Mathematical Analysis: A New Approach (Volume 3)

Author: Zhang Zhusheng
Publisher:
Publish Date: 2002-02-01
Features: This book can serve as a textbook or supplementary reading for the foundational course of mathematical analysis in mathematics departments of colleges and universities. It can also be used as a reference book for teachers in primary and secondary schools, scientists, and engineering professionals. The predecessor of this book was the experimental teaching notes for the teaching reform of the Mathematics Department of Peking University. The reform emphasized inspiration, the inherent unity of mathematics, and the cultivation of students' abilities. The book not only explains the basic principles of mathematical analysis but also introduces some important applications (including deriving the law of universal gravitation from Kepler's laws of planetary motion). From the introduction of concepts to the proof of theorems, the book has made meticulous arrangements to present traditional material in a new way. It also includes some new materials with significant theoretical and practical meaning (e.g., proving the Brouwer fixed-point theorem using the integral of differential forms). The book is divided into three volumes. Volume 1 covers: single-variable calculus, elementary differential equations, and their applications. Volume 2 covers: further discussions on single-variable calculus, improper integrals, differential calculus of multivariable functions, and multiple integrals. Volume 3 covers: geometric applications of differential calculus, line integrals and surface integrals, an introduction to field theory, series, and integrals with parameters.