文档介绍：Differential Equations
Linear, Nonlinear, Ordinary, Partial
When mathematical modelling is used to describe physical, biological or chemical phe-
nomena, one of the mon results of the modelling process is a system of ordinary
or partial differential equations. Finding and interpreting the solutions of these differential
equations is therefore a central part of applied mathematics, and a thorough understand-
ing of differential equations is essential for any applied mathematician. The aim of this
book is to develop the required skills on the part of the reader.
The authors focus on the business of constructing solutions analytically and interpret-
ing their meaning, although they do use rigorous analysis where needed. The reader is
assumed to have some basic knowledge of linear, constant coefficient ordinary differential
equations, real analysis and linear algebra. The book will thus appeal to undergraduates
in mathematics, but would also be of use to physicists and engineers. MATLAB is used
extensively to illustrate the material. There are many worked examples based on in-
teresting real-world problems. A large selection of exercises is provided, including several
lengthier projects, some of which involve the use of MATLAB. The coverage is broad, rang-
ing from basic second-order ODEs including the method of Frobenius, Sturm-Liouville the-
ory, Fourier and Laplace transforms, and existence and uniqueness, through to techniques
for nonlinear differential equations including phase plane methods, bifurcation theory and
chaos, asymptotic methods, and control theory. This broad coverage, the authors’ clear
presentation and the fact that the book has been thoroughly class-tested will increase its
appeal to undergraduates at each stage of their studies.
Differential Equations
Linear, Nonlinear, Ordinary, Partial
. King, J. Billingham and . Otto
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambrid