Advanced Mathematics. Volume 1

Author: Department of Applied Mathematics, Tongji University
Publisher:
Publish Date: 2002-07-01
Features: This book expands its applicability while ensuring the basic teaching requirements, making it suitable for students of different majors in higher engineering colleges. The fifth edition is a comprehensive revision based on the fourth edition, guided by the spirit of teaching reform and the new requirements of textbook reform. In the revision, to better align with the Chinese mathematics curriculum, the concept of functions is introduced from general sets and mappings. To cultivate students' abilities and mathematical literacy, some modern mathematical ideas, language, and methods are integrated. Certain content has been appropriately streamlined and combined, and the text has been simplified with the introduction of some mathematical notations and symbols. Practical examples and exercises on the applications of differentiation in science and technology, economic management, and daily life have been added. This makes the content and system more complete and facilitates self-study. The book is published in two volumes. The first volume covers functions and limits, the differentiation rules of functions, the mean value theorem of differentiation and its applications, indefinite integrals, definite integrals, the applications of definite integrals, and spatial analytical geometry and vector algebra. At the end of the book, there are brief introductions to second- and third-order determinants, several commonly used curves, integral tables, and answers and hints to exercises. The second volume covers the differential calculus of multivariable functions and its applications, multiple integrals, line integrals and surface integrals, infinite series, and differential equations. At the end of the book, there are answers and hints to exercises.