Higher Mathematics Problem Solving Guide. Volume 2: Concepts, Methods, and Techniques

Author: Li Jing, Editor-in-Chief
Publisher:
Publish Date: 2004-06-01
Features: This book is a learning guide for the "Advanced Mathematics" course, a compulsory public mathematics course for science and engineering, economics and management, and finance majors in higher education institutions. It is compatible with the widely used domestic textbook "Advanced Mathematics" and can be used simultaneously. The book is divided into two volumes, with a total of twelve chapters. The first volume includes functions, limits and continuity, derivatives and differentials, mean value theorems and applications of derivatives, indefinite integrals, definite integrals and their applications. The second volume includes spatial analytical geometry and vector algebra, partial differential functions and their applications, multiple integrals, line integrals and surface integrals, infinite series, and differential equations. Each chapter is divided into five parts: content summary, teaching requirements, an overview of problem-solving methods and error analysis, analysis of typical examples, and exercises with answers. The typical examples in the analysis of typical examples are divided into three categories: A, B, and C. Category A represents basic problems, Category B represents comprehensive problems, and most Category C problems are selected from past graduate entrance examination questions. This book is compiled in accordance with the teaching syllabus for "Advanced Mathematics" issued by the Ministry of Education, emphasizing the integration of mathematical thinking, methods, and skills. It combines the cognitive patterns and problem-solving methods summarized by the authors from their teaching experience. The focus of the book is the problem-solving guidance and error analysis provided in the analysis of typical examples in each chapter. The typical examples are carefully arranged to address the difficulties and confusions encountered by students during their learning process. They are designed to be representative, progressive, and multi-faceted, with discussions of different problem-solving methods and an analysis of common errors made by beginners. This aims to deepen students' understanding of concepts in advanced mathematics, summarize and generalize problem-solving methods and skills, and improve their ability to analyze and solve problems. This book can serve as a recommended textbook for undergraduate students in science and engineering, economics and management, and finance majors studying "Advanced Mathematics," as well as a reference book for instructors. For senior undergraduate students preparing for graduate entrance exams, this book is also a valuable guide and companion.