Principles Of Mathematical Analysis

Author: Walter Rudin
Publisher: McGraw-Hill Publishing Company
ISBN: 9780070856134
Size: 41.56 MB
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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.

Foundations Of Mathematical Analysis

Author: Richard Johnsonbaugh
Publisher: Courier Corporation
ISBN: 0486134776
Size: 73.94 MB
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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.

Mathematical Analysis

Author: Andrew Browder
Publisher: Springer Science & Business Media
ISBN: 1461207150
Size: 29.56 MB
Format: PDF, Kindle
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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.

Applied Mathematics Reviews

Author: George A Anastassiou
Publisher: World Scientific
ISBN: 9814492884
Size: 76.75 MB
Format: PDF, ePub, Mobi
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Applied mathematics connects the mathematical theory to the reality by solving real world problems and shows the power of the science of mathematics, greatly improving our lives. Therefore it plays a very active and central role in the scientific world. This volume contains 14 high quality survey articles — incorporating original results and describing the main research activities of contemporary applied mathematics — written by top people in the field. The articles have been written in review style, so that the researcher can have a quick and thorough view of what is happening in the main subfields of applied mathematics. Contents:Two Contemporary Computational Concepts in Numerical Analysis (I K Argyros)On the Simultaneous Approximation of Functions and Their Derivatives (T Kilgore)Copositive Polynomial Approximation Revisited (Y K Hu & X M Yu)Sampling Theory and Function Spaces (H-J Schmeisser & W Sickel)Evaluating Statistical Functionals by Means of Projections onto Convex Cones in Hilbert Spaces: Part I and II (T Rychlik)Extrapolation: From Calculation of π to Finite Element Method of Partial Differential Equations (X-P Shen)A Survey on Scaling Function Interpolation and Approximation (E-B Lin)and other papers Readership: Applied mathematicians, statisticians, economists and engineers. Keywords:Singular Integrals;Numerical Analysis;Convolution Operators;Approximation of Functions;Minimal Projection;Fuzzy Control;Sampling Theory;Stable Financial Modelling;Ill-Posed Problems;Finite Element Method

Real Mathematical Analysis

Author: Charles Chapman Pugh
Publisher: Springer
ISBN: 3319177710
Size: 79.78 MB
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Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis. New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini's theorem from Cavalieri’s Principle, and, in many cases, the ability to see an integral result from measure theory. The presentation includes Vitali’s Covering Lemma, density points — which are rarely treated in books at this level — and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject.

Mathematical Analysis

Author: L. A. Lyusternik
Publisher: Elsevier
ISBN: 1483194361
Size: 75.19 MB
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Mathematical Analysis: Functions, Limits, Series, Continued Fractions provides an introduction to the differential and integral calculus. This book presents the general problems of the theory of continuous functions of one and several variables, as well as the theory of limiting values for sequences of numbers and vectors. Organized into six chapters, this book begins with an overview of real numbers, the arithmetic linear continuum, limiting values, and functions of one variable. This text then presents the theory of series and practical methods of summation. Other chapters consider the theory of numerical series and series of functions and other analogous processes, particularly infinite continued fractions. This book discusses as well the general problems of the reduction of functions to orthogonal series. The final chapter deals with constants and the most important systems of numbers, including Bernoulli and Euler numbers. This book is a valuable resource for mathematicians, engineers, and research workers.