# Search Results for "existence-theorems-for-ordinary-differential-equations-dover-books-on-mathematics"

## Existence Theorems for Ordinary Differential Equations

**Author**: Francis J. Murray,Kenneth S. Miller**Publisher:**Courier Corporation**ISBN:**0486154955**Category:**Mathematics**Page:**176**View:**9529

This text examines fundamental and general existence theorems, along with uniqueness theorems and Picard iterants, and applies them to properties of solutions and linear differential equations. 1954 edition.

## Ordinary Differential Equations

*An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences*

**Author**: Morris Tenenbaum,Harry Pollard**Publisher:**Courier Corporation**ISBN:**0486649407**Category:**Mathematics**Page:**808**View:**5360

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.

## Lectures on Ordinary Differential Equations

**Author**: Witold Hurewicz**Publisher:**Courier Corporation**ISBN:**048679721X**Category:**Mathematics**Page:**144**View:**3757

Introductory treatment explores existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. "A rigorous and lively introduction." — The American Mathematical Monthly. 1958 edition.

## Ordinary Differential Equations

**Author**: Edward L. Ince**Publisher:**Courier Corporation**ISBN:**0486158217**Category:**Mathematics**Page:**576**View:**4486

Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended" — Electronics Industries.

## Ordinary Differential Equations in the Complex Domain

**Author**: Einar Hille**Publisher:**Courier Corporation**ISBN:**9780486696201**Category:**Mathematics**Page:**484**View:**8747

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.

## 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:**1389

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.

## Introduction to Nonlinear Differential and Integral Equations

**Author**: Harold Thayer Davis**Publisher:**Courier Corporation**ISBN:**9780486609713**Category:**Mathematics**Page:**566**View:**6716

Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.

## Ordinary Differential Equations and Dynamical Systems

**Author**: Gerald Teschl**Publisher:**American Mathematical Soc.**ISBN:**0821883283**Category:**Mathematics**Page:**356**View:**6345

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.

## An Introduction to Ordinary Differential Equations

**Author**: Earl A. Coddington**Publisher:**Courier Corporation**ISBN:**0486131831**Category:**Mathematics**Page:**320**View:**4324

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.

## A Second Course in Elementary Differential Equations

**Author**: Paul Waltman**Publisher:**Courier Corporation**ISBN:**0486434788**Category:**Mathematics**Page:**259**View:**7677

Focusing on applicable rather than applied mathematics, this text begins with an examination of linear systems of differential equations and 2-dimensional linear systems and then explores the use of polar coordinate techniques, Liapunov stability and elementary ideas from dynamic systems. Features an in-depth treatment of existence and uniqueness theorems, more. 1986 edition. Includes 39 figures.

## Ordinary Differential Equations

*Qualitative Theory*

**Author**: Luis Barreira,Claudia Valls**Publisher:**American Mathematical Soc.**ISBN:**0821887491**Category:**Mathematics**Page:**248**View:**5417

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.

## Introduction to Linear Algebra and Differential Equations

**Author**: John W. Dettman**Publisher:**Courier Corporation**ISBN:**0486158314**Category:**Mathematics**Page:**432**View:**6865

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 Stability Theory

*An Introduction*

**Author**: David A. Sánchez**Publisher:**Courier Corporation**ISBN:**0486638286**Category:**Mathematics**Page:**164**View:**7559

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.

## Asymptotic Expansions for Ordinary Differential Equations

**Author**: Wolfgang Wasow**Publisher:**Courier Dover Publications**ISBN:**0486824586**Category:**Mathematics**Page:**384**View:**8616

This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.

## Basic Theory of Ordinary Differential Equations

**Author**: Po-Fang Hsieh,Yasutaka Sibuya**Publisher:**Springer Science & Business Media**ISBN:**1461215064**Category:**Mathematics**Page:**469**View:**2142

Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.

## Basic Linear Partial Differential Equations

**Author**: Francois Treves**Publisher:**Courier Corporation**ISBN:**0486150984**Category:**Mathematics**Page:**496**View:**9847

Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students employs nontraditional methods to explain classical material. Nearly 400 exercises. 1975 edition.

## Ordinary Differential Equations

**Author**: Vladimir I. Arnold**Publisher:**Springer Science & Business Media**ISBN:**9783540548133**Category:**Mathematics**Page:**338**View:**9517

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

## Lectures on Differential and Integral Equations

**Author**: K?saku Yoshida**Publisher:**Courier Corporation**ISBN:**9780486666792**Category:**Mathematics**Page:**220**View:**8537

Lucid, self-contained exposition of theory of ordinary differential equations and integral equations. Boundary value problem of second order linear ordinary differential equations, Fredholm integral equations, many other topics. Bibliography. 1960 edition.

## Introduction to Differential Equations

**Author**: Michael Eugene Taylor**Publisher:**American Mathematical Soc.**ISBN:**082185271X**Category:**Mathematics**Page:**409**View:**1596

The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a mini-course on linear algebra, giving detailed treatments of linear transformations, determinants and invertibility, eigenvalues and eigenvectors, and generalized eigenvectors. This treatment is more detailed than that in most differential equations texts, and provides a solid foundation for the next two chapters. Chapter 3 studies linear systems of differential equations. It starts with the matrix exponential, melding material from Chapters 1 and 2, and uses this exponential as a key tool in the linear theory. Chapter 4 deals with nonlinear systems of differential equations. This uses all the material developed in the first three chapters and moves it to a deeper level. The chapter includes theoretical studies, such as the fundamental existence and uniqueness theorem, but also has numerous examples, arising from Newtonian physics, mathematical biology, electrical circuits, and geometrical problems. These studies bring in variational methods, a fertile source of nonlinear systems of differential equations. The reader who works through this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations.

## Modern Elementary Differential Equations

**Author**: Richard Bellman,Kenneth L. Cooke**Publisher:**Courier Corporation**ISBN:**9780486686431**Category:**Mathematics**Page:**228**View:**6604

Designed to introduce students to the theory and applications of differential equations and to help them formulate scientific problems in terms of such equations, this undergraduate-level text emphasizes applications to problems in biology, economics, engineering, and physics. This edition also includes material on discontinuous solutions, Riccati and Euler equations, and linear difference equations.