Introduction to Calculus and Mathematical Analysis. Volume 2 (of 2 volumes)

Author: Courant
Publisher:
Publication Date: 2005-02-01
Features: Introduction to Calculus and Analysis (Volume 2 of 2 volumes) systematically elaborates on the fundamental theories of calculus. In the exposition, the author strives to achieve both rigor and clarity, highlighting the intrinsic connections between concepts and their intuitive background. The original book is divided into two volumes: Volume 1 covers single-variable cases, while Volume 2 covers multivariable cases. This volume systematically elaborates on the fundamental theories of calculus. In the exposition, the author strives to achieve both rigor and clarity, highlighting the intrinsic connections between concepts and their intuitive background. The original book is divided into two volumes: Volume 1 covers single-variable cases, while Volume 2 covers multivariable cases. The Chinese translation of Volume 2 is published in two parts. This book is the first part of Volume 2, including the first three chapters. Chapter 1 thoroughly discusses multivariable functions and their derivatives, including linear differential forms and their integration, supplemented with rigorous proofs of fundamental concepts in mathematical analysis. Chapter 2 in linear algebra provides sufficient material for the foundation of modern mathematical analysis. Chapter 3 presents the development and applications of multivariable differential calculus, including rigorous proofs of the implicit function theorem, the basic theory of multivariable transformations and mappings, differential geometry of curves and surfaces, and fundamental 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). The target audience is faculty and students of science and engineering disciplines in higher education institutions and engineering professionals.