BOOK REVIEWS 1227

COMPUTATIONAL METHODS FOR PARTIAI. IIIFFERENTIAL EQUATIONS, E. H. Twizell, Ellis Horwood, 1984, No. of pages: 377. Price: f27.50.

As more books ofthis type appear on the market, to succeed, a text must be very lucidly presen- ted or contain enough original material of high quality to place it above its competitors. This book falls into neither of these categories.

The book is aimed at those with no knowledge of the numerical solution of partial differential equations. After an introductory chapter, the author deals with, first, finite difference methods and then finite element methods for elliptic equations, followed by chapters on hyperbolic and parabolic equations.

Thumbing through the book reveals an un- attractive feature-pages of long, heavily subs- cripted equations, most of which could, and should, have been left to the student as exercises. Chapters one (Introductory Mathematics) and two (Elliptic Equations: Finite Difference Methods) are adequate although the section on classification of partial differential equations has no motivation whatsoever, simply deriving the quadratic equation defining the characteristics of a partial differential equation without any attempt to explain what a characteristic is. The same fault is repeated in chapter four (Hyperbolic Equations), though it is fair to say that this is common in numerical analysis texts.

Chapter three (Elliptic Equations: Finite Elements) is written in a rather confused manner. There are clearly two poles in the teaching of finite element methods, which may, for want of better

THERMAL DESIGN OF ELECTRONIC CIRCUIT BOARDS AND PACKAGES, D. J. Dean, Electrochemical Pub- lications, 1985, 379 pp. E63.00

The thermal design of electronic circuits and assemblies presents significant problems in terms of layout and performance optimization. The author deals with practical design methods which allow thermal characteristics to be determined for most forms of construction used in the electronics industry.

The first part deals with the basic concepts of heat transfer and introduces a graphical method to explain the principles involved. The following sections describe the use of superposition and reciprocity in developing mathematical models. The bulk of the work relates to practical boundary conditions for circuit boards and components, and transient thermal calculations.

descriptions, be referred to as the mathematical approach (convergence and error analysis, relying heavily on functional analysis) and the engineering approach (construction of reliable and efficient codes). To combine these approaches takes a rather deft touch, it is not enough to introduce some definitions of Hilbert and Sobolev spaces and then go on to describe the construction of basis func- tions. Twizell’s approach falls between two stools, the theoretical part is neither rigorous nor extended enough for those interested in the underlying mathematical theory and is simply confusing for those who only wish to be able to produce pro- grams. Worse, in the fundamental concepts section some of the definitions are loose (e.g. the definition of L 2 ) and others are simply wrong (the definition of a subspace, or the example of an inner product).

In chapter four (Hyperbolic Equations) there is a reasonable explanation of the method of characteristics: however the reniaindcr of the chapter leans too much towards the author’s re- search interests to present a balanced view of the numerical solution of hyperbolic equations.

Chapter 5 (Parabolic Equations) contains material which has been covered more adequately elsewhere. Curiously it does not mention finite element methods for parabolic equations.

One general point is that the book has enough typesetting errors to become distracting. I am afraid I cannot recommend this text at all.

ALAN CRAIG Department of Mathematical Sciences

Uniuersity of Durham

More advanced techniques utilizing finite differ- ence and finite element methods are outlined as a means of solving temperature dependent properties and processes.

Individual chapters deal with methods appro- priate to hybrid microcircuits, d.i. 1. packages and ceramic chip carriers. A useful section on assembly factors provides further practical information.

A substantial supplement deals with the mathe- matical techniques used in the earlier sections. This approach considerably enhances the presentation allowing the reader to concentrate on the relevant methodologies.

The author has produced a significant contribu- tion to the thermal design aspects of electronic systems which will be of use to practising circuit designers and other workers in this area.

A. HOOPER