도서의 소개 |
The book begins with a preliminary chapter on sets, functions, and real numbers. After briefly providing basic set theory, we introduce the completeness property of real numbers and its several consequences. The main body consists of two parts. Part I is devoted to developing the theory of functions of one variable. Functions of several variables which are more difficult and technical are studied in Part II. Part I is self-contained. All the theorems in Part I are deduced from the completeness property of real numbers. But some results in Part II are proved by using standard results from linear algebra such as elementary matrices and determinants. Therefore, readers of Part II should have some knowledge about elementary Linear Algebra. It is also highly recommended to be familiar with basic set theory in the preliminary chapter since set-theoretical arguments are inevitably used to establish many important theorems for functions of several variables. There are two kinds of problems in this book: exercises inside each section and problems at the end of each chapter. Section exercises are relatively easy and provided for self-study. Making efforts to solve exercises by trial and error, readers not only better understand new concepts and theorems in sections but also have chances to generalize them to some extent. Chapter problems are placed at the end of each chapter because materials from more than two sections are often necessary to solve them successfully. Some problems allow readers to obtain interesting new results by applying the concepts and results in the chapter. However, chapter problems are more challenging than section exercises. Problems marked by an * are provided with short hints at the end of the book.
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