Advanced Mathematics·Volume 1

Author: Li Zhong / Zhou Jianying (editors)
Publisher:
Publish Date: 2004-06-01
Features: This textbook is designed for students in comprehensive universities, normal universities, and non-teaching majors in science and engineering universities (especially physics majors). The book is divided into two volumes: Volume 1 covers calculus of single-variable functions, vector algebra, and spatial analytical geometry, as well as differential calculus of multivariable functions; Volume 2 covers integral calculus of multivariable functions, series, and ordinary differential equations. The predecessor of this series, A Concise Course in Advanced Mathematics (3 volumes, Peking University Press, 1998), won the First Prize of the 2002 National Excellent Textbook Award for Higher Education in China by the Ministry of Education. This book is a revised version of the original, and the revisions are detailed in the preface. This is the first volume, which is divided into six chapters, including: Introduction, Functions and Limits, Basic Concepts of Calculus, Calculation of Integrals, Mean Value Theorems and Taylor’s Formula, Vector Algebra and Spatial Analytical Geometry, and Differential Calculus of Multivariable Functions. The book includes answers and hints to exercises at the end for reference. This book is a result of mathematical pilot programs conducted by the authors at Peking University. It appropriately integrates the content system of traditional advanced mathematics courses, emphasizing the essence of mathematical concepts and theories while avoiding excessive formalism, making the material feel natural and straightforward. The book highlights the connection between mathematical theory and other disciplines, with historical notes that briefly describe the development and evolution of relevant concepts and theories, as well as the contributions of important mathematicians. The language is fluent, the narration concise, and the explanations easy to understand, with numerous examples to facilitate self-study. Each section includes a moderate number of exercises, and each chapter is accompanied by comprehensive review questions. Answers or hints are provided for reference.