M Thamban Nair's Books

Measure and Integration

A First Course

By: M Thamban Nair

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This concise text is intended as an introductory course in measure and integration. It covers essentials of the subject, providing ample motivation for new concepts and theorems in the form of discussion and remarks, and with many worked-out examples. The novelty of Measure and Integration: A First Course is in its style of exposition of the standard material in a student-friendly manner. New concepts are introduced progressively from less abstract to more abstract so that the subject is felt on solid footing. The book starts with a review of Riemann integration as a motivation for the necessity of introducing the concepts of measure and integration in a general setting. Then the text slowly evolves from the concept of an outer measure of subsets of the set of real line to the concept of Lebesgue measurable sets and Lebesgue measure, and then to the concept of a measure, measurable function, and integration in a more general setting. Again, integration is first introduced with non-negative functions, and then progressively with real and complex-valued functions. A chapter on Fourier transform is introduced only to make the reader realize the importance of the subject to another area of analysis that is essential for the study of advanced courses on partial differential equations. Key Features Numerous examples are worked out in detail. Lebesgue measurability is introduced only after convincing the reader of its necessity. Integrals of a non-negative measurable function is defined after motivating its existence as limits of integrals of simple measurable functions. Several inquisitive questions and important conclusions are displayed prominently. A good number of problems with liberal hints is provided at the end of each chapter. The book is so designed that it can be used as a text for a one-semester course during the first year of a master's program in mathematics or at the senior undergraduate level. About the Author M. Thamban Nair is a professor of mathematics at the Indian Institute of Technology Madras, Chennai, India. He was a post-doctoral fellow at the University of Grenoble, France through a French government scholarship, and also held visiting positions at Australian National University, Canberra, University of Kaiserslautern, Germany, University of St-Etienne, France, and Sun Yat-sen University, Guangzhou, China. The broad area of Prof. Nair’s research is in functional analysis and operator equations, more specifically, in the operator theoretic aspects of inverse and ill-posed problems. Prof. Nair has published more than 70 research papers in nationally and internationally reputed journals in the areas of spectral approximations, operator equations, and inverse and ill-posed problems. He is also the author of three books: Functional Analysis: A First Course (PHI-Learning, New Delhi), Linear Operator Equations: Approximation and Regularization (World Scientific, Singapore), and Calculus of One Variable (Ane Books Pvt. Ltd, New Delhi), and he is also co-author of Linear Algebra (Springer, New York).

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194

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CRC Press

Published Date

ISBN 10

1000739872

ISBN 13

9781000739879

Calculus of One Variable

By: M. Thamban Nair

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Calculus of One Variable

By: M. Thamban Nair

This book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course.

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350

Publisher

Springer Nature

Published Date

ISBN 10

3030886379

ISBN 13

9783030886370

Linear Operator Equations

Approximation and Regularization

By: M. Thamban Nair

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Linear Operator Equations

Approximation and Regularization

By: M. Thamban Nair

Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be. This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.

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264

Publisher

World Scientific

Published Date

ISBN 10

9812835652

ISBN 13

9789812835659

Measure and Integration

A First Course

By: M Thamban Nair

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Measure and Integration

A First Course

By: M Thamban Nair

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194

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CRC Press

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ISBN 10

1000739872

ISBN 13

9781000739879

Linear Algebra

By: M. Thamban Nair,Arindama Singh

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Linear Algebra

By: M. Thamban Nair,Arindama Singh

This book introduces the fundamental concepts, techniques and results of linear algebra that form the basis of analysis, applied mathematics and algebra. Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by scientists and engineers. It also lays the foundation for the language and framework for modern analysis and its applications. Divided into seven chapters, it discusses vector spaces, linear transformations, best approximation in inner product spaces, eigenvalues and eigenvectors, block diagonalisation, triangularisation, Jordan form, singular value decomposition, polar decomposition, and many more topics that are relevant to applications. The topics chosen have become well-established over the years and are still very much in use. The approach is both geometric and algebraic. It avoids distraction from the main theme by deferring the exercises to the end of each section. These exercises aim at reinforcing the learned concepts rather than as exposing readers to the tricks involved in the computation. Problems included at the end of each chapter are relatively advanced and require a deep understanding and assimilation of the topics.

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348

Publisher

Springer

Published Date

ISBN 10

9811309264

ISBN 13

9789811309267

Calculus of One Variable

By: M. Thamban Nair

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Calculus of One Variable

By: M. Thamban Nair

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350

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Springer Nature

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ISBN 10

3030886379

ISBN 13

9783030886370

FUNCTIONAL ANALYSIS

A FIRST COURSE

By: NAIR, M. THAMBAN

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FUNCTIONAL ANALYSIS

A FIRST COURSE

By: NAIR, M. THAMBAN

Intended as an introductory text on Functional Analysis for the postgraduate students of Mathematics, this compact and well-organized book 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 results), progresses gradually, dealing with operators, and proves some of the basic theorems of Functional Analysis. 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. The present edition is a thoroughly revised version of its first edition, which also includes a section on Hahn-Banach extension theorem for operators and discussions on Lax-Milgram theorem. This student-friendly text, with its clear exposition of concepts, should prove to be a boon to the beginner aspiring to have an insight into Functional Analysis. KEY FEATURES • Plenty of examples have been worked out in detail, which not only illustrate a particular result, but also point towards its limitations so that subsequent stronger results follow. • Exercises, which are designed to aid understanding and to promote mastery of the subject, are interspersed throughout the text. TARGET AUDIENCE • M.Sc. Mathematics

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Page Count

560

Publisher

PHI Learning Pvt. Ltd.

Published Date

ISBN 10

9390544017

ISBN 13

9789390544011

Linear Algebra

By: M. Thamban Nair,Arindama Singh

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Linear Algebra

By: M. Thamban Nair,Arindama Singh

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348

Publisher

Springer

Published Date

ISBN 10

9811309264

ISBN 13

9789811309267

Linear Operator Equations

Approximation and Regularization

By: M. Thamban Nair

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Linear Operator Equations

Approximation and Regularization

By: M. Thamban Nair

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Solve jigsaw puzzle

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Page Count

264

Publisher

World Scientific

Published Date

ISBN 10

9812835652

ISBN 13

9789812835659

Book's by M Thamban Nair

Measure and Integration

Measure and Integration

Calculus of One Variable

Calculus of One Variable

Linear Operator Equations

Linear Operator Equations

Measure and Integration

Measure and Integration

Linear Algebra

Linear Algebra

Calculus of One Variable

Calculus of One Variable

FUNCTIONAL ANALYSIS

FUNCTIONAL ANALYSIS

Linear Algebra

Linear Algebra

Linear Operator Equations

Linear Operator Equations

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