Ordinary and Partial Differential Equations

Author: Ravi P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 9780387791463
Release Date: 2008-11-13
Genre: Mathematics

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.

Applied Partial Differential Equations

Author: Richard Haberman
Publisher: Pearson College Division
ISBN: 0321797051
Release Date: 2013
Genre: Mathematics

Normal 0 false false false This book emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Green's functions, and transform methods. This text is ideal for readers interested in science, engineering, and applied mathematics.

Partial Differential Equations with Fourier Series and Boundary Value Problems

Author: Nakhlé H. Asmar
Publisher: Prentice Hall
ISBN: UCSC:32106018961745
Release Date: 2005
Genre: Mathematics

This example-rich reference fosters a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material accessible even to readers with limited exposure to topics beyond calculus. Encourages computer for illustrating results and applications, but is also suitable for use without computer access. Contains more engineering and physics applications, and more mathematical proofs and theory of partial differential equations, than the first edition. Offers a large number of exercises per section. Provides marginal comments and remarks throughout with insightful remarks, keys to following the material, and formulas recalled for the reader's convenience. Offers Mathematica files available for download from the author's website. A useful reference for engineers or anyone who needs to brush up on partial differential equations.

Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations

Author: Ratan Prakash Agarwal
Publisher: World Scientific
ISBN: 9810213573
Release Date: 1993
Genre: Mathematics

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.


Author: Jean-Paul Penot
Publisher: Springer
ISBN: 9783319324111
Release Date: 2016-12-18
Genre: Mathematics

This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.

Elementary Applied Partial Differential Equations

Author: Richard Haberman
ISBN: 013263807X
Release Date: 1998
Genre: Mathematics

KEY BENEFIT Emphasizing physical interpretations of mathematical solutions, this book introduces applied mathematics and presents partial differential equations. KEY TOPICS Leading readers from simple exercises through increasingly powerful mathematical techniques, this book discusses hear flow and vibrating strings and membranes, for a better understand of the relationship between mathematics and physical problems. It also emphasizes problem solving and provides a thorough approach to solutions. The third edition of , Elementary Applied Partial Differential Equations; With Fourier Series and Boundary Value Problems has been revised to include a new chapter covering dispersive waves. It also includes new sections covering fluid flow past a circular cylinder; reflection and refraction of light and sound waves; the finite element method; partial differential equations with spherical geometry; eigenvalue problems with a continuous and discrete spectrum; and first-order nonlinear partial differential equations. An essential reference for any technical or mathematics professional.

Differential Equations with Boundary Value Problems

Author: James R. Brannan
Publisher: John Wiley & Sons
ISBN: 9780470595350
Release Date: 2010-11-08
Genre: Mathematics

Unlike other books in the market, this second edition presents differential equations consistent with the way scientists and engineers use modern methods in their work. Technology is used freely, with more emphasis on modeling, graphical representation, qualitative concepts, and geometric intuition than on theoretical issues. It also refers to larger-scale computations that computer algebra systems and DE solvers make possible. And more exercises and examples involving working with data and devising the model provide scientists and engineers with the tools needed to model complex real-world situations.

Partial Differential Equations and Boundary Value Problems

Author: Nakhlé H. Asmar
Publisher: Pearson College Division
ISBN: 0139586202
Release Date: 2000
Genre: Mathematics

Packed with examples, this book provides a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material understandable even for readers with limited exposure to topics beyond calculus. Encourages the use of computer resources for illustrating results and applications, but is also suitable for use without computer access. Includes additional specialized topics that can be read as desired, and that can be read independently of each other. Denotes exercises requiring use of a computer with computer icons, asking readers to investigate problems using computer-generated graphics and to generate numerical data that cannot be computed by hand. Offers Mathematica files for download from the author's Web site; can be accessed through the Prentice Hall address http://www.prenhall.com/pubguide/. For engineers or anyone looking to brush up on their advanced mathematics skills.

Partial Differential Equations in Action

Author: Sandro Salsa
Publisher: Springer Science & Business Media
ISBN: 9788847007529
Release Date: 2008-02-01
Genre: Mathematics

This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines. The main purpose is on the one hand to train students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other hand to give them a solid theoretical background for numerical methods. At the end of each chapter, a number of exercises at different level of complexity is included

Fourier Analysis and Boundary Value Problems

Author: Enrique A. Gonzalez-Velasco
Publisher: Elsevier
ISBN: 0080531938
Release Date: 1996-11-28
Genre: Mathematics

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field. Topics are covered from a historical perspective with biographical information on key contributors to the field The text contains more than 500 exercises Includes practical applications of the equations to problems in both engineering and physics

Distributions Partial Differential Equations and Harmonic Analysis

Author: Dorina Mitrea
Publisher: Springer Science & Business Media
ISBN: 9781461482086
Release Date: 2013-09-20
Genre: Mathematics

​The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differential operators: the Laplace, heat, wave, Lam\'e and Schrodinger operators.​

Topological Methods in the Study of Boundary Value Problems

Author: Pablo Amster
Publisher: Springer Science & Business Media
ISBN: 9781461488934
Release Date: 2013-10-23
Genre: Mathematics

This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems. In comparison with other texts in the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties of this interesting branch of mathematics. Exercises and examples are included throughout the book, providing motivation for the reader.

Infinite Interval Problems for Differential Difference and Integral Equations

Author: R.P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 9789401007184
Release Date: 2012-12-06
Genre: Mathematics

Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970's for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applicable only to narrowly defined classes of problems. Thus scientists mainly offer~d and used special devices to construct the numerical solution assuming tacitly the existence of a solution. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study the existence of solutions to infinite interval problems. This has resulted in widely applicable results. This monograph is a cumulation mainly of the authors' research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is that we illustrate almost all the results with examples. The plan of this monograph is as follows. In Chapter 1 we present the existence theory for second order boundary value problems on infinite intervals. We begin with several examples which model real world phenom ena. A brief history of the infinite interval problem is also included. We then present general existence results for several different types of boundary value problems. Here we note that for the infinite interval problem only two major approaches are available in the literature.

Numerical Treatment of Partial Differential Equations

Author: Christian Grossmann
Publisher: Springer Science & Business Media
ISBN: 9783540715849
Release Date: 2007-08-11
Genre: Mathematics

This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques. Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.