Real Analysis with an Introduction to Wavelets and Applications By Don Hong, Jianzhong Wang, Robert Gardner
Publisher: Academic Press Number Of Pages: 392 Publication Date: 2004-12-14 ISBN-10 / ASIN: 0123548616 ISBN-13 / EAN: 9780123548610 Binding: Hardcover
Product Description:
An in-depth look at real analysis and its applications, including an introduction to wavelet
analysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral,
harmonic analysis and wavelet theory with many associated applications.
Reader's review:
Summary: Excellent Intermediate Real Analysis Text
Rating: 5
"Mathematical Analysis (2nd Ed.)," by Tom Apostol, does an excellent job of bridging the gap between standard introductory calculus texts and full-fledged treatments of topics in analysis. Apostol's book covers significantly more material than the gold standard of such texts, "Principles of Mathematical Analysis" by Rudin, and does so in a very different style. Where Rudin is brief and elegant, Apostol is thorough, detailed and friendly. Both Apostol's and Rudin's books have been around a long time, for very good reasons.
Unlike some intermediate texts, Apostol's book spends little time restating the particular results of elementary calculus (e.g., the derivative of sin x or x^n) in the new language of a more theoretical approach. Unlike Rudin and similar texts, Apostol *does* give detailed proofs, with thorough explanations. As a result of this approach, Apostol's book is not particularly well-suited to serve as a reference work for use by more advanced students or by professionals -- it is strictly a vehicle, and a very good vehicle indeed, for moving from elementary calculus to an introductory careful theoretical treatment of the material. Apostol does a particularly good job of presenting the "backbone ideas" of limits and continuity in a brief but very clear chapter (Chapter 4).
Apostol's problems are excellent and should be considered an important part of his presentation of the material. (This is one area in which Apostol perhaps surpasses Rudin, although MIT's online materials contain answers to so many of Rudin's problems that they now must be viewed as "worked-out examples!") Students find Apostol's tone, and the hints given in connection with the problems, to be helpful and engaging.
I suspect that the final few chapters of Apostol's book are used only rarely, due to the typical two-semester structure of real analysis courses (with a third semester being devoted to complex analysis). If true, this is a shame, because Apostol does a nice job of moving from a fairly standard treatment of the Lebesgue integral to Fourier integrals, multiple Riemann integrals and multiple Lebesgue integrals.
Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, 3ed
Publisher: W. W. Norton & Company | Pages: 176 | 1996-10 | ISBN: 0393969975 | DJVU | 2 MB
Product Description:
This well-written new edition contains a healthy balance of explicit and implied calculation. It updates the notation to bring it in line with modern usage and adds new example exercises.
Paolo Ciatti, Eduardo Gonzalez, Massimo Lanza De Cristoforis, Gian Paolo Leonardi
“Topics in Mathematical Analysis"
World Scientific Publishing Company | 2008-06-16 | ISBN: 9812811052 | 500 pages | PDF | 3,3 MB
This volume consists of a series of lecture notes on mathematical analysis. The contributors have been selected on the basis of both their outstanding scientific level and their clarity of exposition. Thus, the present collection is particularly suited to young researchers and graduate students. Through this volume, the editors intend to provide the reader with material otherwise difficult to find and written in a manner which is also accessible to nonexperts.
Contents: Complex Variables and Potential Theory: Integral Representations in Complex, Hypercomplex and Clifford Analysis (H Begehr); Nonlinear Potential Theory in Metric Spaces (O Martio); Differential Equations and Nonlinear Analysis: An Introduction to Mean Curvature Flow (G Bellettini); Introduction to Bifurcation Theory (P Drábek); A Nonlinear Eigenvalue Problems (P Lindqvist); Nonlinear Elliptic Equations with Critical and Supercritical Sobolev Exponents (D Passaseo); Eigenvalue Analysis of Elliptic Operators (G Rozenblum); A Glimpse of the Theory of Nonlinear Semigroups (E Vesentini); Harmonic Analysis: Integral Geometry and Spectral Analysis (M Agranovsky); Fourier Analysis and Geometric Combinatorics (A Iosevich); Lectures on Eigenfunctions of the Laplacian (C D Sogge); Five Lectures on Harmonic Analysis (F Soria); Fractal Analysis, an Approach via Function Spaces (H Triebel).
Principles of Real Analysis, Third Edition By Charalambos D. Aliprantis
<LI qbf1A="0" vyEbW="1">
Publisher: Academic Press
<LI qbf1A="0" vyEbW="1">
Number Of Pages: 451
<LI qbf1A="0" vyEbW="1">
Publication Date: 1998-09-15
<LI qbf1A="0" vyEbW="1">
ISBN-10 / ASIN: 0120502577
<LI qbf1A="0" vyEbW="1">
ISBN-13 / EAN: 9780120502578
<LI qbf1A="0" vyEbW="1">
Binding: Hardcover
Product Description:
With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.
Publisher: Wiley Number Of Pages: 388 Publication Date: 1999-09-21 ISBN-10 / ASIN: 0471321486 ISBN-13 / EAN: 9780471321484 Binding: Hardcover
Product Description:
In recent years, mathematics has become valuable in many areas, including economics and management science as well as the physical sciences, engineering and computer science. Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.
Publisher: Springer Number Of Pages: 485 Publication Date: 2003-07-30 ISBN-10 / ASIN: 0387985921 ISBN-13 / EAN: 9780387985923 Binding: Hardcover
Book Description:
This is the fourth edition of Serge Lang's Complex Analysis. The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than in other texts, and the proofs using these methods often shed more light on the results than the standard proofs do. The first part of Complex Analysis is suitable for an introductory course on the undergraduate level, and the additional topics covered in the second part give the instructor of a graduate course a great deal of flexibility in structuring a more advanced course. This is a revised edition, new examples and exercises have been added, and many minor improvements have been made throughout the text.
An Introduction to Nonstandard Real Analysis, Volume 118 (Pure and Applied Mathematics) By Albert E. Hurd, Peter A. Loeb
Publisher: Academic Press Number Of Pages: 232 Publication Date: 1985-09-28 ISBN-10 / ASIN: 0123624401 ISBN-13 / EAN: 9780123624406 Binding: Hardcover
Product Description:
The aim of this book is to make Robinson's discovery, and some of the subsequent research, available to students with a background in undergraduate mathematics. In its various forms, the manuscript was used by the second author in several graduate courses at the University of Illinois at Urbana-Champaign. The first chapter and parts of the rest of the book can be used in an advanced undergraduate course. Research mathematicians who want a quick introduction to nonstandard analysis will also find it useful. The main addition of this book to the contributions of previous textbooks on nonstandard analysis (12,37,42,46) is the first chapter, which eases the reader into the subject with an elementary model suitable for the calculus, and the fourth chapter on measure theory in nonstandard models.
An Introduction to Multivariable Mathematics (Synthesis Lectures on Mathematics and Statistics)
By Leon Simon
Publisher: Morgan and Claypool Publishers Number Of Pages: 142 Publication Date: 2008-09-19 ISBN-10 / ASIN: 1598298011 ISBN-13 / EAN: 9781598298017 Binding: Paperback
Product Description:
The text is designed for use in a forty-lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis. The core material of the book is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and linear systems, to be covered in the first ten or eleven lectures, followed by a similar number of lectures on basic multivariable analysis, including first theorems on differentiable functions on domains in Euclidean space and a brief introduction to submanifolds. The book then concludes with further essential linear algebra, including the theory of determinants, eigenvalues, and the spectral theorem for real symmetric matrices, and further multivariable analysis, including the contraction mapping principle and the inverse and implicit function theorems. There is also an appendix which provides a nine-lecture introduction to real analysis. There are various ways in which the additional material in the appendix could be integrated into a course--for example in the Stanford Mathematics honors program, run as a four-lecture per week program in the Autumn Quarter each year, the first six lectures of the nine-lecture appendix are presented at the rate of one lecture per week in weeks two through seven of the quarter, with the remaining three lectures per week during those weeks being devoted to the main chapters of the text. It is hoped that the text would be suitable for a quarter or semester course for students who have scored well in the BC Calculus advanced placement examination (or equivalent), particularly those who are considering a possible major in mathematics. The author has attempted to make the presentation rigorous and complete, with the clarity and simplicity needed to make it accessible to an appropriately large group of students. Table of Contents: Linear Algebra / Analysis in R / More Linear Algebra / More Analysis in R / Appendix: Introductory Lectures on Real Analysis
A First Course in Mathematical Analysis By David Alexander Brannan
Publisher: Cambridge University Press Number Of Pages: 472 Publication Date: 2006-09-04 ISBN-10 / ASIN: 0521864399 ISBN-13 / EAN: 9780521864398 Binding: Hardcover
Book Description:
Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard University course on the subject.
