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An Introduction to Ordinary Differential Equations

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An Introduction to Ordinary Differential Equations Cover

 

Synopses & Reviews

Publisher Comments:

"Written in an admirably cleancut and economical style." — Mathematical Reviews.

This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations. Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to master the materials to be presented.

The next four chapters take up linear equations, those of the first order and those with constant coefficients, variable coefficients, and regular singular points. The last two chapters address the existence and uniqueness of solutions to both first order equations and to systems and n-th order equations.

Throughout the book, the author carries the theory far enough to include the statements and proofs of the simpler existence and uniqueness theorems. Dr. Coddington, who has taught at MIT, Princeton, and UCLA, has included many exercises designed to develop the student's technique in solving equations. He has also included problems (with answers) selected to sharpen understanding of the mathematical structure of the subject, and to introduce a variety of relevant topics not covered in the text, e.g. stability, equations with periodic coefficients, and boundary value problems.

Synopsis:

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.

Synopsis:

A thorough and systematic first course in elementary differential equations for undergraduates in mathematics and science, with many exercises and problems (with answers). Index.

Description:

Includes bibliographical references and index.

Table of Contents

Chapter 0. Preliminaries

  1. Introduction

  2 Complex numbers

  3 Functions

  4 Polynomials

  5. Complex series and the exponential function

  6. Determinants

  7. Remarks on methods of discovery and proof

Chapter 1. Introduction--Linear Equations of the First Order

  1. Introduction

  2. Differential equations

  3. Problems associated with differential equations

  4. Linear equations of the first order

  5. The equation y'+ay=0

  6. The equation y'+ay=b(x)

  7. The general linear equation of the first order

Chapter 2. Linear Equations with Constant Coefficients

  1. Introduction

  2. The second order homogeneous equation

  3. Initial value problems for second order equations

  4. Linear dependence and independence

  5. A formula for the Wronskian

  6. The non-homogeneous equation of order two

  7. The homogeneous equation of order n

  8. Initial value problems for n-th order equations

  9. Equations with real constants

  10. The non-homogeneous equation of order n

  11. A special method for solving the non-homogeneous equation

  12. Algebra of constant coefficient operators

Chapter 3. Linear Equations with Variable Coefficients

  1. Introduction

  2. Initial value problems for the homogeneous equation

  3. Solutions of the homogeneous equation

  4. The Wronskian and linear independence

  5. Reduction of the order of a homogeneous equation

  6. The non-homogeneous equation

  7. Homogeneous equations with analytic coefficients

  8. The Legendre equation

  9. Justification of the power series method

Chapter 4. Linear Equations with Regular Singular Points

  1. Introduction

  2. The Euler equation

  3. Second order equations with regular singular points--an example

  4. Second order equations with regular singular points--the general case

  5. A convergence proof

  6. The exceptional cases

  7. The Bessel equation

  8. The Bessel equation (continued)

  9. Regular singular points at infinity

Chapter 5. Existence and Uniqueness of Solutions to First Order Equations

  1. Introduction

  2. Equations with variables separated

  3. Exact equations

  4. The method of successive approximations

  5. The Lipschitz condition

  6. Convergence of the successive approximations

  7. Non-local existence of solutions

  8. Approximations to, and uniqueness of, solutions

  9. Equations with complex-valued functions

Chapter 6. Existence and Uniqueness of Solutions to Systems and n-th Order Equations

  1. Introduction

  2. An example--central forces and planetary motion

  3. Some special equations

  4. Complex n-dimensional space

  5. Systems as vector equations

  6. Existence and uniqueness of solutions to systems

  7. Existence and uniqueness for linear systems

  8. Equations of order n

  References; Answers to Exercises; Index

Product Details

ISBN:
9780486659428
Author:
Landin, Joseph
Author:
Coddington, Earl A.
Author:
Landin, Joseph
Author:
Mathematics
Publisher:
Dover Publications
Location:
New York :
Subject:
General
Subject:
Mathematics
Subject:
Differential Equations
Subject:
General Mathematics
Subject:
Mathematics-Differential Equations
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
no. 14
Publication Date:
19890331
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
320
Dimensions:
8.25 x 5.38 in 0.73 lb

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Related Subjects


Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics
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Young Adult » General

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Product details 320 pages Dover Publications - English 9780486659428 Reviews:
"Synopsis" by ,
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.
"Synopsis" by , A thorough and systematic first course in elementary differential equations for undergraduates in mathematics and science, with many exercises and problems (with answers). Index.

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