Bücher der Reihe Library of Mathematics

The aim of this book is to give an elementary treatment of multiple integrals. The notions of integrals extended over a curve, a plane region, a surface and a solid are introduced in tum, and methods for evaluating these integrals are presented in detail.

THIS book is intended to provide the university student in the physical sciences with information about the differential calculus which he is likely to need. Formulae for differentiating 21 Exerc-bses 2 3 3 Maxima and Minima and Taylor's Theorem 34 I.

LINEAR equations play an important part, not only in mathe matics itself, but also in many fields in which mathematics is used. The actual pro cess of setting up the equations and of interpreting the solution is one which more properly belongs to that field, and in any case is a problem of a different nature altogether.

Linear programming is a relatively modern branch of Mathe matics, which is a result of the more scientific approach to management and planning of the post-war era. The book assumes that the reader is familiar with matrix algebra and the background knowledge required is covered in the book, Linear Equations by P.M.

THIS book is an introduction both to Laplace's equation and its solutions and to a general method of treating partial differential equations.

I have tried to provide an introduction, at an elementary level, to some of the important topics in real analysis, without avoiding reference to the central role which the completeness of the real numbers plays throughout.

Complex numbers, like other kinds of numbers, are essen tially objects with which to perform calculations a:cording to certain rules, and when this principle is borne in mind, the nature of complex numbers is no more mysterious than that of the more familiar types of numbers.

The mathematical ideas involved are des cribed in this book, and only the student familiar with the corresponding ideas for functions of a single variable should attempt to understand the extension of the method of the differential calculus to several variables.