Ordinary Differential Equations In Theory And Practice

Author : Robert Mattheij,Jaap Molenaar
Publisher : SIAM
Page : 423 pages
File Size : 49,9 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0898719178

Get Book

Ordinary Differential Equations in Theory and Practice by Robert Mattheij,Jaap Molenaar Pdf

In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained. Audience: the book is intended for use as a textbook for both undergraduate and graduate courses, and it can also serve as a reference for students and researchers alike.

Author : Robert M. M. Mattheij
Publisher : Unknown
Page : 419 pages
File Size : 43,8 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 0608212512

Get Book

Ordinary Differential Equations in Theory and Practice by Robert M. M. Mattheij Pdf

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 486 pages
File Size : 49,8 Mb
Release : 2008-04-15
Category : Mathematics
ISBN : 0470753757

Get Book

Numerical Methods for Ordinary Differential Equations by J. C. Butcher Pdf

In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book include Introductory work on differential and difference equations. A comprehensive introduction to the theory and practice of solving ordinary differential equations numerically. A detailed analysis of Runge-Kutta methods and of linear multistep methods. A complete study of general linear methods from both theoretical and practical points of view. The latest results on practical general linear methods and their implementation. A balance between informal discussion and rigorous mathematical style. Examples and exercises integrated into each chapter enhancing the suitability of the book as a course text or a self-study treatise. Written in a lucid style by one of the worlds leading authorities on numerical methods for ordinary differential equations and drawing upon his vast experience, this new edition provides an accessible and self-contained introduction, ideal for researchers and students following courses on numerical methods, engineering and other sciences.

Author : John Heading
Publisher : Unknown
Page : 342 pages
File Size : 52,5 Mb
Release : 1975
Category : Differential equations
ISBN : 0236177222

Get Book

Ordinary Differential Equations by John Heading Pdf

Author : Steven G. Krantz
Publisher : CRC Press
Page : 557 pages
File Size : 40,6 Mb
Release : 2014-11-13
Category : Mathematics
ISBN : 9781482247046

Get Book

Differential Equations by Steven G. Krantz Pdf

"Krantz is a very prolific writer. He ... creates excellent examples and problem sets." —Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA Designed for a one- or two-semester undergraduate course, Differential Equations: Theory, Technique and Practice, Second Edition educates a new generation of mathematical scientists and engineers on differential equations. This edition continues to emphasize examples and mathematical modeling as well as promote analytical thinking to help students in future studies. New to the Second Edition Improved exercise sets and examples Reorganized material on numerical techniques Enriched presentation of predator-prey problems Updated material on nonlinear differential equations and dynamical systems A new appendix that reviews linear algebra In each chapter, lively historical notes and mathematical nuggets enhance students’ reading experience by offering perspectives on the lives of significant contributors to the discipline. "Anatomy of an Application" sections highlight rich applications from engineering, physics, and applied science. Problems for review and discovery also give students some open-ended material for exploration and further learning.

Author : Jane Cronin
Publisher : CRC Press
Page : 408 pages
File Size : 53,7 Mb
Release : 2007-12-14
Category : Mathematics
ISBN : 9781420014938

Get Book

Ordinary Differential Equations by Jane Cronin Pdf

Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of

Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 44,5 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717833

Get Book

Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque Pdf

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.

Author : Morris Tenenbaum,Harry Pollard
Publisher : Courier Corporation
Page : 852 pages
File Size : 40,5 Mb
Release : 1985-10-01
Category : Mathematics
ISBN : 9780486649405

Get Book

Ordinary Differential Equations by Morris Tenenbaum,Harry Pollard Pdf

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.

Author : Steven G. Krantz
Publisher : CRC Press
Page : 481 pages
File Size : 55,6 Mb
Release : 2015-10-07
Category : Mathematics
ISBN : 9781498735025

Get Book

Differential Equations by Steven G. Krantz Pdf

Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial diff

Author : James C. Robinson
Publisher : Cambridge University Press
Page : 416 pages
File Size : 54,9 Mb
Release : 2004-01-08
Category : Mathematics
ISBN : 0521533910

Get Book

An Introduction to Ordinary Differential Equations by James C. Robinson Pdf

A first course in ordinary differential equations for mathematicians, scientists and engineers. Solutions are provided.

Author : Marcelo Viana,José M. Espinar
Publisher : American Mathematical Society
Page : 536 pages
File Size : 40,8 Mb
Release : 2021-12-30
Category : Mathematics
ISBN : 9781470465407

Get Book

Differential Equations by Marcelo Viana,José M. Espinar Pdf

This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time—pure and applied alike—ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques. The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman–Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincaré–Hopf index theorem. The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.

Author : V. Lakshmikantham
Publisher : CRC Press
Page : 589 pages
File Size : 45,9 Mb
Release : 2020-12-17
Category : Mathematics
ISBN : 9781000111095

Get Book

Trends in Theory and Practice of Nonlinear Differential Equations by V. Lakshmikantham Pdf

This book is based on an International Conference on Trends in Theory and Practice of Nonlinear Differential Equations held at The University of Texas at Arlington. It aims to feature recent trends in theory and practice of nonlinear differential equations.

Author : Steven G. Krantz
Publisher : CRC Press
Page : 615 pages
File Size : 41,5 Mb
Release : 2022-05-29
Category : Mathematics
ISBN : 9781000592771

Get Book

Differential Equations by Steven G. Krantz Pdf

Differential equations is one of the oldest subjects in modern mathematics. It was not long after Newton and Leibniz invented the calculus that Bernoulli and Euler and others began to consider the heat equation and the wave equation of mathematical physics. Newton himself solved differential equations both in the study of planetary motion and also in his consideration of optics. Today differential equations is the centerpiece of much of engineering, of physics, of significant parts of the life sciences, and in many areas of mathematical modeling. This text describes classical ideas and provides an entree to the newer ones. The author pays careful attention to advanced topics like the Laplace transform, Sturm–Liouville theory, and boundary value problems (on the traditional side) but also pays due homage to nonlinear theory, to modeling, and to computing (on the modern side). This book began as a modernization of George Simmons’ classic, Differential Equations with Applications and Historical Notes. Prof. Simmons invited the author to update his book. Now in the third edition, this text has become the author’s own and a unique blend of the traditional and the modern. The text describes classical ideas and provides an entree to newer ones. Modeling brings the subject to life and makes the ideas real. Differential equations can model real life questions, and computer calculations and graphics can then provide real life answers. The symbiosis of the synthetic and the calculational provides a rich experience for students, and prepares them for more concrete, applied work in future courses. Additional Features Anatomy of an Application sections. Historical notes continue to be a unique feature of this text. Math Nuggets are brief perspectives on mathematical lives or other features of the discipline that will enhance the reading experience. Problems for Review and Discovery give students some open-ended material for exploration and further learning. They are an important means of extending the reach of the text, and for anticipating future work. This new edition is re-organized to make it more useful and more accessible. The most frequently taught topics are now up front. And the major applications are isolated in their own chapters. This makes this edition the most useable and flexible of any previous editions.

Author : George Finlay Simmons,Steven G. Krantz,Donald Hartig
Publisher : McGraw-Hill Science, Engineering & Mathematics
Page : 0 pages
File Size : 49,9 Mb
Release : 2006
Category : Differential equations
ISBN : 0072863161

Get Book

Student's Solutions Manual to Accompany Differential Equations by George Finlay Simmons,Steven G. Krantz,Donald Hartig Pdf

This traditional text is intended for mainstream one- or two-semester differential equations courses taken by undergraduates majoring in engineering, mathematics, and the sciences. Written by two of the world's leading authorities on differential equations, Simmons/Krantz provides a cogent and accessible introduction to ordinary differential equations written in classical style. Its rich variety of modern applications in engineering, physics, and the applied sciences illuminate the concepts and techniques that students will use through practice to solve real-life problems in their careers. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Author : Morris Tenenbaum,Harry Pollard
Publisher : Dover Publications
Page : 852 pages
File Size : 53,7 Mb
Release : 1985-10-01
Category : Mathematics
ISBN : 0486649407

Get Book

Ordinary Differential Equations by Morris Tenenbaum,Harry Pollard Pdf

This unusually well-written, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations — equations which express the relationship between variables and their derivatives. In a disarmingly simple, step-by-step style that never sacrifices mathematical rigor, the authors — Morris Tenenbaum of Cornell University, and Harry Pollard of Purdue University — introduce and explain complex, critically-important concepts to undergraduate students of mathematics, engineering and the sciences. The book begins with a section that examines the origin of differential equations, defines basic terms and outlines the general solution of a differential equation-the solution that actually contains every solution of such an equation. Subsequent sections deal with such subjects as: integrating factors; dilution and accretion problems; the algebra of complex numbers; the linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas; and Picard's Method of Successive Approximations. The book contains two exceptional chapters: one on series methods of solving differential equations, the second on numerical methods of solving differential equations. The first includes a discussion of the Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation. Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. An abundance of solved problems and practice exercises enhances the value of Ordinary Differential Equations as a classroom text for undergraduate students and teaching professionals. The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians.