The Qualitative Theory of Ordinary Differential Equations

An Introduction

Author: Fred Brauer,John A. Nohel

Publisher: Courier Corporation

ISBN: 0486151514

Category: Mathematics

Page: 320

View: 9219

Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.

Ordinary Differential Equations

Qualitative Theory

Author: Luis Barreira,Claudia Valls

Publisher: American Mathematical Soc.

ISBN: 0821887491

Category: Mathematics

Page: 248

View: 6494

This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.

Ordinary Differential Equations and Dynamical Systems

Author: Gerald Teschl

Publisher: American Mathematical Soc.

ISBN: 0821883283

Category: Mathematics

Page: 356

View: 5379

This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

Stability Theory of Differential Equations

Author: Richard Bellman

Publisher: Courier Corporation

ISBN: 0486150135

Category: Mathematics

Page: 176

View: 1484

Suitable for advanced undergraduates and graduate students, this text introduces the stability theory and asymptotic behavior of solutions of linear and nonlinear differential equations. 1953 edition.

Ordinary Differential Equations

Analysis, Qualitative Theory and Control

Author: Hartmut Logemann,Eugene P. Ryan

Publisher: Springer

ISBN: 1447163982

Category: Mathematics

Page: 333

View: 9276

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature. The following topics are particularly emphasised: • existence, uniqueness and continuation of solutions, • continuous dependence on initial data, • flows, • qualitative behaviour of solutions, • limit sets, • stability theory, • invariance principles, • introductory control theory, • feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.

Differential Equations and Dynamical Systems

Author: Lawrence Perko

Publisher: Springer Science & Business Media

ISBN: 1461300037

Category: Mathematics

Page: 557

View: 9671

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.

An Introduction to Ordinary Differential Equations

Author: Earl A. Coddington

Publisher: Courier Corporation

ISBN: 0486131831

Category: Mathematics

Page: 320

View: 9578

A thorough, systematic first course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background. Includes many exercises and problems, with answers. Index.

Qualitative Theory of Differential Equations

Author: Viktor Vladimirovich Nemytskii

Publisher: Princeton University Press

ISBN: 1400875951

Category: Mathematics

Page: 532

View: 8506

Book 22 in the Princeton Mathematical Series. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

An Introduction to Mathematical Modeling

Author: Edward A. Bender

Publisher: Courier Corporation

ISBN: 9780486411804

Category: Mathematics

Page: 256

View: 1376

Accessible text features over 100 reality-based examples pulled from the science, engineering and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

Ordinary Differential Equations and Stability Theory

An Introduction

Author: David A. Sánchez

Publisher: Courier Corporation

ISBN: 0486638286

Category: Mathematics

Page: 164

View: 4293

Beginning with a general discussion of the linear equation, topics developed include stability theory for autonomous and nonautonomous systems. Two appendices are also provided, and there are problems at the end of each chapter — 55 in all. Unabridged republication of the original (1968) edition. Appendices. Bibliography. Index. 55 problems.

An Introduction to Ordinary Differential Equations

Author: James C. Robinson

Publisher: Cambridge University Press

ISBN: 1139450026

Category: Mathematics

Page: N.A

View: 4197

This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.

Nonlinear Differential Equations and Dynamical Systems

Author: Ferdinand Verhulst

Publisher: Springer Science & Business Media

ISBN: 3642614531

Category: Mathematics

Page: 306

View: 9888

For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal. Its excellent pedagogical style typically consists of an insightful overview followed by theorems, illustrative examples, and exercises.

Ordinary Differential Equations

Author: Wolfgang Walter

Publisher: Springer Science & Business Media

ISBN: 1461206014

Category: Mathematics

Page: 384

View: 6783

Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.

A Basic Course in Partial Differential Equations

Author: Qing Han

Publisher: American Mathematical Soc.

ISBN: 0821852558

Category: Mathematics

Page: 293

View: 3749

This is a textbook for an introductory graduate course on partial differential equations. Han focuses on linear equations of first and second order. An important feature of his treatment is that the majority of the techniques are applicable more generally. In particular, Han emphasizes a priori estimates throughout the text, even for those equations that can be solved explicitly. Such estimates are indispensable tools for proving the existence and uniqueness of solutions to PDEs, being especially important for nonlinear equations. The estimates are also crucial to establishing properties of the solutions, such as the continuous dependence on parameters. Han's book is suitable for students interested in the mathematical theory of partial differential equations, either as an overview of the subject or as an introduction leading to further study.

Introduction to Dynamics

Author: I. C. Percival,D. Richards

Publisher: Cambridge University Press

ISBN: 9780521281492

Category: Mathematics

Page: 228

View: 6137

A new approach to dynamics that takes account of recent advances that have wide applications in the sciences and engineering. It introduces the subject at an undergraduate level by means of elementary qualitative theory of differential equations, the geometry of phase curves, and the theory of stability.

Mathematical Foundations of Elasticity

Author: Jerrold E. Marsden,Thomas J. R. Hughes

Publisher: Courier Corporation

ISBN: 0486142272

Category: Technology & Engineering

Page: 576

View: 5507

Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.

A First Course in Discrete Dynamical Systems

Author: Richard A. Holmgren

Publisher: Springer Science & Business Media

ISBN: 1441987320

Category: Mathematics

Page: 223

View: 9021

Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix.


Its Content, Methods and Meaning

Author: A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev

Publisher: Courier Corporation

ISBN: 0486157873

Category: Mathematics

Page: 1120

View: 4994

Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

Ordinary Differential Equations in the Complex Domain

Author: Einar Hille

Publisher: Courier Corporation

ISBN: 9780486696201

Category: Mathematics

Page: 484

View: 5153

Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.

Ordinary Differential Equations

Author: Vladimir I. Arnold

Publisher: Springer Science & Business Media

ISBN: 9783540548133

Category: Mathematics

Page: 338

View: 9184

Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEW