*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: 1682

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### Ordinary Differential Equations

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

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

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

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

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

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.

### Ordinary Differential Equations

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.

### Lectures on Ordinary Differential Equations

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

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 Linear Algebra and Differential Equations

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.

### An Introduction to Ordinary Differential Equations

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.

### Problems in Differential Equations

More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.

### Existence Theorems for Ordinary Differential Equations

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.

### Introduction to Partial Differential Equations with Applications

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.

### Ordinary Differential Equations

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

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

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.

### Elements of Partial Differential Equations

This text features numerous worked examples in its presentation of elements from the theory of partial differential equations, emphasizing forms suitable for solving equations. Solutions to odd-numbered problems appear at the end. 1957 edition.

### Asymptotic Expansions for Ordinary Differential Equations

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.

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*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: 1682

Author: Morris Tenenbaum,Harry Pollard

Publisher: Courier Corporation

ISBN: 9780486134642

Category: Mathematics

Page: 818

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*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

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Author: Jack K. Hale

Publisher: Courier Corporation

ISBN: 0486472116

Category: Mathematics

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ISBN: 9780486696201

Category: Mathematics

Page: 484

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*An Introduction*

Author: David A. Sánchez

Publisher: Courier Corporation

ISBN: 0486638286

Category: Mathematics

Page: 164

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Author: George Moseley Murphy

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ISBN: 0486485919

Category: Mathematics

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ISBN: 0486158217

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ISBN: 048679721X

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Page: 144

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*An Introduction*

Author: Fred Brauer,John A. Nohel

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ISBN: 0486151514

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ISBN: 0486158314

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ISBN: 0486782824

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ISBN: 0486154955

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Publisher: Courier Corporation

ISBN: 048613217X

Category: Mathematics

Page: 432

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*Qualitative Theory*

Author: Luis Barreira,Claudia Valls

Publisher: American Mathematical Soc.

ISBN: 0821887491

Category: Mathematics

Page: 248

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Author: Harold Thayer Davis

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ISBN: 9780486609713

Category: Mathematics

Page: 566

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Author: Wolfgang Walter

Publisher: Springer Science & Business Media

ISBN: 1461206014

Category: Mathematics

Page: 384

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Author: Ian N. Sneddon

Publisher: Courier Corporation

ISBN: 0486162990

Category: Mathematics

Page: 352

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Author: Wolfgang Wasow

Publisher: Courier Dover Publications

ISBN: 0486824586

Category: Mathematics

Page: 384

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