Calculus and Introduction to Mathematical Analysis: Volume 2 (2 volumes in total)

Author: R. Courant (USA), F. John (USA)
Publisher:
Publishing Date: Not available
Features: This book systematically elaborates on the fundamental theories of calculus. In the presentation, the authors strive to achieve both rigor and accessibility, highlighting the intrinsic connections between concepts and their intuitive background. The original book is divided into two volumes: the first volume covers single-variable calculus, while the second volume deals with multivariable calculus. The Chinese translation of the second volume is published in two parts. This book is the second part, covering the first three chapters.
Chapter 1 provides an in-depth discussion of multivariable functions and their derivatives, including linear differential forms and their integration, supplemented with rigorous proofs of fundamental concepts in mathematical analysis.
Chapter 2 prepares sufficient material for modern mathematical analysis in terms of linear algebra.
Chapter 3 describes the development and applications of multivariable differential calculus, including rigorous proofs of the implicit function theorem, the basic theory of multivariable transformations and mappings, fundamental knowledge of differential geometry for curves and surfaces, and basic concepts such as exterior differential forms.
The original book includes solutions to exercises, which are compiled into each part.
Translators (in order of content): Shao Tumin, Zhou Jianying, Zhang Jinyan (Chapter 1), Liu Wanru (Chapter 2), Lin Jianxiang, Zhang Shunyan, Zhu Dewei (Chapter 3), Lin Yuanqu (Solutions).
Target audience: Faculty and students of science and engineering disciplines in higher education institutions and engineering professionals.