Cantitate/Preț
Produs
Total produse
Vezi coșul
Real Analysis and Applications de Kenneth R. Davidson

Real Analysis and Applications

Autor Kenneth R. Davidson, Allan P. Donsig
en Limba Engleză Paperback – 20 oct 2014

În cadrul programelor de studii avansate în matematică, tranziția de la calculul diferențial de bază la analiza riguroasă reprezintă adesea un prag dificil. Notăm cu interes modul în care lucrarea Real Analysis and Applications, semnată de Kenneth R. Davidson și Allan P. Donsig, reușește să faciliteze această trecere prin ancorarea teoriei abstracte în aplicații concrete. Volumul publicat de Springer se încadrează perfect în curriculumul de nivel master sau doctorat, oferind rigoarea demonstrațiilor matematice fără a pierde din vedere utilitatea practică a conceptelor.

Putem afirma că acest manual extinde cadrul conceptual propus de Fundamentals of Analysis with Applications de Atul Kumar Razdan prin diversificarea spectrului de aplicabilitate. În timp ce lucrarea lui Razdan se concentrează pe ecuații cu derivate parțiale, volumul de față introduce date noi din domenii precum sistemele dinamice discrete și optimizarea neliniară. Structura este organizată progresiv: prima jumătate a celor 528 de pagini este dedicată fundamentelor — de la numere reale și serii, la topologie și spații metrice — oferind baza necesară pentru a doua parte, dedicată exclusiv aplicațiilor. Această abordare modulară permite o parcurgere fluidă, unde teoria limitelor de funcții sau a normelor pregătește terenul pentru capitole complexe despre unde (wavelets) și fizica seriilor Fourier. Credem că echilibrul găsit de autori între rigoarea formală și intuiția geometrică transformă analiza matematică dintr-un exercițiu de abstractizare într-un instrument de lucru esențial pentru cercetare.

Citește tot Restrânge

Preț: 46328 lei

Preț vechi: 54503 lei
-15%

Puncte Express: 695

Carte tipărită la comandă

Livrare economică 28 mai-11 iunie

 Adaugă în coș

Wish list
Gift list
Am citit!
Adaugă în listă

Specificații

ISBN-13: 9781461499008
ISBN-10: 1461499003
Pagini: 528
Ilustrații: XII, 513 p.
Dimensiuni: 155 x 235 x 29 mm
Greutate: 0.79 kg
Ediția:2010
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Graduate

De ce să citești această carte

Recomandăm această carte studenților de la facultățile de matematică și fizică care doresc să înțeleagă nu doar „cum”, ci și „unde” se aplică analiza reală. Cititorul câștigă o perspectivă integrată asupra analizei moderne, beneficiind de capitole rare în manualele standard, precum cele despre wavelets și optimizare convexă, toate susținute de exerciții care consolidează capacitatea de a construi demonstrații proprii.

Cuprins

Analysis.- Review.- The Real Numbers.- Series.- Topology of.- Functions.- Differentiation and Integration.- Norms and Inner Products.- Limits of Functions.- Metric Spaces.- Applications.- Approximation by Polynomials.- Discrete Dynamical Systems.- Differential Equations.- Fourier Series and Physics.- Fourier Series and Approximation.- Wavelets.- Convexity and Optimization.

Recenzii

From the reviews:
Real Analysis with Real Applications:
"A well balanced book! The first solid analysis course, with proofs, is central in the offerings of any math.-dept.;-- and yet, the new books that hit the market don't always hit the mark: The balance between theory and applications, --between technical proofs and intuitive ideas,--between classical and modern subjects, and between real life exercises vs. the ones that drill a new concept. The Davidson-Donsig book is outstanding, and it does hit the mark. The writing is both systematic and engaged.- Refreshing! Novel: includes wavelets, approximation theory, discrete dynamics, differential equations, Fourier analysis, and wave mechanics." (Palle E. T. Jorgenson, Review from Amazon.com)
“In this exceptionally rich work, Davidson (Univ. of Waterloo, Canada) and Donsig (Univ. of Nebraska, Lincoln) meld material that is found in standard introductory real analysis works … and applications from both the mathematical and ‘real’ worlds … . The volume contains a substantial collection of exercises. Summing Up: Recommended. Upper-division undergraduates and graduate students.” (D. Robbins, Choice, Vol. 47 (10), June, 2010)
“This book is intended to provide an introduction both to real analysis and to a range of important applications in various fields. … In summary, this book is well conceived, well executed, and richer than many recent volumes in the same field. Teachers wanting a solid and interesting treatment that goes right to the point and does not bore good students with verbose explanations will find this book much to their liking. The volume also contains an adequate supply of exercises.” (Teodora-Liliana Rădulescu, Zentralblatt MATH, Vol. 1179, 2010)

Textul de pe ultima copertă

This new approach to real analysis stresses the use of the subject in applications, showing how the principles and theory of real analysis can be applied in various settings. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. Each chapter has many useful exercises.
 
The treatment of the basic theory covers the real numbers, functions, and calculus, while emphasizing the role of normed vector spaces, and particularly of Rn. The applied chapters are mostly independent, giving the reader a choice of topics. This book is appropriate for students with a prior knowledge of both calculus and linear algebra who want a careful development of both analysis and its use in applications.
 
Review of the previous version of this book, Real Analysis with Real Applications:
 
"A well balanced book! The first solid analysis course, with proofs, is central in the offerings of any math.-dept.; ---and yet, the new books that hit the market don't always hit the mark: the balance between theory and applications, ---between technical proofs and intuitive ideas, ---between classical and modern subjects, and between real life exercises vs. the ones that drill a new concept. The Davidson-Donsig book is outstanding, and it does hit the mark."
 
Palle E. T. Jorgenson, Review from Amazon.com
 
Kenneth R. Davidson is University Professor of Mathematics at the University of Waterloo. Allan P. Donsig is Associate Professor of Mathematics at the University of Nebraska-Lincoln.

Caracteristici

Includes applications that cover: Approximation by polynomials Discrete dynamical systems Differential equations Fourier series and physics Fourier series and approximation Convexity and optimization Appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra Includes supplementary material: sn.pub/extras

Descriere

This new approach to real analysis stresses the use of the subject with respect to applications, i.e., 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. This book is appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra.