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Ordinary Differential Equations

Ordinary Differential Equations Book
Author : Morris Tenenbaum,Harry Pollard
Publisher : Courier Corporation
Release : 1963
ISBN : 0486649407
Language : En, Es, Fr & De

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Book Description :

Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

Differential Equations

Differential Equations  Book
Author : Rukmangadachari
Publisher : Pearson Education India
Release : 2000
ISBN : 9332511640
Language : En, Es, Fr & De

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Book Description :

Differential Equations presents the basics of differential equations. With equal emphasis on theoretical and practical concepts, the book provides a balanced coverage of all topics essential to master the subject at the undergraduate level.

The Theory of Differential Equations

The Theory of Differential Equations Book
Author : Walter G. Kelley,Allan C. Peterson
Publisher : Springer Science & Business Media
Release : 2010-04-22
ISBN : 1441957820
Language : En, Es, Fr & De

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Book Description :

For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as perturbation methods and differential equations and Mathematica. In addition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible with Mathematica, version 7.0. It also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2 concerning fundamental matrices, and many more other enhancements to the first edition. This book can be used either for a second course in ordinary differential equations or as an introductory course for well-prepared students. The prerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from linear algebra are introduced along with examples in the book. An undergraduate course in analysis is needed for the more theoretical subjects covered in the final two chapters.

Ordinary Differential Equations

Ordinary Differential Equations Book
Author : Edward L. Ince
Publisher : Courier Corporation
Release : 1956-01-01
ISBN : 0486603490
Language : En, Es, Fr & De

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Book Description :

Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; further developments in the theory of boundary problems; existence theorems, equations of first order; nonlinear equations of higher order; more. "Highly recommended" — Electronics Industries.

An Introduction to Ordinary Differential Equations

An Introduction to Ordinary Differential Equations Book
Author : Earl A. Coddington
Publisher : Dover
Release : 1961
ISBN : 9780486659428
Language : En, Es, Fr & De

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Book Description :

A thorough and systematic first course in elementary differential equations for undergraduates in mathematics and science, with many exercises and problems (with answers).

An Introduction to Differential Equations and Their Applications

An Introduction to Differential Equations and Their Applications Book
Author : Stanley J. Farlow
Publisher : Courier Corporation
Release : 2006-03-11
ISBN : 048644595X
Language : En, Es, Fr & De

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Book Description :

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.

Ordinary and Partial Differential Equations

Ordinary and Partial Differential Equations Book
Author : Victor Henner,Tatyana Belozerova,Mikhail Khenner
Publisher : CRC Press
Release : 2013-01-29
ISBN : 1466515007
Language : En, Es, Fr & De

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Book Description :

Covers ODEs and PDEs—in One Textbook Until now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn’t exist. Fulfilling this need, Ordinary and Partial Differential Equations provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as intuitive, easy-to-use software. Teaches the Key Topics in Differential Equations The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations. It also discusses other optional but important topics such as integral equations, Fourier series, and special functions. Numerous carefully chosen examples offer practical guidance on the concepts and techniques. Guides Students through the Problem-Solving Process Requiring no user programming, the accompanying computer software allows students to fully investigate problems, thus enabling a deeper study into the role of boundary and initial conditions, the dependence of the solution on the parameters, the accuracy of the solution, the speed of a series convergence, and related questions. The ODE module compares students’ analytical solutions to the results of computations while the PDE module demonstrates the sequence of all necessary analytical solution steps.

Partial Differential Equations for Scientists and Engineers

Partial Differential Equations for Scientists and Engineers Book
Author : Stanley J. Farlow
Publisher : Courier Corporation
Release : 1993
ISBN : 048667620X
Language : En, Es, Fr & De

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Book Description :

This highly useful text shows the reader how to formulate a partial differential equation from the physical problem and how to solve the equation.

ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS

ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS Book
Author : NITA H. SHAH
Publisher : PHI Learning Pvt. Ltd.
Release : 2015-01-17
ISBN : 8120350871
Language : En, Es, Fr & De

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Book Description :

This revised and updated text, now in its second edition, continues to present the theoretical concepts of methods of solutions of ordinary and partial differential equations. It equips students with the various tools and techniques to model different physical problems using such equations. The book discusses the basic concepts of ordinary and partial differential equations. It contains different methods of solving ordinary differential equations of first order and higher degree. It gives the solution methodology for linear differential equations with constant and variable coefficients and linear differential equations of second order. The text elaborates simultaneous linear differential equations, total differential equations, and partial differential equations along with the series solution of second order linear differential equations. It also covers Bessel’s and Legendre’s equations and functions, and the Laplace transform. Finally, the book revisits partial differential equations to solve the Laplace equation, wave equation and diffusion equation, and discusses the methods to solve partial differential equations using the Fourier transform. A large number of solved examples as well as exercises at the end of chapters help the students comprehend and strengthen the underlying concepts. The book is intended for undergraduate and postgraduate students of Mathematics (B.A./B.Sc., M.A./M.Sc.), and undergraduate students of all branches of engineering (B.E./B.Tech.), as part of their course in Engineering Mathematics. New to the SECOND Edition • Includes new sections and subsections such as applications of differential equations, special substitution (Lagrange and Riccati), solutions of non-linear equations which are exact, method of variation of parameters for linear equations of order higher than two, and method of undetermined coefficients • Incorporates several worked-out examples and exercises with their answers • Contains a new Chapter 19 on ‘Z-Transforms and its Applications’.

ADVANCED DIFFERENTIAL EQUATIONS

ADVANCED DIFFERENTIAL EQUATIONS Book
Author : M D RAISINGHANIA
Publisher : S. Chand Publishing
Release : 2018
ISBN : 9352535898
Language : En, Es, Fr & De

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Book Description :

This book has been designed to acquaint the students with advanced concepts of differential equations. Comprehensively written, it covers topics such as Boundary Value Problems and their Separation of Variables, Laplace Transforms with Applications, Fourier Transforms and their Applications, the Hankel Transform and its Applications and Calculus of Variations. While the textbook lucidly explains the theoretical concepts, it also presents the various methods and applications related to differential equations. Students of mathematics would find this book extremely useful as well as the aspirants of various competitive examinations.

Ordinary Differential Equations with Applications

Ordinary Differential Equations with Applications Book
Author : Ali Mason
Publisher : Scientific e-Resources
Release : 2018-10-20
ISBN : 1839473282
Language : En, Es, Fr & De

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Book Description :

Ordinary differential equations (ODEs) arise in many contexts of mathematics and science (social as well as natural). Mathematical descriptions of change use differentials and derivatives. Various differentials, derivatives, and functions become related to each other via equations, and thus a differential equation is a result that describes dynamically changing phenomena, evolution, and variation. Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time), or gradients of quantities, which is how they enter differential equations. Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. Systems of differential equations form the basis of mathematical models in a wide range of fields - from engineering and physical sciences to finance and biological sciences. Differential equations are relations between unknown functions and their derivatives. Computing numerical solutions to differential equations is one of the most important tasks in technical computing, and one of the strengths of MATLAB. The book explains the origins of various types of differential equations. The scope of the book is limited to linear differential equations of the first order, linear differential equation of higher order, partial differential equations and special methods of solution of differential equations of second order, keeping in view the requirement of students.

Ordinary Differential Equations with Applications

Ordinary Differential Equations with Applications Book
Author : Carmen Chicone
Publisher : Springer Science & Business Media
Release : 2006-05-18
ISBN : 0387307699
Language : En, Es, Fr & De

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Book Description :

Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.

Handbook of Differential Equations Ordinary Differential Equations

Handbook of Differential Equations  Ordinary Differential Equations Book
Author : A. Canada,P. Drabek,A. Fonda
Publisher : Elsevier
Release : 2005-09-02
ISBN : 9780080461083
Language : En, Es, Fr & De

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Book Description :

This handbook is the second volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience. . Six chapters covering a variety of problems in ordinary differential equations. . Both, pure mathematical research and real word applications are reflected . Written by leading researchers in the area.

Volterra Integral and Differential Equations

Volterra Integral and Differential Equations Book
Author : Ted A. Burton
Publisher : Elsevier
Release : 2005-04-01
ISBN : 0080459552
Language : En, Es, Fr & De

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Book Description :

Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory. Liapunov's direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential equations, and functional differential equations. By Chapter 7 the momentum has built until we are looking at problems on the frontier. Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability. Chapter 8 presents a solid foundation for the theory of functional differential equations. Many recent results on stability and periodic solutions of functional differential equations are given and unsolved problems are stated. Key Features: - Smooth transition from ordinary differential equations to integral and functional differential equations. - Unification of the theories, methods, and applications of ordinary and functional differential equations. - Large collection of examples of Liapunov functions. - Description of the history of stability theory leading up to unsolved problems. - Applications of the resolvent to stability and periodic problems. 1. Smooth transition from ordinary differential equations to integral and functional differential equations. 2. Unification of the theories, methods, and applications of ordinary and functional differential equations. 3. Large collection of examples of Liapunov functions. 4. Description of the history of stability theory leading up to unsolved problems. 5. Applications of the resolvent to stability and periodic problems.

Partial Differential Equations

Partial Differential Equations Book
Author : E. T. Copson,Edward Thomas Copson
Publisher : CUP Archive
Release : 1975-10-02
ISBN : 9780521098939
Language : En, Es, Fr & De

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Book Description :

In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the theory of partial differential equations, the classical theory retains its relevance in several important respects. Many branches of classical analysing have their origins in the rigourous discussion of problems in applies mathematics and theoretical physics, and the classical treatment of the theory of partial differential equations still provides the best method of treating many physical problems. A knowledge of the classical theory is essential for pure mathematics who intend to undertake research in this field, whatever approach they ultimately adopt. The numerical analyst needs a knowledge of classical theory in order to decide whether a problem has a unique solution or not.

Partial Differential Equations

Partial Differential Equations Book
Author : Avner Friedman
Publisher : Courier Corporation
Release : 2008
ISBN : 0486469190
Language : En, Es, Fr & De

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Book Description :

This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists. Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of weak derivatives, proves various inequalities and imbedding problems, and derives smoothness theorems. Part Two concerns evolution equations in Banach space and develops the theory of semigroups. It solves the initial-boundary value problem for parabolic equations and covers backward uniqueness, asymptotic behavior, and lower bounds at infinity. The final section includes independent topics directly related to the methods and results of the previous material, including the analyticity of solutions of elliptic and parabolic equations, asymptotic behavior of solutions of elliptic equations near infinity, and problems in the theory of control in Banach space.

Analytic Methods for Partial Differential Equations

Analytic Methods for Partial Differential Equations Book
Author : G. Evans,J. Blackledge,P. Yardley
Publisher : Springer Science & Business Media
Release : 1999-11-01
ISBN : 3540761241
Language : En, Es, Fr & De

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Book Description :

This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.

Differential Equations with Symbolic Computation

Differential Equations with Symbolic Computation Book
Author : Dongming Wang
Publisher : Springer Science & Business Media
Release : 2005-08-15
ISBN : 9783764373689
Language : En, Es, Fr & De

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Book Description :

This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.

Mathematical Physics with Partial Differential Equations

Mathematical Physics with Partial Differential Equations Book
Author : James Kirkwood
Publisher : Academic Press
Release : 2011-12-01
ISBN : 0123869943
Language : En, Es, Fr & De

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Book Description :

Mathematical Physics with Partial Differential Equations is for advanced undergraduate and beginning graduate students taking a course on mathematical physics taught out of math departments. The text presents some of the most important topics and methods of mathematical physics. The premise is to study in detail the three most important partial differential equations in the field – the heat equation, the wave equation, and Laplace’s equation. The most common techniques of solving such equations are developed in this book, including Green’s functions, the Fourier transform, and the Laplace transform, which all have applications in mathematics and physics far beyond solving the above equations. The book’s focus is on both the equations and their methods of solution. Ordinary differential equations and PDEs are solved including Bessel Functions, making the book useful as a graduate level textbook. The book’s rigor supports the vital sophistication for someone wanting to continue further in areas of mathematical physics. Examines in depth both the equations and their methods of solution Presents physical concepts in a mathematical framework Contains detailed mathematical derivations and solutions— reinforcing the material through repetition of both the equations and the techniques Includes several examples solved by multiple methods—highlighting the strengths and weaknesses of various techniques and providing additional practice

An Introduction to Stochastic Differential Equations

An Introduction to Stochastic Differential Equations Book
Author : Lawrence C. Evans
Publisher : American Mathematical Soc.
Release : 2012-12-11
ISBN : 1470410540
Language : En, Es, Fr & De

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Book Description :

These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).