**Author**: John B. Conway

**Publisher:** Cambridge University Press

**ISBN:** 1107173140

**Category : **Mathematics

**Languages : **en

**Pages : **357

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**Book Description**
This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.

**Author**: John B. Conway

**Publisher:** Cambridge University Press

**ISBN:** 1107173140

**Category : **Mathematics

**Languages : **en

**Pages : **357

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**Book Description**
This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.

**Author**: David Alexander Brannan

**Publisher:** Cambridge University Press

**ISBN:** 9780521684248

**Category : **Mathematics

**Languages : **en

**Pages : **468

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**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.

**Author**: Murray H. Protter

**Publisher:** Springer Science & Business Media

**ISBN:** 0387974377

**Category : **Mathematics

**Languages : **en

**Pages : **558

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**Book Description**
Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.

**Author**: Sterling K. Berberian

**Publisher:** Springer

**ISBN:** 0387942173

**Category : **Mathematics

**Languages : **en

**Pages : **240

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**Book Description**
Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

**Author**: Andrew L. Comrey

**Publisher:** Psychology Press

**ISBN:** 1317844068

**Category : **Psychology

**Languages : **en

**Pages : **442

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**Book Description**
The goal of this book is to foster a basic understanding of factor analytic techniques so that readers can use them in their own research and critically evaluate their use by other researchers. Both the underlying theory and correct application are emphasized. The theory is presented through the mathematical basis of the most common factor analytic models and several methods used in factor analysis. On the application side, considerable attention is given to the extraction problem, the rotation problem, and the interpretation of factor analytic results. Hence, readers are given a background of understanding in the the theory underlying factor analysis and then taken through the steps in executing a proper analysis -- from the initial problem of design through choice of correlation coefficient, factor extraction, factor rotation, factor interpretation, and writing up results. This revised edition includes introductions to newer methods -- such as confirmatory factor analysis and structural equation modeling -- that have revolutionized factor analysis in recent years. To help remove some of the mystery underlying these newer, more complex methods, the introductory examples utilize EQS and LISREL. Updated material relating to the validation of the Comrey Personality Scales also has been added. Finally, program disks for running factor analyses on either an IBM-compatible PC or a mainframe with FORTRAN capabilities are available. The intended audience for this volume includes talented but mathematically unsophisticated advanced undergraduates, graduate students, and research workers seeking to acquire a basic understanding of the principles supporting factor analysis. Disks are available in 5.25" and 3.5" formats for both mainframe programs written in Fortran and IBM PCs and compatibles running a math co-processor.

**Author**: David W. Kammler

**Publisher:** Cambridge University Press

**ISBN:** 0521883407

**Category : **Mathematics

**Languages : **en

**Pages : **863

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**Book Description**
This book introduces applied mathematics through Fourier analysis, with applications to studying sampling theory, PDEs, probability, diffraction, musical tones, and wavelets.

**Author**: S. Kesavan

**Publisher:** Springer Nature

**ISBN:** 9811663475

**Category : **Electronic books

**Languages : **en

**Pages : **161

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**Book Description**
The book discusses the basic theory of topological and variational methods used in solving nonlinear equations involving mappings between normed linear spaces. It is meant to be a primer of nonlinear analysis and is designed to be used as a text or reference book by graduate students. Frechet derivative, Brouwer fixed point theorem, Borsuk's theorem, and bifurcation theory along with their applications have been discussed. Several solved examples and exercises have been carefully selected and included in the present edition. The prerequisite for following this book is the basic knowledge of functional analysis and topology.

**Author**: Albert Boggess

**Publisher:** John Wiley & Sons

**ISBN:** 1118211154

**Category : **Mathematics

**Languages : **en

**Pages : **336

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**Book Description**
A comprehensive, self-contained treatment of Fourier analysisand waveletsâ€”now in a new edition Through expansive coverage and easy-to-follow explanations, AFirst Course in Wavelets with Fourier Analysis, SecondEdition provides a self-contained mathematical treatment of Fourieranalysis and wavelets, while uniquely presenting signal analysisapplications and problems. Essential and fundamental ideas arepresented in an effort to make the book accessible to a broadaudience, and, in addition, their applications to signal processingare kept at an elementary level. The book begins with an introduction to vector spaces, innerproduct spaces, and other preliminary topics in analysis.Subsequent chapters feature: The development of a Fourier series, Fourier transform, anddiscrete Fourier analysis Improved sections devoted to continuous wavelets andtwo-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signalprocessing The construction, smoothness, and computation of Daubechies'wavelets Advanced topics such as wavelets in higher dimensions,decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout thebook, most involving the filtering and compression of signals fromaudio or video. Some of these applications are presented first inthe context of Fourier analysis and are later explored in thechapters on wavelets. New exercises introduce additionalapplications, and complete proofs accompany the discussion of eachpresented theory. Extensive appendices outline more advanced proofsand partial solutions to exercises as well as updated MATLABroutines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, SecondEdition is an excellent book for courses in mathematics andengineering at the upper-undergraduate and graduate levels. It isalso a valuable resource for mathematicians, signal processingengineers, and scientists who wish to learn about wavelet theoryand Fourier analysis on an elementary level.

**Author**: Donald Yau

**Publisher:** World Scientific

**ISBN:** 9814417858

**Category : **Mathematics

**Languages : **en

**Pages : **206

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**Book Description**
This book is an introductory text on real analysis for undergraduate students. The prerequisite for this book is a solid background in freshman calculus in one variable. The intended audience of this book includes undergraduate mathematics majors and students from other disciplines who use real analysis. Since this book is aimed at students who do not have much prior experience with proofs, the pace is slower in earlier chapters than in later chapters. There are hundreds of exercises, and hints for some of them are included.

**Author**: Dennis Zill

**Publisher:** Jones & Bartlett Learning

**ISBN:** 0763757721

**Category : **Mathematics

**Languages : **en

**Pages : **471

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**Book Description**
The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manor. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.