Mathematical Analysis (Upper and Lower Volumes)

Author: Zhao Huanguang, Lin Changsheng
Publisher:
Publish Date: 2006-06-01
Features: The core content of Mathematical Analysis is calculus—the general term for differential calculus and integral calculus. In differential calculus, we primarily study differentiation, derivatives, and their applications, with the central question being how to find the rate of change of things (phenomena) (e.g., the slope of a tangent, instantaneous velocity, etc.). In integral calculus, we mainly study indefinite integrals, definite integrals, and their applications, with the central question being how to find total quantities (e.g., area, work, etc.). In the history of mathematical development, the concept and methods of integration preceded those of differentiation. The concept of differentiation almost emerged and developed simultaneously with modern mechanics (second half of the 16th century), and before the mid-17th century, differentiation and integration were unrelated, developing independently yet in balance. Mathematical Analysis (Volume 1) includes three parts: the fundamentals of mathematical analysis, differential calculus of single-variable functions, and integral calculus of single-variable functions; Mathematical Analysis (Volume 2) includes three parts: series, differential calculus of multivariable functions, and integral calculus of multivariable functions. This book can serve as a teaching reference for instructors of Mathematical Analysis and Advanced Mathematics courses in universities and colleges, as well as a reference material for undergraduate students of mathematics majors studying Mathematical Analysis (including postgraduate entrance exams).