Introduction to Ordinary Differential Equations, 4th Edition

by Ross, Shepley L.

• ISBN13: 9780471098812
• ISBN10: 0471098817
• Edition: 4th
• Format: Paperback
• Copyright: 1991-01-16
• Publisher: Wiley
• More Book Details

Summary

The Fourth Edition of the best-selling text on the basic concepts, theory, methods, and applications of ordinary differential equations retains the clear, detailed style of the first three editions. Includes new material on matrix methods, numerical methods, the Laplace transform, and an appendix on polynomial equations. Stresses fundamental methods, and features traditional applications and brief introductions to the underlying theory.

Author Biography

Shepley L. Ross is the author of Introduction to Ordinary Differential Equations, 4th Edition, published by Wiley.

Table of Contents

Differential Equations and Their Solutions	1	(23)
Classification of Differential Equations; Their Origin and Application	1	(5)
Solutions	6	(8)
Initial-Value Problems, Boundary-Value Problems, and Existence of Solutions	14	(10)
First-Order Equations for Which Exact Solutions Are Obtainable	24	(47)
Exact Differential Equations and Integrating Factors	24	(14)
Separable Equations and Equations Reducible to This Form	38	(10)
Linear Equations and Bernoulli Equations	48	(12)
Special Integrating Factors and Transformations	60	(11)
Applications of First-Order Equations	71	(39)
Orthogonal and Oblique Trajectories	71	(7)
Problems in Mechanics	78	(13)
Rate Problems	91	(19)
Explicit Methods of Solving Higher-Order Linear Differential Equations	110	(79)
Basic Theory of Linear Differential Equations	110	(24)
The Homogeneous Linear Equation with Constant Coefficients	134	(11)
The Method of Undetermined Coefficients	145	(17)
Variation of Parameters	162	(9)
The Cauchy--Euler Equation	171	(6)
Statements and Proofs of Theorems on the Second-Order Homogeneous Linear Equation	177	(12)
Applications of Second-Order Linear Differential Equations With Constant Coefficients	189	(48)
The Differential Equation of the Vibrations of a Mass on a spring	189	(3)
Free, Undamped Motion	192	(8)
Free Damped Motion	200	(12)
Forced Motion	212	(7)
Resonance Phenomena	219	(5)
Electric Circuit Problems	224	(13)
Series Solutions of Linear Differential Equations	237	(46)
Power Series Solutions About an Ordinary Point	237	(13)
Solutions About Singular Points; The Method of Frobenius	250	(20)
Bessel's Equation and Bessel Functions	270	(13)
Systems of Linear Differential Equations	283	(134)
Differential Operators and an Operator Method	283	(14)
Applications	297	(11)
Basic Theory of Linear Systems in Normal Form: Two Equations in Two Unknown Functions	308	(11)
Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions	319	(12)
Matrices and Vectors	331	(37)
The Matrix Method for Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions	368	(10)
The Matrix Method for Homogeneous Linear Systems with constant Coefficients: n Equations in n Unknown Functions	378	(24)
Statements and Proofs of Basic Theorems on Homogeneous Linear Systems	402	(15)
Approximate Methods of Solving First-Order Equations	417	(63)
Graphical Methods	417	(11)
Power Series Methods	428	(6)
The Method of Successive Approximations	434	(4)
The Euler Method	438	(11)
The Improved Euler Method	449	(6)
The Runge-Kutta Method	455	(8)
The Adams-Bashforth/Adams-Moulton (ABAM) Method	463	(6)
Higher-Order Equations; Systems	469	(11)
The Laplace Transform	480	(67)
Definition, Existence, and Basic Properties of the Laplace Transform	480	(17)
The Inverse Transform and the Convolution	497	(13)
Laplace Transform Solution of Linear Differential Equations with Constant Coefficients	510	(10)
Laplace Transform Solution of Linear Differential Equations With Discontinuous Nonhomogeneous Terms	520	(19)
Laplace Transform Solution of Linear Systems	539	(8)
Appendix 1	547	(4)
Appendix 2	551	(5)
Appendix 3	556	(2)
Suggested Reading	558	(1)
Answers to Odd-Numbered Exercises	559	(46)
Index	605