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The “lost notebook” contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan’s life.

It should be emphasized that the material on mock theta functions is perhaps Ramanujan’s deepest work. Mathematicians are probably several decades away from a complete understanding of those functions. More than half of the material in the book is on q-series, including mock theta functions; the remaining part deals with theta function identities, modular equations, incomplete elliptic integrals of the first kind and other integrals of theta functions, Eisenstein series, particular values of theta functions, the Rogers-Ramanujan continued fraction, other q-continued fractions, other integrals, and parts of Hecke’s theory of modular forms.

Account Options Sign in. Intended as an introductory-level text on Functional Analysis for the postgraduate students in Mathematics, this compact and well-organized text covers all the topics considered essential to the subject. In so doing, it provides a very good understanding of the subject to the reader. The book begins with a review of linear algebra, and then it goes on to give the basic notion of a norm on linear space proving thereby most of the basic resultsprogresses gradually, dealing with operators, and proves some of the basic theorems of Functional Analysis.

Functional Analysis A First Course 1st Edition – 9788120317352

Besides, the book analyzes more advanced topics like dual space considerations, compact operators, and spectral theory of Banach and Hilbert space operators. The text is so organized that it strives, particularly in the last chapter, to apply and relate the basic theorems to problems which arise while solving operator equations.

He has held visiting positions at Australian National University, Canberra, and University of Kaiserslautern Germany on several occasions. Besides, he has given many nxir talks at various institutions in India and abroad. A vigorous researcher in the area of Numerical Functional Analysis, Dr. It syncs automatically with your account and allows you to read online or offline wherever you are.


Please follow the detailed Help center instructions to transfer the files to supported eReaders. Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and analhsis of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied.

Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership.

Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda’s lemma; adjoints; monads.

An extra topic of cartesian closed categories and the lambda-calculus is also provided – a must for computer scientists, logicians and linguists!

Analsyis Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories.

Nearly a hundred new exercises have also been fknctional, many with solutions, to make the book more useful as a course text and for self-study. Among these papers, Andrews discovered a sheaf of pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, “Ramanujan’s lost notebook. Introduction to Calculus and Analysis I. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises.

There are three aspects of Courant and John in which it outshines some contemporaries: The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, fucntional lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract.

Richard Silverman’s new translation makes available to English readers the work of the famous contemporary Russian mathematician N. Though extensive treatises on special functions are available, these do not serve the student wnalysis the applied mathematician as well as Lebedev’s introductory and practically oriented approach.

His systematic treatment vunctional the basic theory of the more important special functions and the applications of this theory to specific problems of physics and engineering results in a practical course in the use of special functions for the student and for those concerned with actual mathematical applications or uses.

In consideration of the practical nature of the coverage, most space has been devoted to the application of cylinder functions and funtional of spherical harmonics. Lebedev, however, also treats in some detail: The arrangement of the material in the separate chapters, to a certain degree, makes the different parts of the book independent of each other.


Although a familiarity with analysiw variable theory is needed, a serious attempt has been made to keep to a minimum the required background in this area.

Various useful properties of the special functions which do not appear in the text proper will be found in the problems at the end of the appropriate chapters.

– Functional Analysis by n Nair

This edition closely adheres to the revised Russian edition Moscow, Richard Silverman, however, has made the book even more useful to the English reader. The bibliography and references have been slanted toward books available in English or the West European languages, and a number of additional problems have been added to this edition.

Elements of Real Analysis. This classic text in introductory analysis delineates and explores the intermediate steps between the basics of calculus and the ultimate stage of mathematics: Since many abstractions and generalizations originate with the real line, the author has made it the unifying theme of the text, constructing the real number system from the point of view of a Cauchy sequence a step which Dr.

9788120317352 – Functional Analysis by M.Thamban Nair

Sprecher feels is essential to learn what the real number system is. The material covered in Elements of Real Analysis should be accessible to those who have completed a course in calculus. Fhamban help give students a sound footing, Part One of the text reviews the fundamental concepts of sets and functions and the rational numbers.

Part Two explores the real line in terms of the real number system, sequences and series of number and the structure of point sets. Part Three examines the functions of a real variable in terms of continuity, differentiability, spaces of continuous functions, measure and integration, and the Fourier series. An especially valuable feature of the book is the exercises which follow each section. There are over five hundred, ranging from the simple to the highly difficult, each focusing on a concept previously introduced.