Typical problem-solving methods in mathematical analysis

Author: Pei Liwen
Publisher:
Publish Date: 2003-03-01
Features: This book is written for readers who are currently studying mathematical analysis (calculus), those who are reviewing mathematical analysis (calculus) to prepare for postgraduate entrance exams, and young teachers engaged in teaching in this field. Following the order of current textbooks, this book comprehensively and systematically summarizes and organizes the basic types of problems in mathematical analysis, as well as the fundamental methods for each type. For each method, it first outlines the key points, then selects typical and moderately challenging examples to analyze layer by layer and explain them categorically. Subsequently, a set of corresponding exercises is provided for each category. The aim is to broaden the foundation, inspire thinking, and cultivate students' abilities to analyze and solve problems, serving as a supplement and extension to the textbook. Additionally, the book appropriately expands on relatively weaker parts of current textbooks, such as semi-continuity, convex functions, inequalities, and equicontinuity. The book is divided into 7 chapters, 33 sections, 220 entries, and 1200 problems, covering single-variable functions (limits, continuity, differentiation, integration, series) and multivariable functions (limits, continuity, differentiation, integration). The book extensively adopts past entrance exam questions for master's candidates in mathematical analysis from some universities across the country, as well as competition problems from Soviet universities, and references over 70 textbooks, academic papers, and reference materials. It has been meticulously revised, edited, and selected over generations of long-term teaching experience in middle schools. The topics are highly typical, flexible, thought-provoking, engaging, and comprehensive, making them extremely beneficial for cultivating students' abilities. It is recommended for reference by faculty and students of all majors in mathematics departments and related readers.