Author : Yusof Yaacob
ISBN : 978-983-521-030-3
A student’s first encounter with mathematical analysis has been widely regarded as the most difficult course in the undergraduate mathematics curriculum. After years of emphasizing computation in the previous mathematics curriculum, the student is now expected to be able to read, understand and construct mathematical proof. This book enhances students understanding on mathematical analysis in four ways. Firstly, the text of the book is self-contained. Proofs of lemmas and theorems in the text are given within the text itself, not in the problem set. Hence the development of the material does not depend on the problems and therefore does not disrupt the continuity of the presentation. Secondly, the review materials in this book contain materials for reference. Various methods of mathematical proofs are outlined here. It also contains some elementary facts about sets and functions. Thirdly, this book uses cross-reference extensively. If a fact is used in a proof or solution to an example or a problem, then a reference is given in parenthesis to what theorem number (if it is a theorem) together with the page number. This will help the student to easily locate the fact being used. Finally, the problems in this book are carefully selected to strengthen students understanding. Solutions to odd-numbered problems are given in the appendix. Based on the solutions to the odd- numbered problems and examples in text, students should be able to provide solutions to the even-numbered problems.
The book is suitable for a one semester course on mathematical analysis at undergraduate level meeting three hours per week. A background in undergraduate ordinary calculus is sufficient as a prerequisite. The book covers the topics usually included in an analysis of functions of one real variable: a brief development of real numbers, sequences of real numbers, elementary topology, limits, continuity, differentiation, integration, series of real numbers, power series, sequences of functions and series of functions.