Transform Methods For Solving Partial Differential Equations

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Transform Methods For Solving Partial Differential Equations

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Author : Dean G. Duffy
language : en
Publisher: CRC Press
Release Date : 2004-07-15

Transform Methods For Solving Partial Differential Equations written by Dean G. Duffy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-15 with Mathematics categories.

Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found ana

Transform Methods For Solving Partial Differential Equations

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Author : Dean G. Duffy
language : en
Publisher: CRC Press
Release Date : 2004-07-15

Transform Methods For Solving Partial Differential Equations written by Dean G. Duffy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-15 with Mathematics categories.

Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found ana

Transform Methods For Solving Partial Differential Equations

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Author :
language : en
Publisher:
Release Date : 1994

Transform Methods For Solving Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Differential equations categories.

Partial Differential Equations Of Applied Mathematics

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Author : Erich Zauderer
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-24

Partial Differential Equations Of Applied Mathematics written by Erich Zauderer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-24 with Mathematics categories.

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

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Author : Victor Henner
language : en
Publisher: CRC Press
Release Date : 2019-11-20

Partial Differential Equations written by Victor Henner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-20 with Mathematics categories.

Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners’ course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor. This text introduces and promotes practice of necessary problem-solving skills. The presentation is concise and friendly to the reader. The "teaching-by-examples" approach provides numerous carefully chosen examples that guide step-by-step learning of concepts and techniques. Fourier series, Sturm-Liouville problem, Fourier transform, and Laplace transform are included. The book’s level of presentation and structure is well suited for use in engineering, physics and applied mathematics courses. Highlights: Offers a complete first course on PDEs The text’s flexible structure promotes varied syllabi for courses Written with a teach-by-example approach which offers numerous examples and applications Includes additional topics such as the Sturm-Liouville problem, Fourier and Laplace transforms, and special functions The text’s graphical material makes excellent use of modern software packages Features numerous examples and applications which are suitable for readers studying the subject remotely or independently

Applied Partial Differential Equations

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Author : Donald W. Trim
language : en
Publisher: PWS Publishing Company
Release Date : 1990

Applied Partial Differential Equations written by Donald W. Trim and has been published by PWS Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

The emphasis in this book is placed on techniques for solving partial differential equations found in physics and engineering but discussions on existence and uniqueness of solutions are included. Several different methods of solution are presented, with the primary emphasis on the classical method of separation of variables. Secondary emphasis is placed on transform solutions, as well as on the method of Green's functions.

Modern Differential Equations

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Author : Martha L. Abell
language : en
Publisher: Thomson Brooks/Cole
Release Date : 2001

Modern Differential Equations written by Martha L. Abell and has been published by Thomson Brooks/Cole this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

1. Introduction to Differential Equations. Introduction. A Graphical Approach to Solutions: Slope Fields and Direction Fields. Summary. Review Exercises. 2. First Order Equations. Separable Equations. First-Order Linear Equations. Substitution Methods and Special Equations. Exact Equations. Theory of First-Order-Equations. Numerical Methods for First-Order Equations. Summary. Review Exercises. Differential Equations at Work. Modeling the Spread of a Disease. Linear Population Model with Harvesting. Logistic Model with Harvesting. Logistic Model with Predation. 3. Applications of First Order Equations. Population Growth and Decay. Newton's Law of Cooling and Related Problems. Free-Falling Bodies. Summary. Review Exercises. Chapter 3 Differential Equations at Work. Mathematics of Finance. Algae Growth. Dialysis. Antibiotic Production. 4. Higher Order Equations. Second-Order Equations: An Introduction. Solutions of Second-Order Linear Homogeneous Equations with Constant Coefficients. Higher Order Equations: An Introduction. Solutions to Higher Order Linear Homogeneous Equations with Constant Coefficients. Introduction to Solving Nonhomogeneous Equations with Constant Coefficients: Method of Undetermined Coefficients. Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters. Cauchy-Euler Equations. Series Solutions of Ordinary Differential Equations. Summary. Review Exercises. Differential Equations at Work. Testing for Diabetes. Modeling the Motion of a Skier. The Schröinger Equation. 5. Applications of Higher Order Equations. Simple Harmonic Motion. Damped Motion. Forced Motion. Other Applications. The Pendulum Problem. Summary. Review Exercises. Differential Equations at Work. Rack-and-Gear Systems. Soft Springs. Hard Springs. Aging Springs. Bodé Plots. 6. Systems of First Order Equations. Introduction. Review of Matrix Algebra and Calculus. Preliminary Definitions and Notation. First-Order Linear Homogeneous Systems with Constant Coefficients. First-Order Linear Nonhomogeneous Systems: Undetermined Coefficients and Variation of Parameters. Phase Portraits. Nonlinear Systems. Numerical Methods. Summary. Review Exercises. Differential Equations at Work. Modeling a Fox Population in Which Rabies is Present. Controlling the Spread of Disease. FitzHugh-Nagumo Model. 7. Applications of First-Order Systems. Mechanical and Electrical Problems with First-Order Linear Systems. Diffusion and Population Problems with First-Order Linear Systems. Nonlinear Systems of Equations. Summary. Review Exercises. Differential Equations at Work. Competing Species. Food Chains. Chemical Reactor. 8. Laplace Transforms. The Laplace Transform: Preliminary Definitions and Notation. Solving Initial-Value Problems with the Laplace Transform. Laplace Transforms of Several Important Functions. The Convolution Theorem. Laplace Transform Methods for Solving Systems. Applications Using Laplace Transforms. Summary. Review Exercises. Differential Equations at Work. The Tautochrone. Vibration Absorbers. Airplane Wing. Free Vibration of a Three-Story Building. Control Systems. 9. Fourier Series. Boundary-Value Problems, Eigenvalue Problems, Sturm-Liouville Problems. Fourier Sine Series and Cosine Series. Fourier Series. Generalized Fourier Series. Summary. Review Exercises. Differential Equations at Work. Free Vibration of a Three-Story Building. Forced Damped Spring-Mass System. Approximations with Fourier Series. 10. Partial Differential Equations. Introduction to Partial Differential Equations and Separation of Variables. The One-Dimensional Heat Equation. The One-Dimensional Wave Equation. Problems in Two Dimensions: Laplace's Equation. Two-Dimensional Problems in a Circular Region. Summary. Review Exercises. Differential Equations at Work. Laplace Transforms. Waves in a Steel Rod. Media Sterilization. Numerical Methods for Solving Partial Differential Equations. Answers to Selected Questions. Index.

An Introduction To Fast Fourier Transform Methods For Partial Differential Equations With Applications

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Author : Morgan Pickering
language : en
Publisher:
Release Date : 1986

An Introduction To Fast Fourier Transform Methods For Partial Differential Equations With Applications written by Morgan Pickering and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Analyse numérique categories.

Ordinary And Partial Differential Equations

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Author : NITA H. SHAH
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2015-01-17

Ordinary And Partial Differential Equations written by NITA H. SHAH and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-17 with Mathematics categories.

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’.

Transforms And Partial Differential Equations Combo

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Author : P. Sivaramakrishna Das
language : en
Publisher: Pearson Education India
Release Date :

Transforms And Partial Differential Equations Combo written by P. Sivaramakrishna Das and has been published by Pearson Education India this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Transforms and Partial Differential Equations, 6e is designed to provide a firm foundation on the basic concepts of partial differential equations, Fourier series analysis, Fourier series techniques in solving heat flow problems, Fourier transform techniques and Z-transforms. In their trademark student-friendly style, the authors have endeavored to provide an in-depth understanding of the important principles, methods and processes of obtaining results in a systematic way with emphasis on clarity and academic rigor. Features: • More than 320 solved examples • More than 250 exercises with answers • More than 150 Part A questions with answers • Plenty of hints for problems • Includes a free book containing FAQs Table of Contents: Preface Acknowledgements About the Authors 1. Partial Differential Equations 2. Fourier Series 3. Application of Partial Differential Equations 4. Fourier Transforms 5. Z-transforms and Difference Equations Formulae To Remember