Calculus I

Author: Li Zhong
Publisher:
Publish Date: 2004-07-01
Features: This series of textbooks is designed for students in non-mathematics majors at comprehensive universities, normal universities, and other science and engineering universities (especially physics majors). The entire series is divided into two volumes. The first volume covers calculus of single-variable functions, vector algebra and spatial analytical geometry, and differential calculus of multivariable functions. The second volume covers integral calculus of multivariable functions, series, and ordinary differential equations. The predecessor of this series, "A Concise Course in Advanced Mathematics" (3 volumes, Peking University Press, 1998), won the First Prize of the 2002 National Excellent Textbook for Higher Education in China awarded by the Ministry of Education. This book is a revised version of the original, with revisions detailed in the preface. This is the first volume, divided into six chapters. It includes: Introduction, Functions and Limits, Basic Concepts of Calculus, Calculation of Integrals, Mean Value Theorems and Taylor's Formula, Vector Algebra and Spatial Analytical Geometry, and Differential Calculus of Multivariable Functions, etc. At the end of the book, there are answers and hints to exercises for reference. This book is the result of teaching pilot programs by the author at Peking University. It appropriately integrates the content system of traditional advanced mathematics courses, aiming to highlight the essence of mathematical concepts and theories while avoiding excessive formalism, making the material feel natural and straightforward to readers. The book emphasizes the connection between mathematical theory and other disciplines. Historical notes are included, briefly summarizing the development and evolution of relevant concepts and theories, as well as the contributions of important mathematicians. The language is fluent, the exposition concise and clear, with numerous examples to facilitate self-study. Each section includes a moderate number of exercises, and each chapter is accompanied by comprehensive review questions. Answers or hints to exercises are provided for reference.
This series of textbooks is designed for students in non-teaching majors at comprehensive universities, normal universities, and other science and engineering universities (especially physics majors). The entire series consists of two volumes. The first volume covers calculus of single-variable functions, vector algebra and spatial analytical geometry, and differential calculus of multivariable functions. The second volume covers integral calculus of multivariable functions, series, and ordinary differential equations. The predecessor of this series, "A Concise Course in Advanced Mathematics" (3 volumes, Peking University Press, 1998), won the First Prize of the 2002 National Excellent Textbook for Higher Education in China awarded by the Ministry of Education. This book is a revised version of the original, with revisions detailed in the preface. This is the first volume, divided into six chapters, including: Introduction, Functions and Limits, Basic Concepts of Calculus, Calculation of Integrals, Mean Value Theorems and Taylor's Formula, Vector Algebra and Spatial Analytical Geometry, and Differential Calculus of Multivariable Functions, etc. At the end of the book, there are answers and hints to exercises for reference. This book is the result of teaching pilot programs by the author at Peking University. It appropriately integrates the content system of traditional advanced mathematics courses, aiming to highlight the essence of mathematical concepts and theories while avoiding excessive formalism, making the material feel natural and straightforward to readers. The book emphasizes the connection between mathematical theory and other disciplines, with historical notes included that briefly summarize the development and evolution of relevant concepts and theories, as well as the contributions of important mathematicians. The language is fluent, the exposition concise and clear, with numerous examples to facilitate self-study. Each section includes a moderate number of exercises, and each chapter is accompanied by comprehensive review questions. Answers or hints to exercises are provided for reference.