Ravi Y.'s Books

Uniqueness And Nonuniqueness Criteria For Ordinary Differential Equations

By: Ravi P Agarwal,Vangipuram Lakshmikantham

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Uniqueness And Nonuniqueness Criteria For Ordinary Differential Equations

By: Ravi P Agarwal,Vangipuram Lakshmikantham

This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.

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332

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813104619

ISBN 13

9789813104617

500 Examples and Problems of Applied Differential Equations

By: Ravi P. Agarwal,Simona Hodis,Donal O’Regan

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500 Examples and Problems of Applied Differential Equations

By: Ravi P. Agarwal,Simona Hodis,Donal O’Regan

This book highlights an unprecedented number of real-life applications of differential equations together with the underlying theory and techniques. The problems and examples presented here touch on key topics in the discipline, including first order (linear and nonlinear) differential equations, second (and higher) order differential equations, first order differential systems, the Runge–Kutta method, and nonlinear boundary value problems. Applications include growth of bacterial colonies, commodity prices, suspension bridges, spreading rumors, modeling the shape of a tsunami, planetary motion, quantum mechanics, circulation of blood in blood vessels, price-demand-supply relations, predator-prey relations, and many more. Upper undergraduate and graduate students in Mathematics, Physics and Engineering will find this volume particularly useful, both for independent study and as supplementary reading. While many problems can be solved at the undergraduate level, a number of challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field.

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394

Publisher

Springer Nature

Published Date

ISBN 10

3030263843

ISBN 13

9783030263843

Functional Equations And Inequalities: Solutions And Stability Results

By: John Michael Rassias,E Thandapani,K Ravi,B V Senthil Kumar

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Functional Equations And Inequalities: Solutions And Stability Results

By: John Michael Rassias,E Thandapani,K Ravi,B V Senthil Kumar

This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.

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397

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813147628

ISBN 13

9789813147621

An Introduction to Ordinary Differential Equations

By: Ravi P. Agarwal,Donal O'Regan

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An Introduction to Ordinary Differential Equations

By: Ravi P. Agarwal,Donal O'Regan

Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.

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333

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387712763

ISBN 13

9780387712765

Recent Trends in Optimization Theory and Applications

By: Ratan Prakash Agarwal,Ravi P. Agarwal

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Recent Trends in Optimization Theory and Applications

By: Ratan Prakash Agarwal,Ravi P. Agarwal

World Scientific Series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering, and social problems. This volume contains 30 research articles on the theory of optimization and its applications by the leading scientists in the field. It is hoped that the material in the present volume will open new vistas in research.Contributors: B D O Anderson, M Bertaja, O J Boxma, O Burdakov, A Cantoni, D J Clements, B D Craven, J B Cruz, Jr., P Diamond, S V Drakunov, Y G Evtushenko, N M Filatov, I Galligani, J C Geromel, F Giannessi, M J Grimble, G O Guardabassi, D-W Gu, C H Houpis, D G Hull, C Itiki, X Jian, M A Johnson, R E Kalaba, J C Kalkkuhl, M R Katebi, T J Kim, P Kloeden, T Kobylarz, A J Laub, C S Lee, G Leitmann, B-G Liu, J Liu, Z-Q Luo, K A Lurie, P Maponi, J B Matson, A Mess, G Pacelli, M Pachter, I Postlethwaite, T Rapcsak, M C Recchioni, Y Sakawa, S V Savastyuk, K Schittkowski, Y Shi, M A Sikora, D D Siljak, K L Teo, C Tovey, P Tseng, F E Udwadia, H Unbehauen, A Vladimirov, B Vo, J F Whidborne, R Xu, P L Yu, V G Zhadan, F Zirilli.

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506

Publisher

World Scientific

Published Date

ISBN 10

981022382X

ISBN 13

9789810223823

Fixed Point Theory in Metric Type Spaces

By: Ravi P. Agarwal,Erdal KARAPINAR,Donal O’Regan,Antonio Francisco Roldán-López-de-Hierro

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Fixed Point Theory in Metric Type Spaces

By: Ravi P. Agarwal,Erdal KARAPINAR,Donal O’Regan,Antonio Francisco Roldán-López-de-Hierro

Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise naturally in applications. As a result, fixed point theory is an important area of study in pure and applied mathematics and it is a flourishing area of research.

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395

Publisher

Springer

Published Date

ISBN 10

331924082X

ISBN 13

9783319240824

Fixed Point Theory in Generalized Metric Spaces

By: Erdal Karapinar,Ravi P. Agarwal

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Fixed Point Theory in Generalized Metric Spaces

By: Erdal Karapinar,Ravi P. Agarwal

This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.

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141

Publisher

Springer Nature

Published Date

ISBN 10

3031149696

ISBN 13

9783031149696

Discrete Oscillation Theory

By: Ravi P. Agarwal

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Discrete Oscillation Theory

By: Ravi P. Agarwal

This book is devoted to a rapidly developing branch of the qualitative theory of difference equations with or without delays. It presents the theory of oscillation of difference equations, exhibiting classical as well as very recent results in that area. While there are several books on difference equations and also on oscillation theory for ordinary differential equations, there is until now no book devoted solely to oscillation theory for difference equations. This book is filling the gap, and it can easily be used as an encyclopedia and reference tool for discrete oscillation theory. In nine chapters, the book covers a wide range of subjects, including oscillation theory for second-order linear difference equations, systems of difference equations, half-linear difference equations, nonlinear difference equations, neutral difference equations, delay difference equations, and differential equations with piecewise constant arguments. This book summarizes almost 300 recent research papers and hence covers all aspects of discrete oscillation theory that have been discussed in recent journal articles. The presented theory is illustrated with 121 examples throughout the book. Each chapter concludes with a section that is devoted to notes and bibliographical and historical remarks. The book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. Besides serving as a reference tool for researchers in difference equations, this book can also be easily used as a textbook for undergraduate or graduate classes. It is written at a level easy to understand for college students who have had courses in calculus.

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977

Publisher

Hindawi Publishing Corporation

Published Date

ISBN 10

9775945194

ISBN 13

9789775945198

Ideals and Reality

Projective Modules and Number of Generators of Ideals

By: Friedrich Ischebeck,Ravi A. Rao

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Ideals and Reality

Projective Modules and Number of Generators of Ideals

By: Friedrich Ischebeck,Ravi A. Rao

Besides giving an introduction to Commutative Algebra - the theory of c- mutative rings - this book is devoted to the study of projective modules and the minimal number of generators of modules and ideals. The notion of a module over a ring R is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules possessing a basis are called free. So a finitely generated free R-module is of the form Rn for some n E IN, equipped with the usual operations. A module is called p- jective, iff it is a direct summand of a free one. Especially a finitely generated R-module P is projective iff there is an R-module Q with P @ Q S Rn for some n. Remarkably enough there do exist nonfree projective modules. Even there are nonfree P such that P @ Rm S Rn for some m and n. Modules P having the latter property are called stably free. On the other hand there are many rings, all of whose projective modules are free, e. g. local rings and principal ideal domains. (A commutative ring is called local iff it has exactly one maximal ideal. ) For two decades it was a challenging problem whether every projective module over the polynomial ring k[X1,. . .

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339

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540263705

ISBN 13

9783540263708

Ordinary and Partial Differential Equations

With Special Functions, Fourier Series, and Boundary Value Problems

By: Ravi P. Agarwal,Donal O'Regan

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Ordinary and Partial Differential Equations

With Special Functions, Fourier Series, and Boundary Value Problems

By: Ravi P. Agarwal,Donal O'Regan

In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.

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422

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387791469

ISBN 13

9780387791463

Nonoscillation and Oscillation Theory for Functional Differential Equations

By: Ravi P. Agarwal,Martin Bohner,Wan-Tong Li

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Nonoscillation and Oscillation Theory for Functional Differential Equations

By: Ravi P. Agarwal,Martin Bohner,Wan-Tong Li

This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential eq

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Page Count

400

Publisher

CRC Press

Published Date

ISBN 10

0203025741

ISBN 13

9780203025741

Inequalities And Applications

By: Ravi P Agarwal

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Inequalities And Applications

By: Ravi P Agarwal

World Scientific Series in Applicable Analysis (WSSIAA) reports new developments of a high mathematical standard and of current interest. Each volume in the series is devoted to mathematical analysis that has been applied, or is potentially applicable to the solution of scientific, engineering, and social problems. The third volume of WSSIAA contains 47 research articles on inequalities by leading mathematicians from all over the world and a tribute by R.M. Redheffer to Wolfgang Walter — to whom this volume is dedicated — on his 66th birthday.Contributors: A Acker, J D Aczél, A Alvino, K A Ames, Y Avishai, C Bandle, B M Brown, R C Brown, D Brydak, P S Bullen, K Deimling, J Diaz, Á Elbert, P W Eloe, L H Erbe, H Esser, M Essén, W D Evans, W N Everitt, V Ferone, A M Fink, R Ger, R Girgensohn, P Goetgheluck, W Haussmann, S Heikkilä, J Henderson, G Herzog, D B Hinton, T Horiuchi, S Hu, B Kawohl, V G Kirby; N Kirchhoff, G H Knightly, H W Knobloch, Q Kong, H König, A Kufner, M K Kwong, A Laforgia, V Lakshmikantham, S Leela, R Lemmert, E R Love, G Lüttgens, S Malek, R Manásevich, J Mawhin, R Medina, M Migda, R J Nessel, Z Páles, N S Papageorgiou, L E Payne, J Pe…ariƒ, L E Persson, A Peterson, M Pinto, M Plum, J Popenda, G Porru, R M Redheffer, A A Sagle, S Saitoh, D Sather, K Schmitt, D F Shea, A Simon, S Sivasundaram, R Sperb, C S Stanton, G Talenti, G Trombetti, S Varošanec, A S Vatsala, P Volkmann, H Wang, V Weckesser, F Zanolin, K Zeller, A Zettl.

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606

Publisher

World Scientific

Published Date

ISBN 10

9814501859

ISBN 13

9789814501859

Dynamic Inequalities On Time Scales

By: Ravi Agarwal,Donal O'Regan,Samir Saker

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Dynamic Inequalities On Time Scales

By: Ravi Agarwal,Donal O'Regan,Samir Saker

This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics. In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebyšv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.

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264

Publisher

Springer

Published Date

ISBN 10

3319110020

ISBN 13

9783319110028

OPERATIONS RESEARCH

By: NITA H. SHAH,RAVI M. GOR,HARDIK SONI

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OPERATIONS RESEARCH

By: NITA H. SHAH,RAVI M. GOR,HARDIK SONI

This comprehensive book deals with the theoretical aspects of operations research, and explains the concepts with practical examples. It begins by focusing on the need and prerequisites of operations research and moves on to discuss topics such as linear programming, integer programming, nonlinear programming, assignment problems, and inventory models in sufficient detail. Besides, this text also explains how to achieve different goals in the order of priority to optimize the objective function, various criteria of decision making under certainty, uncertainty and risk, and different techniques of analyzing the time involved in completing the project and the related cost. KEY FEATURES : Gives well-defined algorithms to illustrate the different techniques of operations research. Inventory problems are discussed with calculus. Provides worked-out examples in each chapter to illustrate the concepts discussed. This text is intended for the undergraduate and postgraduate students of Mathematics, Statistics, Engineering, and postgraduate students of Computer Applications and Business Administration. In addition, practising executives, consultants and managers will also find the book very useful.

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574

Publisher

PHI Learning Pvt. Ltd.

Published Date

ISBN 10

8120331281

ISBN 13

9788120331280

The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary

By: Kiran S. Kedlaya,Bjorn Poonen,Ravi Vakil

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The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary

By: Kiran S. Kedlaya,Bjorn Poonen,Ravi Vakil

This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.

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353

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470451247

ISBN 13

9781470451240

A First Course in Linear Models and Design of Experiments

By: N. R. Mohan Madhyastha,S. Ravi,A. S. Praveena

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A First Course in Linear Models and Design of Experiments

By: N. R. Mohan Madhyastha,S. Ravi,A. S. Praveena

This textbook presents the basic concepts of linear models, design and analysis of experiments. With the rigorous treatment of topics and provision of detailed proofs, this book aims at bridging the gap between basic and advanced topics of the subject. Initial chapters of the book explain linear estimation in linear models and testing of linear hypotheses, and the later chapters apply this theory to the analysis of specific models in designing statistical experiments. The book includes topics on the basic theory of linear models covering estimability, criteria for estimability, Gauss–Markov theorem, confidence interval estimation, linear hypotheses and likelihood ratio tests, the general theory of analysis of general block designs, complete and incomplete block designs, general row column designs with Latin square design and Youden square design as particular cases, symmetric factorial experiments, missing plot technique, analyses of covariance models, split plot and split block designs. Every chapter has examples to illustrate the theoretical results and exercises complementing the topics discussed. R codes are provided at the end of every chapter for at least one illustrative example from the chapter enabling readers to write similar codes for other examples and exercise.

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Page Count

230

Publisher

Springer Nature

Published Date

ISBN 10

9811586594

ISBN 13

9789811586590

Hardy Type Inequalities on Time Scales

By: Ravi P. Agarwal,Donal O'Regan,Samir H. Saker

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Hardy Type Inequalities on Time Scales

By: Ravi P. Agarwal,Donal O'Regan,Samir H. Saker

The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and Littlewood type inequalities, Hardy-Knopp type inequalities via convexity, Copson type inequalities, Copson-Beesack type inequalities, Liendeler type inequalities, Levinson type inequalities and Pachpatte type inequalities, Bennett type inequalities, Chan type inequalities, and Hardy type inequalities with two different weight functions. These dynamic inequalities contain the classical continuous and discrete inequalities as special cases when T = R and T = N and can be extended to different types of inequalities on different time scales such as T = hN, h > 0, T = qN for q > 1, etc.In this book the authors followed the history and development of these inequalities. Each section in self-contained and one can see the relationship between the time scale versions of the inequalities and the classical ones. To the best of the authors’ knowledge this is the first book devoted to Hardy-typeinequalities and their extensions on time scales.

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Page Count

309

Publisher

Springer

Published Date

ISBN 10

3319442996

ISBN 13

9783319442990

Set Valued Mappings with Applications in Nonlinear Analysis

By: Donal O'Regan,Ravi P. Agarwal

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Set Valued Mappings with Applications in Nonlinear Analysis

By: Donal O'Regan,Ravi P. Agarwal

Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.

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Page Count

498

Publisher

CRC Press

Published Date

ISBN 10

0203216490

ISBN 13

9780203216491

Fixed Point Theory for Lipschitzian-type Mappings with Applications

By: Ravi P. Agarwal,Donal O'Regan,D. R. Sahu

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Fixed Point Theory for Lipschitzian-type Mappings with Applications

By: Ravi P. Agarwal,Donal O'Regan,D. R. Sahu

In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis. This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields. This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.

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373

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387758186

ISBN 13

9780387758183

Oscillation Theory for Second Order Dynamic Equations

By: Ravi P. Agarwal,Said R. Grace,Donal O'Regan

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Oscillation Theory for Second Order Dynamic Equations

By: Ravi P. Agarwal,Said R. Grace,Donal O'Regan

The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journa

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416

Publisher

CRC Press

Published Date

ISBN 10

020322289X

ISBN 13

9780203222898

Econometrics

By: K. Nirmal Ravi Kumar

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Econometrics

By: K. Nirmal Ravi Kumar

This book harbors an updated and standard material on the various aspects of Econometrics. It covers both fundamental and applied aspects and is intended to serve as a basis for a course in Econometrics and attempts at satisfying a need of postgraduate and doctoral students of Economics. It is hoped that, this book will also be worthwhile to teachers, researchers, professionals etc. Note: T& F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

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