Mathematical Analysis: Selected Topics

Author: Li Kedian
Publisher:
Publish Date: 2006-06-01
Features: This book systematically summarizes the basic concepts and theories of mathematical analysis and introduces the fundamental methods and techniques for solving mathematical analysis problems through typical examples. The entire book is divided into nine chapters, with each chapter and section including four parts: basic concepts, basic theories, basic methods, and typical examples. Each chapter and section introduces relevant concepts, propositions, and important conclusions, along with their equivalent descriptions and characterizations, which helps deepen readers' understanding of the main content of mathematical analysis. A selection of typical examples has been carefully chosen (some of which are entrance examination questions for postgraduate studies in some universities), introducing the methods of solving mathematical analysis problems in a step-by-step manner. This process encourages readers to broaden their thinking and master techniques, thereby cultivating their ability to independently analyze and solve problems. This book was written based on an elective course on mathematical analysis. Its content breaks the conventional arrangement of chapters and sections in typical mathematical analysis textbooks and organizes related materials into comprehensive categories. For example, in the chapter on limit theory, some content involves knowledge from differential calculus, integral calculus, and series. This approach is beneficial for a profound understanding and mastery of mathematical analysis methods, as well as improving problem-solving skills for comprehensive questions. This book can serve as a textbook for elective courses on mathematical analysis, a review guide for students preparing for postgraduate entrance examinations, and a teaching reference for instructors.