Mathematics for Engineers and Scientists

Alan Jeffrey

• Publisher: Chapman and Hall/CRC
• Year: 2004
• ISBN:
  9781000687897
• Edition: 6
• Topic: Mathematik
• Subtopic: Angewandte Mathematik

Since its original publication in 1969, Mathematics for Engineers and Scientists has built a solid foundation in mathematics for legions of undergraduate science and engineering students. It continues to do so, but as the influence of computers has grown and syllabi have evolved, once again the time has come for a new edition.Thoroughly rev

1	Numbers, trigonometric functions and coordinate geometry

The topics reviewed in this chapter represent the essential mathematical prerequisites necessary for a proper understanding of the remainder of the book. Applications of these underlying concepts arise repeatedly, and in many different contexts. The material covered is necessarily of a somewhat diverse nature and not all of it is closely related.

The chapter starts with an account of the real number system, together with its arithmetic laws and their consequences, because these represent the basis for the development of the theory of functions of one or more real variables. Inequalities are introduced because they serve both to define intervals on a line and regions in space when working with functions and, also in connection with functions, to make precise the meaning of analytical concepts like limit and continuity.

The technique of mathematical induction is included because it finds applications throughout mathematics. It enables a conjecture concerning the form taken by a general mathematical proposition depending on an integer n to be tested and found to be either true or false. Thus, for example, mathematical induction can be used to verify or reject an expression for the form taken by the general term in a series that has been found by observing the pattern of a few successive terms, to check the correctness of a closed-form expression for the sum of a finite numerical series that has been arrived at intuitively, or to prove the binomial theorem.

Trigonometric functions and their associated identities are reviewed because they belong to the group of elementary functions on which most of mathematics is based, and because of the need to use their properties in most chapters of the book.

A knowledge of the elements of rectangular Cartesian coordinate geometry and of polar coordinates is essential for an understanding of the geometrical implications of many properties of functions, and also for applications of mathematics to physical problems. Discussions of the effect of a rotation or a shift of origin on a coordinate system, and of a transformation from Cartesian to polar coordinates, are included because changes of this type often simplify problem...