Higher Mathematics Problem Solving Guide (Concepts, Methods, and Techniques) (Volume 1)

Author: Li Jing
Publisher:
Publish Date: 2003-09-01
Features: This book is a learning guide for the "Advanced Mathematics" public course in science and engineering, economics, management, and finance majors at higher education institutions. It is designed to be used alongside the commonly used "Advanced Mathematics" textbooks in China and can be used synchronously. 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 derivatives of multivariate functions and their applications, multiple integrals, line and surface integrals, infinite series, and differential equations. Each chapter is divided into five parts: content summary (including chapter framework), important concepts and properties, teaching requirements, an overview of problem-solving methods and error analysis, analysis of typical examples, and exercises with answers. The 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 written according to the teaching syllabus for "Advanced Mathematics" issued by the Ministry of Education, emphasizing the integration of mathematical thinking, methods, and techniques. It combines the cognitive patterns and problem-solving methods summarized by the author in teaching. 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 confusion exposed 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 helps students deepen their understanding of concepts in advanced mathematics, summarize and generalize problem-solving methods and techniques, and improve their ability to analyze and solve problems. This book can be used as a supplementary textbook for undergraduate students in science and engineering, finance and economics, and economics and management majors studying "Advanced Mathematics." It can also serve as a teaching reference for instructors. For senior undergraduate students preparing for graduate entrance exams, this book is an excellent guide and companion.