und haben schon mehrere erfolgreiche Bücher geschrieben. "[......] Oh, by the way, I suggest immediate purchase of all three volumes!" The Mathematical Association of America Online, 7.7.04
A Special Course
Author: G. Ye. Shilov
Mathematical Analysis: A Special Course covers the fundamentals, principles, and theories that make up mathematical analysis. The title first provides an account of set theory, and then proceeds to detailing the elements of the theory of metric and normed linear spaces. Next, the selection covers the calculus of variations, along with the theory of Lebesgue integral. The text also tackles the geometry of Hilbert space and the relation between integration and differentiation. The last chapter of the title talks about the Fourier transform. The book will be of great use to individuals who want to expand and enhance their understanding of mathematical analysis.
Author: Monica Conti,Davide L. Ferrario,Susanna Terracini,Gianmaria Verzini
Publisher: Apogeo Editore
La formulazione del concetto di limite, pur partendo da un’osservazione esprimibile in termini intuitivi, richiede un certo sforzo di astrazione. Il salto concettuale è visibile anche dal punto di vista storico: nonostante esso sia alla base di moltissimi ragionamenti della matematica classica, rinascimentale e settecentesca, fu soltanto con un lavoro del matematico tedesco Heine, pubblicato nel 1872, che apparve la definizione di limite usata al giorno d'oggi.