Advanced Mathematics Step-by-Step Tutorial

Author: Zhang Zhiyu
Publisher:
Publishing Date: 2005-01-01
Features: This book is a learning guide for the "Advanced Mathematics" public course in engineering majors at higher education institutions. It is compatible with multiple current national excellent textbooks on "Advanced Mathematics" in China and can be used synchronously. To match the teaching of "Advanced Mathematics" courses and the learning needs of students in similar higher education institutions, the authors meticulously planned and organized this "Advanced Mathematics Step-by-Step Practice and Exercise Series" guidebook, written by experienced frontline teachers who have participated in and achieved rich results in teaching reform. This book is part of the "Advanced Mathematics Step-by-Step Practice and Exercise" series. The entire book is divided into twelve topics, including functions, limits and continuity, derivatives and differentials, mean value theorems and applications of derivatives, indefinite integrals, definite integrals, applications of definite integrals, vector algebra and spatial analytical geometry, differential calculus of multivariable functions and its applications, multiple integrals, line integrals and surface integrals, and infinite series and differential equations. Each topic is divided into the following six modules: content summary, basic requirements, problem-solving guidance, method guidance, synchronous training (divided into A and B levels of exercises), and learning notes. The book also includes three final exam simulation tests after the sixth and twelfth topics, respectively, for use by teachers and readers. The key focus of the book is "problem-solving guidance" and "method guidance." The "problem-solving guidance" section provides concise and clear explanations of easily confused concepts and common errors in problem-solving to help students overcome difficulties. The "method guidance" aims to strengthen students' understanding and mastery of basic concepts and methods through exercises in this section. It emphasizes problem-solving methods, especially by providing multiple solutions to a single problem, inspiring students to grasp general methods, learn to apply techniques, and develop flexible, diverse, and adaptable scientific qualities. The book is written in accordance with the "Basic Requirements for Teaching Advanced Mathematics in Higher Education Institutions for Engineering Undergraduates" issued by the Ministry of Education. It emphasizes the integration of mathematical thinking, methods, and techniques, combining the cognitive patterns and problem-solving methods summarized by the authors from frontline teaching. This book can serve as a supplementary textbook for undergraduate engineering students studying "Advanced Mathematics" and also as a teaching reference for instructors. For senior undergraduate students preparing for postgraduate entrance exams, this book is also a valuable guide and companion. The book is divided into twelve topics, including functions, limits and continuity, derivatives and differentials, mean value theorems and applications of derivatives, indefinite integrals, definite integrals, and applications of definite integrals, among others.