Fundamentals of university mathematics.

*(English)*Zbl 0823.00001
Chichester: Albion Publishing. 540 p. £ 21.00/hbk; £ 15.00/pbk (1994).

This book is based on lectures of the authors to first year students at the University of Glasgow. The book contains nineteen chapters and six appendices. Every chapter is divided into several sections. The text of the book is completed by many examples with solutions and each chapter is finished by suitably chosen exercises and problems. The book can be used also as a supplementary text for preuniversity work.

Short survey about the contents of chapters and appendices: chapters 1-6 contain number systems, sets, and functions, chapters 7-10 are concerned with differential calculus, chapter 11 contains matrices and their applications, chapters 12-13 deal with vectors and their applications to three dimensional geometry, chapters 14-16 contain integral calculus, chapter 17 is devoted to differential equations of first and second order and chapters 18-19 deal with sequences and series. Appendices A–F contain answers to the exercises and solutions of problems, rigorous treatment of limits and continuity, trigonometric formulae and tables of integrals and series.

From the methodical point of view it is interesting that the concept of limit is introduced at first intuitively. The concept of continuity of functions of intervals is then defined by using the concept of limit. Similarly one introduces at first the concept of limits of sequences and consequently also the concept of sums of infinite series. The rigorous definitions of the previous notions are given in the appendices after a certain practice in using these notions in calculus.

The book can be used successfully as textbook for an introductory study of university mathematics.

Short survey about the contents of chapters and appendices: chapters 1-6 contain number systems, sets, and functions, chapters 7-10 are concerned with differential calculus, chapter 11 contains matrices and their applications, chapters 12-13 deal with vectors and their applications to three dimensional geometry, chapters 14-16 contain integral calculus, chapter 17 is devoted to differential equations of first and second order and chapters 18-19 deal with sequences and series. Appendices A–F contain answers to the exercises and solutions of problems, rigorous treatment of limits and continuity, trigonometric formulae and tables of integrals and series.

From the methodical point of view it is interesting that the concept of limit is introduced at first intuitively. The concept of continuity of functions of intervals is then defined by using the concept of limit. Similarly one introduces at first the concept of limits of sequences and consequently also the concept of sums of infinite series. The rigorous definitions of the previous notions are given in the appendices after a certain practice in using these notions in calculus.

The book can be used successfully as textbook for an introductory study of university mathematics.

Reviewer: T.Šalát (Bratislava)

##### MSC:

00A05 | Mathematics in general |

00-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general |