Calculus, Volume 1

Author: Hou Yunchang
Publisher:
Publish Date: 2003-05-04
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. It aligns with the fundamental requirements for teaching higher mathematics in engineering undergraduate programs, as promulgated 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 mathematical 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. The book enhances mathematical modeling training, focusing on practical applications and the cultivation of innovative abilities. Exercises are divided into two categories: Category A consists of problems designed to help readers grasp concepts and master the textbook material, while Category B broadens the scope of the content, presents more challenging and innovative problems, 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, as well as for science majors and for readers in the general public.