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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.      .

Differential equations, partial. --- Functional analysis. --- Functional differential equations. --- Functions, special. --- Mathematics. --- Functional differential equations --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations --- Oscillation theory. --- 517.91 Differential equations --- Partial differential equations. --- Special functions. --- Partial Differential Equations. --- Special Functions. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Special functions --- Mathematical analysis --- Partial differential equations

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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.

Approximation theory. --- Differential equations, partial. --- Global analysis (Mathematics). --- Harmonic analysis. --- Mathematics. --- Operator theory. --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Theory of approximation --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Approximations and Expansions. --- Operator Theory. --- Analysis. --- Partial Differential Equations. --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Partial differential equations --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- 517.1 Mathematical analysis --- Mathematical analysis

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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.

Mathematics --- Differential geometry. Global analysis --- Operator theory --- Partial differential equations --- Differential equations --- Mathematical analysis --- Computer science --- differentiaalvergelijkingen --- analyse (wiskunde) --- informatica --- statistiek --- wiskunde --- Approximation theory.

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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.

Mathematics. --- History. --- History of Mathematical Sciences. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Annals --- Auxiliary sciences of history --- Math --- Science

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This textbook provides a rigorous and lucid introduction to the theory of ordinary differential equations (ODEs), which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines. Key Features of this textbook: Effectively organizes the subject into easily manageable sections in the form of 42 class-tested lectures Provides a theoretical treatment by organizing the material around theorems and proofs 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 excellent grounding and inspiration for future research contributions to the field of ODEs and related areas This book is ideal for a senior undergraduate or a graduate-level course on ordinary differential equations. Prerequisites include a course in calculus. Series: Universitext 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. Donal 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 14 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. 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.

Mathematics. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Appl.Mathematics/Computational Methods of Engineering. --- Differential Equations. --- Differential equations, partial. --- Engineering mathematics. --- Mathématiques --- Mathématiques de l'ingénieur --- Differential equations --- Differential equations. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential-algebraric equations. --- 517.91 Differential equations --- Partial differential equations. --- Applied mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Partial differential equations --- Math --- Science --- Differential-algebraic equations. --- Algebraic-differential equations --- Differential-algebraic systems --- Equations, Algebraic-differential --- Equations, Differential-algebraic --- Systems, Differential-algebraic --- Mathematical and Computational Engineering. --- Differential equations, Partial.