Typical Problems and Methods in Mathematical Analysis - (2nd Edition)

Author: Pei Liwen
Publisher:
Publish Date: 2006-04-01
Features: This book is written for readers who are currently studying mathematical analysis (calculus), those who are reviewing mathematical analysis (calculus) in preparation for postgraduate entrance exams, and young teachers engaged in teaching in this field. Following the sequence of current textbooks, this book comprehensively and systematically summarizes and organizes the basic types of mathematical analysis problems, the fundamental methods for each type, and provides an overview of each method before selecting typical and relatively challenging examples for step-by-step analysis and classification explanations. Corresponding sets of exercises are provided for each type. 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 textbooks. Additionally, the book appropriately expands on weaker parts of current textbooks, such as semi-continuity, convex functions, inequalities, and equicontinuity. The book is divided into 7 chapters, 36 sections, 246 entries, and 1,382 problems, covering single-variable functions (limits, continuity, differentiation, integration, series) and multivariable functions (limits, continuity, differentiation, integration).
The book extensively uses past entrance exam questions from some universities in China for master's degree candidates in mathematical analysis, as well as selected international competition problems. It references over 70 textbooks, academic papers, and reference materials, and has been meticulously revised, edited, and selected based on long-term teaching practices across generations. The problems are highly representative, flexible, thought-provoking, engaging, and comprehensive, making them extremely beneficial for cultivating students' abilities. It is suitable for faculty and students of mathematics departments (schools) and related readers. The fundamental content (not marked with or ※ symbols) can also be used by candidates preparing for the postgraduate entrance exam's "Mathematical Analysis I" section for reference.
For this revision, a significant number of representative new problems and foundational questions have been added and updated. A "Guidance" section has been added, and exercises are provided with hints, additional hints, or solutions. The problems are categorized into five difficulty levels, with the ☆ section recommended as key content.
Mathematical Analysis: Typical Problems and Methods (2nd Edition) - Blue Dreamscape
Author: Pei Liwen