Advanced Mathematics (Volumes 1 and 2) - (Science and Engineering Category)

Author: None
Publisher:
Publish Date: 2006-08-01
Features: Since the 21st century, China's higher education has made remarkable progress, and textbook development has also seen significant advancements. Currently, with the rapid development of science and technology, the widespread application of computers, and the popularity of mathematical software, we have fully entered the information age. These developments undoubtedly impose updated and stricter requirements on basic course textbooks, especially those for mathematics. In this context, we have compiled this advanced mathematics textbook suitable for all majors of science and engineering undergraduates, based on years of experience in undergraduate mathematics teaching, exploration of the development trends of undergraduate mathematics teaching, and analysis of the trends of similar textbooks domestically and internationally. This book is compiled in accordance with the "Basic Requirements for the Teaching of Advanced Mathematics" formulated by the Ministry of Education (hereinafter referred to as "Basic Requirements"). It adheres to the principles of emphasizing fundamental concepts, cultivating basic abilities, and striving for practical applications, while fully considering the trend of reducing teaching hours for advanced mathematics courses. This book has the following features:
First, it highlights the fundamental ideas and methods of advanced mathematics. The purpose of emphasizing these ideas and methods is to help students better understand the internal connections of different content sections and grasp the overall thinking and methods of advanced mathematics. It also assists students in mastering fundamental concepts, clarifying the relationships between concepts, and improving teaching effectiveness. In terms of teaching philosophy, it does not overly emphasize rigorous proofs or research processes but instead focuses more on allowing students to experience the thinking and academic value of advanced mathematics.
Second, it strengthens the cultivation of basic abilities. This book includes numerous examples and exercises, with in-depth discussions on problem-solving methods. The intention is to enable students, after grasping the fundamental concepts, to become familiar with computational processes, master problem-solving techniques, and ultimately achieve faster calculation speeds and improved problem-solving skills.
Third, it is closely related to practical applications. The presentation of fundamental concepts in this book strives to start from real-world problems encountered in daily life, naturally leading to them. Examples and exercises often involve practical issues frequently faced in the objective world, such as those in natural sciences, engineering technology, and daily life, with the hope of enhancing students' interest in learning advanced mathematics and their ability to apply mathematical knowledge to solve real-world problems.
This book is divided into two volumes. The first volume includes: Limits and Continuity of Functions, Derivatives and Differentiation, Mean Value Theorems and Applications of Derivatives, Indefinite Integrals, Definite Integrals and Their Applications, Vector Algebra and Space Analytic Geometry. The second volume includes: Differentiation of Multivariable Functions and Its Applications, Multiple Integrals, Line Integrals and Surface Integrals, Infinite Series, and Differential Equations. Exercises are provided after each section, and comprehensive exercises are included at the end of each chapter. The reference answers to all exercises are appended at the end of the book.
This book is the result of collaboration among multiple institutions. The participating institutions are listed in alphabetical order by the first character of their names: Northeastern University, Changjiang Institute of Technology (East China Institute of Technology), Shunhua Energy College (Liaoning University of Petroleum and Chemical Technology), Science and Technology College (Jiangxi Normal University), Shenyang University of Technology, Qindao College (Qingdao University of Technology), City University of Technology (Chongqing University), Binjiang College (Nanjing University of Information Science & Technology), Laiyang Agricultural College, and Science and Technology College (Xinjiang Agricultural University).