Principles Of Mathematical Analysis

Author : Walter Rudin
Publisher : McGraw-Hill Publishing Company
Page : 342 pages
File Size : 46,7 Mb
Release : 1976
Category : Mathematics
ISBN : 0070856133

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Principles of Mathematical Analysis by Walter Rudin Pdf

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 : Raffi Grinberg
Publisher : Princeton University Press
Page : 200 pages
File Size : 44,6 Mb
Release : 2017-01-10
Category : Mathematics
ISBN : 9780691172934

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The Real Analysis Lifesaver by Raffi Grinberg Pdf

The essential "lifesaver" that every student of real analysis needs Real analysis is difficult. For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovative guide that helps students through their first real analysis course while giving them the solid foundation they need for further study in proof-based math. Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach, first showing students how to work backwards to solve the crux of the problem, then showing them how to write it up formally. It takes the time to provide plenty of examples as well as guided "fill in the blanks" exercises to solidify understanding. Newcomers to real analysis can feel like they are drowning in new symbols, concepts, and an entirely new way of thinking about math. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humor. It is the lifesaver that every drowning student needs. The essential “lifesaver” companion for any course in real analysis Clear, humorous, and easy-to-read style Teaches students not just what the proofs are, but how to do them—in more than 40 worked-out examples Every new definition is accompanied by examples and important clarifications Features more than 20 “fill in the blanks” exercises to help internalize proof techniques Tried and tested in the classroom

Author : N. L. Carothers
Publisher : Cambridge University Press
Page : 420 pages
File Size : 48,6 Mb
Release : 2000-08-15
Category : Mathematics
ISBN : 0521497566

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Real Analysis by N. L. Carothers Pdf

A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.

Author : Charles Chapman Pugh
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 55,6 Mb
Release : 2013-03-19
Category : Mathematics
ISBN : 9780387216843

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Real Mathematical Analysis by Charles Chapman Pugh Pdf

Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Author : Terence Tao
Publisher : Hindustan Book Agency and Indian National Science Academy
Page : 0 pages
File Size : 55,6 Mb
Release : 2009
Category : Mathematical analysis
ISBN : 8185931941

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Analysis by Terence Tao Pdf

Suitable for undergraduates who have already been exposed to calculus, this title includes material that starts at the very beginning - the construction of number systems and set theory, then goes on to the basics of analysis, through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 591 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208976

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Real and Functional Analysis by Serge Lang Pdf

This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations. The organization avoids long chains of logical interdependence, so that chapters are mostly independent. This allows a course to omit material from some chapters without compromising the exposition of material from later chapters.

Author : Maxwell Rosenlicht
Publisher : Courier Corporation
Page : 272 pages
File Size : 45,8 Mb
Release : 2012-05-04
Category : Mathematics
ISBN : 9780486134680

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Introduction to Analysis by Maxwell Rosenlicht Pdf

Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

Author : Kenneth A. Ross
Publisher : CUP Archive
Page : 192 pages
File Size : 42,9 Mb
Release : 2014-01-15
Category : Mathematics
ISBN : 8210379456XXX

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Elementary Analysis by Kenneth A. Ross Pdf

Author : Vladimir A. Zorich
Publisher : Springer Science & Business Media
Page : 610 pages
File Size : 50,5 Mb
Release : 2004-01-22
Category : Mathematics
ISBN : 3540403868

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Mathematical Analysis I by Vladimir A. Zorich Pdf

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 : Walter Rudin
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 47,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806333

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The Way I Remember It by Walter Rudin Pdf

Walter Rudin's memoirs should prove to be a delightful read specifically to mathematicians, but also to historians who are interested in learning abou his colourful history and ancestry. Characterized by his personal style of elegance, clarity, and brevity, Rudin presents in the first part of the book his early memories about his family history, his boyhood in Vienna throughout the 1920s and 1930s, and his experiences during World War II. Part II offers samples of his work, in which he relates where problems came from, what their solutions led to, and who else was involved. As those who are familiar with Rudin's writing will recognize, he brings to this book the same care, depth, and originality that is the hallmark of his work. Co-published with the London Mathematical Society

Author : Miklós Laczkovich,Vera T. Sós
Publisher : Springer
Page : 483 pages
File Size : 53,6 Mb
Release : 2015-10-08
Category : Mathematics
ISBN : 9781493927661

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Real Analysis by Miklós Laczkovich,Vera T. Sós Pdf

Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.

Author : Andrew Browder
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207153

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Mathematical Analysis by Andrew Browder Pdf

Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.

Author : Kenneth R. Davidson,Allan P. Donsig
Publisher : Unknown
Page : 652 pages
File Size : 47,8 Mb
Release : 2002
Category : Mathematical analysis
ISBN : UVA:X004589672

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Real Analysis with Real Applications by Kenneth R. Davidson,Allan P. Donsig Pdf

Using a progressive but flexible format, this book contains a series of independent chapters that show how the principles and theory of real analysis can be applied in a variety of settings-in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization. Users will be prepared for more intensive work in each topic through these applications and their accompanying exercises. Chapter topics under the abstract analysis heading include: the real numbers, series, the topology of R^n, functions, normed vector spaces, differentiation and integration, and limits of functions. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. For math enthusiasts with a prior knowledge of both calculus and linear algebra.

Author : Charalambos D. Aliprantis,Owen Burkinshaw
Publisher : Gulf Professional Publishing
Page : 434 pages
File Size : 55,9 Mb
Release : 1998-08-26
Category : Mathematics
ISBN : 0120502577

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Principles of Real Analysis by Charalambos D. Aliprantis,Owen Burkinshaw Pdf

The new, Third Edition of this successful text covers the basic theory of integration in a clear, well-organized manner. The authors present an imaginative and highly practical synthesis of the "Daniell method" and the measure theoretic approach. It is the ideal text for undergraduate and first-year graduate courses in real analysis. This edition offers a new chapter on Hilbert Spaces and integrates over 150 new exercises. New and varied examples are included for each chapter. Students will be challenged by the more than 600 exercises. Topics are treated rigorously, illustrated by examples, and offer a clear connection between real and functional analysis. This text can be used in combination with the authors' Problems in Real Analysis, 2nd Edition, also published by Academic Press, which offers complete solutions to all exercises in the Principles text. Key Features: * Gives a unique presentation of integration theory * Over 150 new exercises integrated throughout the text * Presents a new chapter on Hilbert Spaces * Provides a rigorous introduction to measure theory * Illustrated with new and varied examples in each chapter * Introduces topological ideas in a friendly manner * Offers a clear connection between real analysis and functional analysis * Includes brief biographies of mathematicians "All in all, this is a beautiful selection and a masterfully balanced presentation of the fundamentals of contemporary measure and integration theory which can be grasped easily by the student." --J. Lorenz in Zentralblatt für Mathematik "...a clear and precise treatment of the subject. There are many exercises of varying degrees of difficulty. I highly recommend this book for classroom use." --CASPAR GOFFMAN, Department of Mathematics, Purdue University

Author : S. C. Malik
Publisher : New Age International
Page : 24 pages
File Size : 54,9 Mb
Release : 2008
Category : Functions of real variables
ISBN : 9788122422771

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Principles of Real Analysis by S. C. Malik Pdf