Ordinary and Partial Differential Equations
Ordinary and Partial Differential Equations

Author: Ravi P. Agarwal

Publisher: Springer Science & Business Media

Published: 2008-11-13

Total Pages: 422

ISBN-13: 0387791469

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In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.

Finite Difference Methods for Ordinary and Partial Differential Equations
Finite Difference Methods for Ordinary and Partial Differential Equations

Author: Randall J. LeVeque

Publisher: SIAM

Published: 2007-01-01

Total Pages: 356

ISBN-13: 9780898717839

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This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Ordinary and Partial Differential Equations
Ordinary and Partial Differential Equations

Author: Victor Henner

Publisher: CRC Press

Published: 2013-01-29

Total Pages: 647

ISBN-13: 1466515007

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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.

Notes on Diffy Qs
Notes on Diffy Qs

Author: Jiri Lebl

Publisher:

Published: 2019-11-13

Total Pages: 468

ISBN-13: 9781706230236

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Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.

Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations
Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations

Author: Ratan Prakash Agarwal

Publisher: World Scientific

Published: 1993

Total Pages: 328

ISBN-13: 9789810213572

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This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.

Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition)
Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition)

Author: Granville Sewell

Publisher: World Scientific

Published: 2014-12-16

Total Pages: 346

ISBN-13: 9814635111

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This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions.The Windows version of PDE2D comes free with every purchase of this book. More information at www.pde2d.com/contact.

Ordinary and Partial Differential Equations
Ordinary and Partial Differential Equations

Author: M.D.Raisinghania

Publisher: S. Chand Publishing

Published:

Total Pages: 1161

ISBN-13: 9385676164

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This book has been designed for Undergraduate (Honours) and Postgraduate students of various Indian Universities.A set of objective problems has been provided at the end of each chapter which will be useful to the aspirants of competitve examinations

Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB
Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB

Author: H.J. Lee

Publisher: CRC Press

Published: 2003-11-24

Total Pages: 528

ISBN-13: 0203010515

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This book provides a set of ODE/PDE integration routines in the six most widely used computer languages, enabling scientists and engineers to apply ODE/PDE analysis toward solving complex problems. This text concisely reviews integration algorithms, then analyzes the widely used Runge-Kutta method. It first presents a complete code before discussin

Introduction to Partial Differential Equations with Applications
Introduction to Partial Differential Equations with Applications

Author: E. C. Zachmanoglou

Publisher: Courier Corporation

Published: 2012-04-20

Total Pages: 434

ISBN-13: 048613217X

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This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.