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" course, a common mathematics requirement for science and engineering, economics, management, and finance majors in higher education institutions. It is designed to be used alongside the widely adopted domestic textbook "Advanced Mathematics" 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 covers 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 analysis of typical examples is categorized into three types: A, B, and C. Type A examples are basic problems, Type B examples are comprehensive problems, and most Type C examples are selected from past graduate entrance examination questions. This book is compiled in accordance with the "Advanced Mathematics" teaching syllabus 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 from teaching experience. The focus of the book lies in 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 students encounter during their learning process. They are designed to be representative, progressive, and multifaceted, with discussions of different solution methods and an analysis of common errors made by beginners. This helps students deepen their understanding of advanced mathematical concepts, summarize and refine problem-solving methods and techniques, and improve their ability to analyze and solve problems. This book can serve as a supplementary textbook for undergraduate students in science and engineering, finance and economics, and management majors studying "Advanced Mathematics." It can also be used as a teaching reference for instructors. For senior undergraduate students preparing for graduate entrance exams, this book is an excellent study guide.