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Ordinary Differential Equations

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: 8115
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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.

Ordinary Differential Equations

Ordinary Differential Equations

  • Author: Morris Tenenbaum,Harry Pollard
  • Publisher: Courier Corporation
  • ISBN: 9780486134642
  • Category: Mathematics
  • Page: 818
  • View: 6560
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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.

Ordinary Differential Equations

Ordinary Differential Equations

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

  • Author: Morris Tenenbaum,Harry Pollard
  • Publisher: N.A
  • ISBN: N.A
  • Category: Differential equations
  • Page: 808
  • View: 2316
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Ordinary Differential Equations

Ordinary Differential Equations

  • Author: Jack K. Hale
  • Publisher: Courier Corporation
  • ISBN: 0486472116
  • Category: Mathematics
  • Page: 361
  • View: 2404
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This rigorous treatment prepares readers for the study of differential equations and shows them how to research current literature. It emphasizes nonlinear problems and specific analytical methods. 1969 edition.

Ordinary Differential Equations in the Complex Domain

Ordinary Differential Equations in the Complex Domain

  • Author: Einar Hille
  • Publisher: Courier Corporation
  • ISBN: 9780486696201
  • Category: Mathematics
  • Page: 484
  • View: 4103
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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 and Stability Theory

Ordinary Differential Equations and Stability Theory

An Introduction

  • Author: David A. Sánchez
  • Publisher: Courier Corporation
  • ISBN: 0486638286
  • Category: Mathematics
  • Page: 164
  • View: 7847
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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.

Ordinary Differential Equations and Their Solutions

Ordinary Differential Equations and Their Solutions

  • Author: George Moseley Murphy
  • Publisher: Courier Corporation
  • ISBN: 0486485919
  • Category: Mathematics
  • Page: 451
  • View: 7133
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This treatment presents most of the methods for solving ordinary differential equations and systematic arrangements of more than 2,000 equations and their solutions. The material is organized so that standard equations can be easily found. Plus, the substantial number and variety of equations promises an exact equation or a sufficiently similar one. 1960 edition.

An Introduction to Ordinary Differential Equations

An Introduction to Ordinary Differential Equations

  • Author: Earl A. Coddington
  • Publisher: Courier Corporation
  • ISBN: 0486131831
  • Category: Mathematics
  • Page: 320
  • View: 5173
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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.

Lectures on Ordinary Differential Equations

Lectures on Ordinary Differential Equations

  • Author: Witold Hurewicz
  • Publisher: Courier Corporation
  • ISBN: 048679721X
  • Category: Mathematics
  • Page: 144
  • View: 8829
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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.

The Qualitative Theory of Ordinary Differential Equations

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: 4238
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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

Ordinary Differential Equations

  • Author: Edward L. Ince
  • Publisher: Courier Corporation
  • ISBN: 0486158217
  • Category: Mathematics
  • Page: 576
  • View: 2378
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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.

Introduction to Linear Algebra and Differential Equations

Introduction to Linear Algebra and Differential Equations

  • Author: John W. Dettman
  • Publisher: Courier Corporation
  • ISBN: 0486158314
  • Category: Mathematics
  • Page: 432
  • View: 7671
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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.

Introduction to Partial Differential Equations with Applications

Introduction to Partial Differential Equations with Applications

  • Author: E. C. Zachmanoglou,Dale W. Thoe
  • Publisher: Courier Corporation
  • ISBN: 048613217X
  • Category: Mathematics
  • Page: 432
  • View: 3805
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This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Existence Theorems for Ordinary Differential Equations

Existence Theorems for Ordinary Differential Equations

  • Author: Francis J. Murray,Kenneth S. Miller
  • Publisher: Courier Corporation
  • ISBN: 0486154955
  • Category: Mathematics
  • Page: 176
  • View: 2176
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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

Ordinary Differential Equations

Qualitative Theory

  • Author: Luis Barreira,Claudia Valls
  • Publisher: American Mathematical Soc.
  • ISBN: 0821887491
  • Category: Mathematics
  • Page: 248
  • View: 5125
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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 Nonlinear Differential and Integral Equations

Introduction to Nonlinear Differential and Integral Equations

  • Author: Harold Thayer Davis
  • Publisher: Courier Corporation
  • ISBN: 9780486609713
  • Category: Mathematics
  • Page: 566
  • View: 5287
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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

Ordinary Differential Equations and Dynamical Systems

  • Author: Gerald Teschl
  • Publisher: American Mathematical Soc.
  • ISBN: 0821883283
  • Category: Mathematics
  • Page: 356
  • View: 9689
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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.

Basic Linear Partial Differential Equations

Basic Linear Partial Differential Equations

  • Author: Francois Treves
  • Publisher: Courier Corporation
  • ISBN: 0486150984
  • Category: Mathematics
  • Page: 496
  • View: 9653
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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

Ordinary Differential Equations

  • Author: Wolfgang Walter
  • Publisher: Springer Science & Business Media
  • ISBN: 1461206014
  • Category: Mathematics
  • Page: 384
  • View: 2829
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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.

Ordinary Differential Equations with Applications

Ordinary Differential Equations with Applications

Second Edition

  • Author: Sze-Bi Hsu
  • Publisher: World Scientific Publishing Company
  • ISBN: 9814452920
  • Category: Mathematics
  • Page: 312
  • View: 4543
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During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE). This useful book, which is based on the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques. Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook and as a valuable resource for researchers. This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.