# partial differential equations theory and completely solved problems

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## Partial Differential Equations

**Author :**Thomas Hillen

**ISBN :**9781118438435

**Genre :**Mathematics

**File Size :**79. 78 MB

**Format :**PDF

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Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.

## Partial Differential Equations

**Author :**T. Hillen

**ISBN :**9781525550263

**Genre :**Mathematics

**File Size :**54. 18 MB

**Format :**PDF, Kindle

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Provides more than 150 fully solved problems for linear partial differential equations and boundary value problems. Partial Differential Equations: Theory and Completely Solved Problems offers a modern introduction into the theory and applications of linear partial differential equations (PDEs). It is the material for a typical third year university course in PDEs. The material of this textbook has been extensively class tested over a period of 20 years in about 60 separate classes. The book is divided into two parts. Part I contains the Theory part and covers topics such as a classification of second order PDEs, physical and biological derivations of the heat, wave and Laplace equations, separation of variables, Fourier series, D’Alembert’s principle, Sturm-Liouville theory, special functions, Fourier transforms and the method of characteristics. Part II contains more than 150 fully solved problems, which are ranked according to their difficulty. The last two chapters include sample Midterm and Final exams for this course with full solutions.

## Exam Prep For Partial Differential Equations Theory And

**Author :**David Mason

**ISBN :**PKEY:QA3068743

**Genre :**Education

**File Size :**23. 68 MB

**Format :**PDF, Mobi

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5,600 Exam Prep questions and answers. Ebooks, Textbooks, Courses, Books Simplified as questions and answers by Rico Publications. Very effective study tools especially when you only have a limited amount of time. They work with your textbook or without a textbook and can help you to review and learn essential terms, people, places, events, and key concepts.

## Ordinary And Partial Differential Equations

**Author :**NITA H. SHAH

**ISBN :**9788120350878

**Genre :**Mathematics

**File Size :**80. 28 MB

**Format :**PDF

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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’.

## Applications Of Lie S Theory Of Ordinary And Partial Differential Equations

**Author :**L Dresner

**ISBN :**1420050788

**Genre :**Science

**File Size :**66. 91 MB

**Format :**PDF, Kindle

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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.

## Boundary Value Problems

**Author :**David L. Powers

**ISBN :**9780125637381

**Genre :**Mathematics

**File Size :**46. 4 MB

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Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering. * CD with animations and graphics of solutions, additional exercises and chapter review questions * Nearly 900 exercises ranging in difficulty * Many fully worked examples

## Partial Differential Equations In Economics And Finance

**Author :**Suren Basov

**ISBN :**1600217060

**Genre :**Mathematics

**File Size :**58. 5 MB

**Format :**PDF, ePub

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This book reviews the basic theory of partial differential equations of the first and second order and discusses their applications in economics and finance. It starts with well-known applications to consumer and producer theory, and to the theory of option pricing and then introduces new applications that emerge from current research (some of which is the author's own) in bounded rationality, game theory, and multi-dimensional screening.

## Partial Differential Equations Of Applied Mathematics

**Author :**Erich Zauderer

**ISBN :**9781118031407

**Genre :**Mathematics

**File Size :**42. 96 MB

**Format :**PDF, ePub, Docs

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This new edition features the latest tools for modeling, characterizing, and solving partial differential equations The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples. Among the new and revised material, the book features: * A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically. * Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically. * A related FTP site that includes all the Maple code used in the text. * New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available. The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems. With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material.

## Partial Differential Equations

**Author :**Jürgen Jost

**ISBN :**9780387493190

**Genre :**Mathematics

**File Size :**35. 87 MB

**Format :**PDF, ePub

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This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. It also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. It also explores connections between elliptic, parabolic, and hyperbolic equations as well as the connection with Brownian motion and semigroups. This second edition features a new chapter on reaction-diffusion equations and systems.

## A First Course In Partial Differential Equations

**Author :**J Robert Buchanan

**ISBN :**9789813226456

**Genre :**Mathematics

**File Size :**67. 89 MB

**Format :**PDF, ePub, Mobi

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Resources for instructors who adopt this textbook:Lecture SlidesInstructors' Manual (complete solutions and supporting work)Students' Manual (final answers to computational exercises) Kindly send your requests to [email protected] This textbook gives an introduction to Partial Differential Equations (PDEs), for any reader wishing to learn and understand the basic concepts, theory, and solution techniques of elementary PDEs. The only prerequisite is an undergraduate course in Ordinary Differential Equations. This work contains a comprehensive treatment of the standard second-order linear PDEs, the heat equation, wave equation, and Laplace's equation. First-order and some common nonlinear PDEs arising in the physical and life sciences, with their solutions, are also covered. This textbook includes an introduction to Fourier series and their properties, an introduction to regular Sturm–Liouville boundary value problems, special functions of mathematical physics, a treatment of nonhomogeneous equations and boundary conditions using methods such as Duhamel's principle, and an introduction to the finite difference technique for the numerical approximation of solutions. All results have been rigorously justified or precise references to justifications in more advanced sources have been cited. Appendices providing a background in complex analysis and linear algebra are also included for readers with limited prior exposure to those subjects. The textbook includes material from which instructors could create a one- or two-semester course in PDEs. Students may also study this material in preparation for a graduate school (masters or doctoral) course in PDEs. The lecture slides, instructors' manual and students' manual is available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected]