Advanced Mathematics (Volume 1)

Author: Hou Yunchang
Publisher:
Publish Date: 1999-10-01
Features: This book is a research outcome of the "Reform Plan for Teaching and Curriculum Systems in Higher Education Towards the 21st Century" by the Ministry of Education. It is a curriculum textbook for the 21st century and a national key textbook for the "Nineth Five-Year Plan" in general higher education, aligning with the fundamental requirements for teaching higher mathematics in undergraduate engineering programs issued by the former State Education Commission. The book has made significant adjustments to the traditional higher mathematics curriculum, clarifying the intrinsic connections between concepts. It emphasizes the use of modern mathematical language and symbols, incorporating "windows" to showcase modern mathematics content. Building on the introduction of the real number system, it strengthens the theory of limits. Vector and matrix tools are employed to express relevant content, and mathematical modeling training is enhanced to focus on practical applications and the cultivation of innovative abilities. Exercises are categorized into two types: Type A, designed to help readers grasp concepts and master the course material, and Type B, which extends the course content, presents challenges with novelty, and includes hints and answers.
The first volume covers functions and limits, calculus of functions of one variable, and vector algebra with spatial analytical geometry. The second volume includes calculus of functions of multiple variables, infinite series, and ordinary differential equations. This book can serve as a textbook for undergraduate engineering programs in general higher education institutions and is also suitable for students in science programs and for general readers.