Advanced Mathematics

Author: Li Zhong, Zhou Jianying (editors)
Publisher:
Publishing Date: 2004-06-01
Features: This textbook is designed for non-mathematics majors in comprehensive universities, normal universities, and other technological universities. The book is divided into two volumes. The first volume covers calculus of single-variable functions, vector algebra, and spatial analytical geometry, as well as differential calculus of multivariable functions. The second volume includes integral calculus of multivariable functions, series, and ordinary differential equations. The predecessor of this textbook, A Concise Course in Advanced Mathematics, 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, with revisions detailed in the preface. This is the second volume, divided into six chapters. It includes: multiple integrals, line integrals and surface integrals, ordinary differential equations, infinite series, improper integrals and integrals with parameters, and Fourier series, among others. This book is a result of mathematical pilot programs conducted by the authors at Peking University. It appropriately integrates the traditional content of 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. Historical notes are included, briefly summarizing the development and evolution of relevant concepts and theories, as well as the contributions of important mathematicians. The language is fluent, the exposition concise and clear, with numerous examples to facilitate self-study. Each section includes a moderate number of exercises, and each chapter concludes with comprehensive review questions. Answers or hints are provided for reference.