Mathematical Analysis Second Edition

Author: Zhou Minqiang (Editor)
Publisher:
Publication Date: 2003-01-01
Features: This textbook covers the fundamental course of advanced mathematics—Mathematical Analysis, with its core content being calculus. The series consists of three volumes, and this is the second volume. The book is divided into six chapters: Definite Integrals, Improper Integrals, Series with Constant Terms, Series with Variable Terms, Power Series, Taylor Series, and an Introduction to Fourier Analysis. It primarily focuses on definite integrals, improper integrals, series theory, and Fourier analysis. This book is revised based on the lecture notes used by the author for many years at the School of Mathematical Sciences, Peking University. It is rich in content and presents concepts in a clear and accessible manner. For more challenging theorems, definitions, and in-depth problems, the book provides supplementary notes to aid readers in better understanding new knowledge. At the end of each chapter, there are also remarks to help readers gain a clearer understanding of the background knowledge and to facilitate rapid improvement in mathematical ability. The book includes a selection of representative and thought-provoking examples, as well as a sufficient number of exercises and discussion questions. The exercises and questions range from general difficulty to more challenging ones, allowing readers to choose based on their needs. This textbook can serve as a teaching material for undergraduate students in mathematics, probability and statistics, mechanics, computer science, and related fields. It can also be used as a reference book for mathematicians and enthusiasts.