A Modern Introduction To Mathematical Analysis

Author : Alessandro Fonda
Publisher : Springer Nature
Page : 442 pages
File Size : 45,6 Mb
Release : 2023-03-21
Category : Mathematics
ISBN : 9783031237133

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A Modern Introduction to Mathematical Analysis by Alessandro Fonda Pdf

This textbook presents all the basics for the first two years of a course in mathematical analysis, from the natural numbers to Stokes-Cartan Theorem. The main novelty which distinguishes this book is the choice of introducing the Kurzweil-Henstock integral from the very beginning. Although this approach requires a small additional effort by the student, it will be compensated by a substantial advantage in the development of the theory, and later on when learning about more advanced topics. The text guides the reader with clarity in the discovery of the many different subjects, providing all necessary tools – no preliminaries are needed. Both students and their instructors will benefit from this book and its novel approach, turning their course in mathematical analysis into a gratifying and successful experience.

Author : Tom Lindstrøm
Publisher : Unknown
Page : 384 pages
File Size : 43,9 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 1470443112

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Spaces by Tom Lindstrøm Pdf

Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years

Author : Andrew Browder
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 45,8 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 : Robert A. Rankin
Publisher : Elsevier
Page : 624 pages
File Size : 41,9 Mb
Release : 2016-06-06
Category : Mathematics
ISBN : 9781483137308

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An Introduction to Mathematical Analysis by Robert A. Rankin Pdf

An Introduction to Mathematical Analysis is an introductory text to mathematical analysis, with emphasis on functions of a single real variable. Topics covered include limits and continuity, differentiability, integration, and convergence of infinite series, along with double series and infinite products. This book is comprised of seven chapters and begins with an overview of fundamental ideas and assumptions relating to the field operations and the ordering of the real numbers, together with mathematical induction and upper and lower bounds of sets of real numbers. The following chapters deal with limits of real functions; differentiability and maxima, minima, and convexity; elementary properties of infinite series; and functions defined by power series. Integration is also considered, paying particular attention to the indefinite integral; interval functions and functions of bounded variation; the Riemann-Stieltjes integral; the Riemann integral; and area and curves. The final chapter is devoted to convergence and uniformity. This monograph is intended for mathematics students.

Author : Avner Friedman
Publisher : Courier Corporation
Page : 276 pages
File Size : 53,9 Mb
Release : 1982-01-01
Category : Mathematics
ISBN : 0486640620

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Foundations of Modern Analysis by Avner Friedman Pdf

Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

Author : Mariano Giaquinta,Giuseppe Modica
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 55,6 Mb
Release : 2010-07-25
Category : Mathematics
ISBN : 9780817646127

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Mathematical Analysis by Mariano Giaquinta,Giuseppe Modica Pdf

This superb and self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include the differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This text motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Author : Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher : Courier Corporation
Page : 450 pages
File Size : 43,9 Mb
Release : 2012-09-11
Category : Mathematics
ISBN : 9780486134772

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Foundations of Mathematical Analysis by Richard Johnsonbaugh,W.E. Pfaffenberger Pdf

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Author : Frank Loxley Griffin
Publisher : Unknown
Page : 546 pages
File Size : 43,6 Mb
Release : 1936
Category : Calculus
ISBN : LCCN:10164935

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An Introduction to Mathematical Analysis by Frank Loxley Griffin Pdf

Author : Sterling K. Berberian
Publisher : Springer Science & Business Media
Page : 249 pages
File Size : 51,8 Mb
Release : 2012-09-10
Category : Mathematics
ISBN : 9781441985484

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A First Course in Real Analysis by Sterling K. Berberian Pdf

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 : Nikolaos Katzourakis,Eugen Varvaruca
Publisher : CRC Press
Page : 558 pages
File Size : 54,7 Mb
Release : 2018-01-02
Category : Mathematics
ISBN : 9781351765336

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An Illustrative Introduction to Modern Analysis by Nikolaos Katzourakis,Eugen Varvaruca Pdf

Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.

Author : Vicente Montesinos,Peter Zizler,Václav Zizler
Publisher : Springer
Page : 863 pages
File Size : 40,6 Mb
Release : 2015-05-04
Category : Mathematics
ISBN : 9783319124810

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An Introduction to Modern Analysis by Vicente Montesinos,Peter Zizler,Václav Zizler Pdf

Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.

Author : Sadri Hassani
Publisher : Springer Science & Business Media
Page : 1052 pages
File Size : 52,9 Mb
Release : 2002-02-08
Category : Science
ISBN : 0387985794

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Mathematical Physics by Sadri Hassani Pdf

For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.

Author : Werner Römisch,Thomas Zeugmann
Publisher : Springer
Page : 703 pages
File Size : 45,8 Mb
Release : 2016-10-04
Category : Computers
ISBN : 9783319427553

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Mathematical Analysis and the Mathematics of Computation by Werner Römisch,Thomas Zeugmann Pdf

This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.

Author : W. Light
Publisher : CRC Press
Page : 212 pages
File Size : 53,5 Mb
Release : 1990-07-01
Category : Mathematics
ISBN : 0412310902

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Introduction to Abstract Analysis by W. Light Pdf

Abstract analysis, and particularly the language of normed linear spaces, now lies at the heart of a major portion of modern mathematics. Unfortunately, it is also a subject which students seem to find quite challenging and difficult. This book presumes that the student has had a first course in mathematical analysis or advanced calculus, but it does not presume the student has achieved mastery of such a course. Accordingly, a gentle introduction to the basic notions of convergence of sequences, continuity of functions, open and closed set, compactness, completeness and separability is given. The pace in the early chapters does not presume in any way that the readers have at their fingertips the techniques provided by an introductory course. Instead, considerable care is taken to introduce and use the basic methods of proof in a slow and explicit fashion. As the chapters progress, the pace does quicken and later chapters on differentiation, linear mappings, integration and the implicit function theorem delve quite deeply into interesting mathematical areas. There are many exercises and many examples of applications of the theory to diverse areas of mathematics. Some of these applications take considerable space and time to develop, and make interesting reading in their own right. The treatment of the subject is deliberately not a comprehensive one. The aim is to convince the undergraduate reader that analysis is a stimulating, useful, powerful and comprehensible tool in modern mathematics. This book will whet the readers' appetite, not overwhelm them with material.

Author : Dean Corbae,Maxwell Stinchcombe,Juraj Zeman
Publisher : Princeton University Press
Page : 696 pages
File Size : 46,6 Mb
Release : 2009-02-17
Category : Business & Economics
ISBN : 9781400833085

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An Introduction to Mathematical Analysis for Economic Theory and Econometrics by Dean Corbae,Maxwell Stinchcombe,Juraj Zeman Pdf

Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory