Calculus Textbook. Volume 1

Author: Department of Mathematics, School of Science, Shanghai University
Publisher:
Publish Date: 2005-08-01
Features: This book is written in accordance with the "Basic Requirements for Higher Education Mathematics Curriculum" formulated by the National Advisory Committee on Engineering Mathematics Education in Higher Education. It is divided into three volumes: Upper, Middle, and Lower. The upper volume covers functions and limits, derivatives and differentials, mean value theorems and applications of derivatives, and indefinite integrals. The middle volume includes definite integrals, applications of definite integrals, series, and differential equations. The lower volume contains spatial analytical geometry and vector algebra, multivariable differential calculus, multiple integrals, and line and surface integrals. This volume strives to introduce fundamental ideas of mathematical modeling based on the practical application background of mathematics, focusing on the main ideas, theories, and methods of advanced calculus while highlighting its broad applications. To meet students' learning needs, exercises (A) and (B) are arranged at the end of each section, and comprehensive review questions are provided at the end of each chapter for systematic practice and review. The logical reasoning is rigorous and clear, the exposition is straightforward and easy to understand, and the examples are typical and diverse, making it suitable for self-study. It can be used by undergraduate students in non-mathematics science and engineering, as well as management disciplines in comprehensive universities and normal universities.