A Concise Course in Mathematical Analysis, Volume 1

Author: Deng Donggao
Publisher:
Publish Date: 2000-06-01
Features: This book can be used as a textbook for mathematics majors in science and normal schools at colleges and universities, and is also suitable for students in computer science, mechanics, and physics majors, as well as for general readers. It is a research outcome of the Ministry of Education's "Reform Plan for Teaching Content and Curriculum Systems in Higher Education Toward the 21st Century" and is a 21st-century curriculum textbook. The book is guided by the novel perspective of "the calculus system of continuous quantities and its mathematical theory" throughout, while retaining the fundamental content of traditional mathematical analysis. It handles the relationship between limits and calculus operations and applications in a relatively good way, establishing a systematic approach that is both progressive, vivid, and intuitive, while maintaining rigor, differing significantly from traditional textbooks. The book offers unique and insightful perspectives on the origins and essence of concepts and methods. It is divided into two volumes. The first volume mainly includes: the continuum of real numbers, functions, limits and function continuity, derivatives and differentials, mean value theorems and their applications, indefinite integrals, definite integrals, further applications of calculus, and a re-examination of the real number system. The second volume mainly includes: series of terms, improper integrals, series of functions, power series, Fourier series, limits and continuity of multivariable functions, partial derivatives and total differentials, the existence theorem of implicit functions, extrema and conditional extrema, integrals with parameters, multiple integrals, line integrals and surface integrals, the relationships between various types of integrals, and an introduction to field theory. This book is the result of the author's decades of experience in teaching and curriculum reform, and has achieved positive results in practical teaching reform.