An Introduction to Ordinary Differential Equations

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Paperback | 6 April 2004

At a Glance

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414 Pages

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24.41 x 16.99 x 2.16

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This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.

Industry Reviews

'The presentation is sensitive to the needs of students, with careful algebraic steps included in most cases. Appendices on basic required mathematical techniques are also included.' Mathematical Reviews 'The book is recommended as a textbook for one-term or one-semester course.' Zentralblatt MATH '... will be useful to anybody wanting to teach or learn elements of ordinary differential equations in the beginnings of their mathematical studies.' European Mathematical Society Newsletter '... it is written in a friendly and informal style and covers a wide and interesting collection of topics.' Contemporary Physics 'This is an excellent book which probably would have been most welcome to older students of differential equations had it existed and which will be of great value to those currently studying the subject.' The Mathematical Gazette

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Introduction
First Order Differential Equations
Radioactive decay and carbon dating
Integration variables
Classification of differential equations
Graphical representation of solutions using MATLAB
'Trivial' differential equations
Existence and uniqueness of solutions
Scalar autonomous ODEs
Separable equations
First order linear equations and the integrating factor
Two 'tricks' for nonlinear equations
Second Order Linear Equations With Constant Coefficients
Second order linear equations: general theory
Homogeneous 2nd order linear ODEs
Oscillations
Inhomogeneous 2nd order linear equations
Resonance
Higher order linear equations
Linear Second Order Equations With Variable Coefficients
Reduction of order
The variation of constants formula
Cauchy-Euler equations
Series solutions of second order linear equations
Numerical Methods and Difference Equations
Euler's method
Difference equations
Nonlinear first order difference equations
The logistic map
Coupled Linear Equations
Vector first order equations and higher order equations
Explicit solutions of coupled linear systems
Eigenvalues and eigenvectors
Distinct real eigenvalues
Complex eigenvalues
A repeated real eigenvalue
Summary of phase portraits for linear equations
Coupled Nonlinear Equations
Coupled nonlinear equations
Ecological models
Newtonian dynamics
The 'real' pendulum
Periodic orbits
The Lorenz equations
What next?
Table of Contents provided by Publisher. All Rights Reserved.

An Introduction to Ordinary Differential Equations

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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