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Book
Nonoscillation theory of functional differential equations with applications
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ISBN: 1461434548 1489998500 1280802766 9786613711113 1461434556 Year: 2012 Publisher: New York : Springer,

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This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types,  equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material. Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.      .

Focal boundary value problems for differential and difference equations.
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ISBN: 0792349784 Year: 1998 Publisher: Dordrecht Kluwer Academic Publishers

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Book
Convergence estimates in approximation theory
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ISBN: 3319027646 3319027654 Year: 2014 Publisher: Cham, Switzerland : Springer,

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The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new and more efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches.


Book
Combined measure and shift invariance theory of time scales and applications
Authors: ---
ISBN: 3031116194 3031116186 Year: 2022 Publisher: Cham, Switzerland : Springer,

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Keywords

Equacions diferencials --- Anàlisi funcional --- Teoria de la mesura --- Anells (Àlgebra) --- Integrals generalitzades --- Integral de Lebesgue --- Teoria ergòdica --- Teoria de la mesura geomètrica --- Àlgebres de mesura --- Càlcul funcional --- Càlcul de variacions --- Àlgebres de Hilbert --- Àlgebres topològiques --- Anàlisi funcional no lineal --- Anàlisi microlocal --- Espais analítics --- Espais de Hardy --- Espais d'Orlicz --- Espais funcionals --- Espais vectorials normats --- Espais vectorials --- Filtres digitals (Matemàtica) --- Funcionals --- Funcions vectorials --- Multiplicadors (Anàlisi matemàtica) --- Pertorbació (Matemàtica) --- Teoria d'operadors --- Teoria de distribucions (Anàlisi funcional) --- Teoria de functors --- Teoria de l'aproximació --- Teoria del funcional de densitat --- Teoria espectral (Matemàtica) --- Equacions funcionals --- Equacions integrals --- Càlcul --- Funcions de Bessel --- Àlgebra diferencial --- Càlcul integral --- Càlcul operacional --- Equacions d'evolució --- Equacions de camp d'Einstein --- Equacions de Lagrange --- Equacions de Pfaff --- Equacions diferencials algebraiques --- Equacions diferencials ordinàries --- Equacions en derivades parcials --- Funcions de Green --- Funcions de Lyapunov --- Problemes de contorn --- Problemes inversos (Equacions diferencials) --- Teoria d'estabilitat (Matemàtica) --- Transformació de Laplace --- Differential equations. --- 517.91 Differential equations --- Differential equations


Book
Regularity of difference equations on Banach spaces
Authors: --- ---
ISBN: 3319064479 3319064460 1322135436 Year: 2014 Publisher: Cham : Springer International Publishing : Imprint: Springer,

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This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semigroup and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.


Book
Creators of Mathematical and Computational Sciences
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ISBN: 3319108700 3319108697 Year: 2014 Publisher: Cham : Springer International Publishing : Imprint: Springer,

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The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life. … presents a picture of mathematics as a creation of the human imagination. … brings the history of mathematics to life by describing the contributions of the world’s greatest mathematicians. —Rex F. Gandy, Provost and Vice President for Academic Affairs, TAMUK   It starts with the explanation and history of numbers, arithmetic, geometry, algebra, trigonometry, and follows by describing highlights of  contributions of nearly 500 creators of mathematics back to Krishna Dwaipayana or Sage Veda Vyasa born in 3374 BC to a recent Field medalist Terence Chi–Shen Tao born in 1975. —Anthony To-Ming Lau, Ex-President, Canadian Mathematical Society   …authors explain what mathematics, mathematical science, mathematical proof, computational science, and computational proofs are. …book is strongly recommendable to mathematicians or non-mathematicians and teachers or students in order to enhance their mathematical knowledge or ability. —Sehie Park, Ex-President, Korean Mathematical Society.


Book
Dynamic Inequalities On Time Scales
Authors: --- ---
ISBN: 3319110020 3319110012 Year: 2014 Publisher: Cham : Springer International Publishing : Imprint: Springer,

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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.


Book
Ordinary and Partial Differential Equations : With Special Functions, Fourier Series, and Boundary Value Problems
Authors: ---
ISBN: 0387791450 0387791469 Year: 2009 Publisher: New York, NY : Springer New York : Imprint: Springer,

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This textbook provides a genuine treatment of ordinary and partial differential equations (ODEs and PDEs) through 50 class tested lectures. Key Features: Explains mathematical concepts with clarity and rigor, using fully worked-out examples and helpful illustrations. Develops ODEs in conjunction with PDEs and is aimed mainly toward applications. Covers important applications-oriented topics such as solutions of ODEs in the form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomicals, Legendre, Chebyshev, Hermite, and Laguerre polynomials, and the theory of Fourier series. Provides exercises at the end of each chapter for practice. This book is ideal for an undergraduate or first year graduate-level course, depending on the university. Prerequisites include a course in calculus. About the Authors: Ravi P. Agarwal received his Ph.D. in mathematics from the Indian Institute of Technology, Madras, India. He is a professor of mathematics at the Florida Institute of Technology. His research interests include numerical analysis, inequalities, fixed point theorems, and differential and difference equations. He is the author/co-author of over 800 journal articles and more than 20 books, and actively contributes to over 40 journals and book series in various capacities. Donald O’Regan received his Ph.D. in mathematics from Oregon State University, Oregon, U.S.A. He is a professor of mathematics at the National University of Ireland, Galway. He is the author/co-author of 15 books and has published over 650 papers on fixed point theory, operator, integral, differential and difference equations. He serves on the editorial board of many mathematical journals. Previously, the authors have co-authored/co-edited the following books with Springer: Infinite Interval Problems for Differential, Difference and Integral Equations; Singular Differential and Integral Equations with Applications; Nonlinear Analysis and Applications: To V. Lakshmikanthan on his 80th Birthday; An Introduction to Ordinary Differential Equations. In addition, they have collaborated with others on the following titles: Positive Solutions of Differential, Difference and Integral Equations; Oscillation Theory for Difference and Functional Differential Equations; Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations.


Book
Inequalities for differential forms
Authors: --- ---
ISBN: 1489983511 0387360344 9786612363061 1282363069 0387684174 Year: 2009 Publisher: New York : Springer Science,

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During the recent years, differential forms have played an important role in many fields. In particular, the forms satisfying the A-harmonic equations, have found wide applications in fields such as general relativity, theory of elasticity, quasiconformal analysis, differential geometry, and nonlinear differential equations in domains on manifolds. This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms. The presentation concentrates on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are also covered. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous text requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.


Book
An Introduction to Complex Analysis
Authors: --- ---
ISBN: 1461401941 146140195X Year: 2011 Publisher: New York, NY : Springer US : Imprint: Springer,

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This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner.   Key features of this textbook: -Effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures - Uses detailed examples to drive the presentation -Includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section -covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics -Provides a concise history of complex numbers     An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.

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