Half-Linear Differential Equations

Half-Linear Differential Equations
Author: Ondrej Dosly
Publisher: Elsevier
Total Pages: 533
Release: 2005-07-06
Genre: Mathematics
ISBN: 0080461239

The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations.- The first complete treatment of the qualitative theory of half-linear differential equations.- Comparison of linear and half-linear theory.- Systematic approach to half-linear oscillation and asymptotic theory.- Comprehensive bibliography and index.- Useful as a reference book in the topic.

Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations
Author: R.P. Agarwal
Publisher: Springer Science & Business Media
Total Pages: 700
Release: 2002-07-31
Genre: Mathematics
ISBN: 9781402008023

In this monograph, the authors present a compact, thorough, systematic, and self-contained oscillation theory for linear, half-linear, superlinear, and sublinear second-order ordinary differential equations. An important feature of this monograph is the illustration of several results with examples of current interest. This book will stimulate further research into oscillation theory. This book is written at a graduate level, and is intended for university libraries, graduate students, and researchers working in the field of ordinary differential equations.

Finite Difference Methods for Ordinary and Partial Differential Equations

Finite Difference Methods for Ordinary and Partial Differential Equations
Author: Randall J. LeVeque
Publisher: SIAM
Total Pages: 356
Release: 2007-01-01
Genre: Mathematics
ISBN: 9780898717839

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.

Linear Partial Differential Equations for Scientists and Engineers

Linear Partial Differential Equations for Scientists and Engineers
Author: Tyn Myint-U
Publisher: Springer Science & Business Media
Total Pages: 790
Release: 2007-04-05
Genre: Mathematics
ISBN: 0817645608

This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.

Partial Differential Equations

Partial Differential Equations
Author: Walter A. Strauss
Publisher: John Wiley & Sons
Total Pages: 467
Release: 2007-12-21
Genre: Mathematics
ISBN: 0470054565

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Introduction to Linear Algebra and Differential Equations

Introduction to Linear Algebra and Differential Equations
Author: John W. Dettman
Publisher: Courier Corporation
Total Pages: 442
Release: 2012-10-05
Genre: Mathematics
ISBN: 0486158314

Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

Ordinary Differential Equations and Dynamical Systems

Ordinary Differential Equations and Dynamical Systems
Author: Thomas C. Sideris
Publisher: Springer Science & Business Media
Total Pages: 230
Release: 2013-10-17
Genre: Mathematics
ISBN: 9462390215

This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.

Ordinary and Partial Differential Equations

Ordinary and Partial Differential Equations
Author: Ravi P. Agarwal
Publisher: Springer Science & Business Media
Total Pages: 422
Release: 2008-11-13
Genre: Mathematics
ISBN: 0387791469

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.

Ordinary Differential Equations

Ordinary Differential Equations
Author: Morris Tenenbaum
Publisher: Courier Corporation
Total Pages: 852
Release: 1985-10-01
Genre: Mathematics
ISBN: 0486649407

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.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Functional Analysis, Sobolev Spaces and Partial Differential Equations
Author: Haim Brezis
Publisher: Springer Science & Business Media
Total Pages: 600
Release: 2010-11-02
Genre: Mathematics
ISBN: 0387709142

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.