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Encouraged by the response to the first edition the authors have thoroughly revised Metric Spaces by incorporating suggestions received from the readers.
The Book Is Intended To Serve As A Textbook For An Introductory Course In Functional Analysis For The Senior Undergraduate And Graduate Students. It Can Also Be Useful For The Senior Students Of Applied Mathematics, Statistics, Operations Research, Engineering And Theoretical Physics. The Text Starts With A Chapter On Preliminaries Discussing Basic Concepts And Results Which Would Be Taken For Granted Later In The Book. This Is Followed By Chapters On Normed And Banach Spaces, Bounded Linear Operators, Bounded Linear Functionals. The Concept And Specific Geometry Of Hilbert Spaces, Functionals And Operators On Hilbert Spaces And Introduction To Spectral Theory. An Appendix Has Been Given On Schauder Bases.The Salient Features Of The Book Are: * Presentation Of The Subject In A Natural Way * Description Of The Concepts With Justification * Clear And Precise Exposition Avoiding Pendantry * Various Examples And Counter Examples * Graded Problems Throughout Each ChapterNotes And Remarks Within The Text Enhances The Utility Of The Book For The Students.
Key Features:Lebesgue Measure and Integration theory explained for beginners.The text is arranged in sections with a chapter on preliminaries.Numerous examples and problems for effective learning..Bibliography at the end gives contributions of authors to the subject.About the Book:The book is intended to provide a basic course in Lebesgue Measure and Integration for the Honours and Postgraduate students of various universities in India and abroad with the hope that it will open a path to the Lebesgue Theory to the students. Pains have been taken to give detailed explanations of reasons of work and of the method used together with numerous examples and counter examples at different places in ...
he book is intended to serve as a textbook for a course on Measure and Integration, for the graduate and M Phil level students at various Universities. It can be equally useful as a reference book for those who are involved in research in areas requiring the Lebesgue Theory of Integration in its generality. Pains have been taken to give detailed explanations of reasons of work and of the method used. Details are explicitly presented keeping the interest of students in view. The material has been arranged by sections, spread out in eleven chapters. The text starts with a chapter on preliminaries discussing basic concepts and results which would be taken for granted later. This is followed by chapters on Lebesgue Measurable Sets, Measure Spaces, Measurable Functions, Integration, Signed Measures, The Spaces Lp , Product Measure Spaces and Lebesgue-Stieltjes Integral.
This textbook has been conceptualized to provide a detailed description of the various aspects of Systems and Synthetic Biology, keeping the requirements of M.Sc. and Ph.D. students in mind. Also, it is hoped that this book will mentor young scientists who are willing to contribute to this area but do not know from where to begin. The book has been divided into two sections. The first section will deal with systems biology – in terms of the foundational understanding, highlighting issues in biological complexity, methods of analysis and various aspects of modelling. The second section deals with the engineering concepts, design strategies of the biological systems ranging from simple DNA/RNA fragments, switches and oscillators, molecular pathways to a complete synthetic cell will be described. Finally, the book will offer expert opinions in legal, safety, security and social issues to present a well-balanced information both for students and scientists.
Developed from the proceedings an international conference held in 1997, Function Spaces and Applications presents the work of leading mathematicians in the vital and rapidly growing field of functional analysis.
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The book presents a comprehensive study of important topics in Mechanics of pure and applied sciences. It provides knowledge of scalar and vector in optimum depth to make the students understand the concepts of Mechanics in simple, coherent and lucid manner and grasp its principles & theory. It caters to the requirements of students of B.Sc. Pass and Honours courses. Students of engineering disciplines and the ones aspiring for competitive exams such as AIME and others, will also find it useful for their preparations.