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Author : Viktor Vladimirovich Nemytskii
Publisher :
ISBN 13 :
Total Pages : 523 pages
Book Rating : 4.:/5 (52 download)
Download or read book Quantitative Theory of Differential Equations written by Viktor Vladimirovich Nemytskii and published by . This book was released on 1960 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James Hetao Liu
Publisher :
ISBN 13 :
Total Pages : 584 pages
Book Rating : 4.X/5 (4 download)
Download or read book A First Course in the Qualitative Theory of Differential Equations written by James Hetao Liu and published by . This book was released on 2003 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete analysis of those subjects that are of fundamental importance to the qualitative theory of differential equations and related to current research-including details that other books in the field tend to overlook. Chapters 1-7 cover the basic qualitative properties concerning existence and uniqueness, structures of solutions, phase portraits, stability, bifurcation and chaos. Chapters 8-12 cover stability, dynamical systems, and bounded and periodic solutions. A good reference book for teachers, researchers, and other professionals.
Author : Courtney Brown
Publisher : SAGE
ISBN 13 : 1412941083
Total Pages : 121 pages
Book Rating : 4.4/5 (129 download)
Download or read book Differential Equations written by Courtney Brown and published by SAGE. This book was released on 2007-05-18 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Differential Equations: A Modeling Approach' explains the mathematics and theory of differential equations. Graphical methods of analysis are emphasized over formal proofs, making the text even more accessible for newcomers to the subject matter.
Author : Fred Brauer
Publisher : Courier Corporation
ISBN 13 : 0486151514
Total Pages : 325 pages
Book Rating : 4.4/5 (861 download)
Download or read book The Qualitative Theory of Ordinary Differential Equations written by Fred Brauer and published by Courier Corporation. This book was released on 2012-12-11 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.
Author : Robert Mattheij
Publisher : SIAM
ISBN 13 : 9780898719178
Total Pages : 423 pages
Book Rating : 4.7/5 (191 download)
Download or read book Ordinary Differential Equations in Theory and Practice written by Robert Mattheij and published by SIAM. This book was released on 1996-01-01 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained. Audience: the book is intended for use as a textbook for both undergraduate and graduate courses, and it can also serve as a reference for students and researchers alike.
Author : Jianfeng Zhang
Publisher : Springer
ISBN 13 : 1493972561
Total Pages : 392 pages
Book Rating : 4.4/5 (939 download)
Download or read book Backward Stochastic Differential Equations written by Jianfeng Zhang and published by Springer. This book was released on 2017-08-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
Author : V. DHARMAIAH
Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 8120346661
Total Pages : 403 pages
Book Rating : 4.1/5 (23 download)
Download or read book INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION written by V. DHARMAIAH and published by PHI Learning Pvt. Ltd.. This book was released on 2012-09-19 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematically-organized text on the theory of differential equations deals with the basic concepts and the methods of solving ordinary differential equations. Various existence theorems, properties of uniqueness, oscillation and stability theories, have all been explained with suitable examples to enhance students’ understanding of the subject. The book also discusses in sufficient detail the qualitative, the quantitative, and the approximation techniques, linear equations with variable and constants coefficients, regular singular points, and homogeneous equations with analytic coefficients. Finally, it explains Riccati equation, boundary value problems, the Sturm–Liouville problem, Green’s function, the Picard’s theorem, and the Sturm–Picone theorem. The text is supported by a number of worked-out examples to make the concepts clear, and it also provides a number of exercises help students test their knowledge and improve their skills in solving differential equations. The book is intended to serve as a text for the postgraduate students of mathematics and applied mathematics. It will also be useful to the candidates preparing to sit for the competitive examinations such as NET and GATE.
Author : Christian Seifert
Publisher : Springer Nature
ISBN 13 : 3030893979
Total Pages : 321 pages
Book Rating : 4.0/5 (38 download)
Download or read book Evolutionary Equations written by Christian Seifert and published by Springer Nature. This book was released on 2022 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.
Author : Luis Barreira
Publisher : American Mathematical Soc.
ISBN 13 : 0821887491
Total Pages : 266 pages
Book Rating : 4.8/5 (218 download)
Download or read book Ordinary Differential Equations written by Luis Barreira and published by American Mathematical Soc.. This book was released on 2012-06-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.
Author : P. F. Hsieh
Publisher : Springer
ISBN 13 : 3540364544
Total Pages : 234 pages
Book Rating : 4.5/5 (43 download)
Download or read book Analytic Theory of Differential Equations written by P. F. Hsieh and published by Springer. This book was released on 2006-11-15 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : L Dresner
Publisher : CRC Press
ISBN 13 : 9781420050783
Total Pages : 242 pages
Book Rating : 4.0/5 (57 download)
Download or read book Applications of Lie's Theory of Ordinary and Partial Differential Equations written by L Dresner and published by CRC Press. This book was released on 1998-01-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.
Author : S. Leela
Publisher : Springer Science & Business Media
ISBN 13 : 9491216252
Total Pages : 218 pages
Book Rating : 4.4/5 (912 download)
Download or read book THEORY OF CAUSAL DIFFERENTIAL EQUATIONS written by S. Leela and published by Springer Science & Business Media. This book was released on 2010-01-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.
Author : Stanley J. Farlow
Publisher : Courier Corporation
ISBN 13 : 0486135136
Total Pages : 642 pages
Book Rating : 4.4/5 (861 download)
Download or read book An Introduction to Differential Equations and Their Applications written by Stanley J. Farlow and published by Courier Corporation. This book was released on 2012-10-23 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.
Author : C.M. Dafermos
Publisher : Elsevier
ISBN 13 : 008046565X
Total Pages : 653 pages
Book Rating : 4.0/5 (84 download)
Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2011-09-22 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's. Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savaré discusses the most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionary partial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell's capability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other. The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function. The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class of non-linear equations is investigated, with applications to stochastic control and differential games. The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models. - Volume 1 focuses on the abstract theory of evolution - Volume 2 considers more concrete probelms relating to specific applications - Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs
Author : Alexander V. Prasolov
Publisher : Nova Science Publishers
ISBN 13 : 9781634849371
Total Pages : 0 pages
Book Rating : 4.8/5 (493 download)
Download or read book Some Quantitative Methods and Models in Economic Theory written by Alexander V. Prasolov and published by Nova Science Publishers. This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes an intermediate place between monographs and textbooks: on the one hand, it contains known, yet unusually portrayed facts, and on the other hand, the author brings his own results corresponding to the field of research. It is already obvious from the title that while reading the book, attention and concentration are required, as it is always necessary when studying books with mathematical content. Mathematical models and methods in the economic theory are very various. They are as follows: econometrics, the game theory, operation research, nonlinear and chaotic dynamics and many other aspects as well. The book will be interesting only to those who are already familiar with corresponding tasks as well as to students at all levels specializing in economic dynamics, in decision-making methods, in forecasting effects of management and in the analysis of interaction of economic agents. In terms of the most interesting and new models of economic dynamics, the authors emphasize multidimensional nonlinear systems of the differential equations of Lotka-Volterra type. These models have been constructed and analyzed, and scopes of their application and various methods of coefficients identification have been offered for them. The analysis of the competition between various economic agents (i.e. branches of economy, rival companies and sellers in the market) has been made. Another fact unusual to similar monographs is the inclusion of the theory of differential equations with the retarded argument. In economic theory, there are numerous examples of models being used with discrete time (they also have been given attention here) and with time lags (concentrated or distributed). Such an approach gives more adequate models without lags, but in the differential equations with continuous time, the introduction of delay complicates systems while the growth of delay the qualitative behavior of trajectories is changed. Additionally, there appear fluctuations such as stability being changed by instability, etc. As the author has belonged to the St. Petersburg Mathematical School for more than thirty-five years, the list of references contains many Russian names which may be unknown to Western readers. However, the list also includes world classical scientists who devoted their works to mathematical methods in economics. In this monograph, an attentive reader will find numerous points for further analysis which can become a subject of publications or theses. In some cases, the text is conducted in a polemic manner that is, the author is always open for discussions and does not consider his work to be "the ultimate truth".
Author : Maria C. Mariani
Publisher : John Wiley & Sons
ISBN 13 : 1118629965
Total Pages : 496 pages
Book Rating : 4.1/5 (186 download)
Download or read book Quantitative Finance written by Maria C. Mariani and published by John Wiley & Sons. This book was released on 2019-11-06 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a multitude of topics relevant to the quantitative finance community by combining the best of the theory with the usefulness of applications Written by accomplished teachers and researchers in the field, this book presents quantitative finance theory through applications to specific practical problems and comes with accompanying coding techniques in R and MATLAB, and some generic pseudo-algorithms to modern finance. It also offers over 300 examples and exercises that are appropriate for the beginning student as well as the practitioner in the field. The Quantitative Finance book is divided into four parts. Part One begins by providing readers with the theoretical backdrop needed from probability and stochastic processes. We also present some useful finance concepts used throughout the book. In part two of the book we present the classical Black-Scholes-Merton model in a uniquely accessible and understandable way. Implied volatility as well as local volatility surfaces are also discussed. Next, solutions to Partial Differential Equations (PDE), wavelets and Fourier transforms are presented. Several methodologies for pricing options namely, tree methods, finite difference method and Monte Carlo simulation methods are also discussed. We conclude this part with a discussion on stochastic differential equations (SDE’s). In the third part of this book, several new and advanced models from current literature such as general Lvy processes, nonlinear PDE's for stochastic volatility models in a transaction fee market, PDE's in a jump-diffusion with stochastic volatility models and factor and copulas models are discussed. In part four of the book, we conclude with a solid presentation of the typical topics in fixed income securities and derivatives. We discuss models for pricing bonds market, marketable securities, credit default swaps (CDS) and securitizations. Classroom-tested over a three-year period with the input of students and experienced practitioners Emphasizes the volatility of financial analyses and interpretations Weaves theory with application throughout the book Utilizes R and MATLAB software programs Presents pseudo-algorithms for readers who do not have access to any particular programming system Supplemented with extensive author-maintained web site that includes helpful teaching hints, data sets, software programs, and additional content Quantitative Finance is an ideal textbook for upper-undergraduate and beginning graduate students in statistics, financial engineering, quantitative finance, and mathematical finance programs. It will also appeal to practitioners in the same fields.
Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
ISBN 13 : 3642971490
Total Pages : 287 pages
Book Rating : 4.6/5 (429 download)
Download or read book Nonlinear Differential Equations and Dynamical Systems written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.
