التحليل Real and Complex Analysis

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Lecture Notes on Complex Analysis
World Scientific Publishing Company | Pages: 260 | 2006-04-11 | ISBN: 1860946429 | PDF | 7 Mb​


This book is based on lectures presented over many years to second and third year mathematics students in the Mathematics Departments at Bedford College, London, and King's College, London, as part of the BSc. and MSci. program. Its aim is to provide a gentle yet rigorous first course on complex analysis. Metric space aspects of the complex plane are discussed in detail, making this text an excellent introduction to metric space theory. The complex exponential and trigonometric functions are defined from first principles and great care is taken to derive their familiar properties. In particular, the appearance of π, in this context, is carefully explained. The central results of the subject, such as Cauchy's Theorem and its immediate corollaries, as well as the theory of singularities and the Residue Theorem are carefully treated while avoiding overly complicated generality. Throughout, the theory is illustrated by examples. A number of relevant results from real analysis are collected, complete with proofs, in an appendix. The approach in this book attempts to soften the impact for the student who may feel less than completely comfortable with the logical but often overly concise presentation of mathematical analysis elsewhere.​


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Alain M. Robert
“Nonstandard Analysis"
Dover Publications | 2003-10-17 | ISBN: 0486432793 | 176 pages | PDF | 3 Mb​

"This wonderful little book by Alain Robert should bring about a complete change in the learning of NSA. The author has accomplished a rare feat in the educational literature. He has succeeded in writing a book which is simple and brilliant, deep and witty, short and far-ranging. This is mathematics teaching at its best."—J.-M. Lévy-Leblond, European Journal of Physics
Brief and readable, this introduction to nonstandard analysis is based on the axiomatic IST (internal set theory) approach. The two-part treatment starts with a clear, rigorous exposition of theory, followed by self-contained chapters on applications. Exercises appear at the conclusion of each chapter, with hints in addition to full solutions. Theoretical topics include idealization, standardization and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Chapters involving applications cover invariant means, approximation of functions, differential equations, perturbation of a Green function, and an invariant subspaces problem. 1988 edition

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J.D. Murray - Asymptotic Analysis

Springer | 1992-02-02 | ISBN: 0387909370 | 164 pages | Djvu | 1,3 Mb​

From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's Asymptotic Expansions or N.G. de Bruijn's Asymptotic Methods in Analysis (1958), any academic library would do well to have this excellent introduction." (S. Puckette, University of the South) #Choice Sept. 1984#1


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Inside Calculus
(Undergraduate Texts in Mathematics)
by George R. Exner
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Publisher: Springer
Number Of Pages: 211
Publication Date: 1999-12-22
Sales Rank: 1183861
ISBN / ASIN: 0387989323
EAN: 9780387989327
Binding: Hardcover
Manufacturer: Springer
Studio: Springer
Average Rating: 3
Total Reviews: 5




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Real and Functional Analysis
(Graduate Texts in Mathematics)
By Serge Lang


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Publisher: Springer
Number Of Pages: 600
Publication Date: 1993-04-29
ISBN-10 / ASIN: 0387940014
ISBN-13 / EAN: 9780387940014
Binding: Hardcover


Book Description:
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This book is meant as a text for a first-year graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus - linear algebra, differentiation, integration - but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with point-set topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the Riemann-Stjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. It includes several major spectral theorems of analysis, showing how one can extend to infinite dimensions certain results from finite-dimensional linear algebra; a discussion of compact and Fredholm operators; and spectral theorems for Hermitian operators. The final part, on global analysis, provides an introduction to differentiable manifolds. The text includes worked examples and numerous exercises, which should be viewed as an integral part of the book. The organization of the book avoids long chains of logical interdependence, so that chapters are as independent as possible. This allows a course using the book to omit material from some chapters without compromising the exposition of material from later chapters

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An Introduction to Complex Analysis for Engineers
by Michael D. Alde​


An Introduction to Complex Analysis for Engineers Michael D. Alder June 3, 1997 Preface 1 These notes are intended to be of use to Third year Electrical and Electronic Engineers at the University of Western Australia coming to grips with Complex Function Theory. There are many text books for just this purpose, and I have insucient time to write a text book, so this is not a substitute for, say, Matthews and Howell's Complex Analysis for Mathematics and Engineering,[1], but perhaps a complement to it. At the same time, knowing how reluctant students are to use a textbook



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http://www.amazon.com/exec/obidos/ASIN/0387952187/ebooksclub-20/


Harmonic Function Theory
by Sheldon Axler


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Publisher: Springer
Number Of Pages: 259
Publication Date: 2001-01-25
Sales Rank: 1305566
ISBN / ASIN: 0387952187
EAN: 9780387952185
Binding: Hardcover
Manufacturer: Springer
Studio: Springer
Average Rating:
Total Reviews:



Book Description:
This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher¿s Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by email-supplements the text for readers who wish to explore harmonic function theory on a computer

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A Course in Modern Analysis and its Applications | Graeme L. Cohen | 0521819962


Designed for one-semester courses at the senior undergraduate level, this book will appeal to mathematics undergraduates, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance. Topics such as completeness and compactness are approached initially through convergence of sequences in metric space, and the emphasis remains on this approach. However, the alternative topological approach is described in a separate chapter. This gives the book more flexibility, making it especially useful as an introduction to more advanced areas such as functional analysis. Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for what further developments might look like. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.



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Real and Complex Analysis
By Walter Rudin

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Real and Complex Analysis
By Walter Rudin

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Real and Complex Analysis (McGraw-Hill International Editions: Mathematics Series)
by: W. Rudin


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جزاك الله كل خير وجعله في ميزان حسناتك
أخي العزيز أبحث عن ملخصات سلسلة شوم في الرياضيات
يوجد البعض منها في المنتدى ولكن ليست جميعها، ووجدت أيضا في المنتدى
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