内容简介

　　本书以五幕数学剧的形式直观地讲述微分几何和微分形式，包括“空间的本质”“度量”“曲率”“平行移动”和“微分形式”。在前四幕中，古典几何被重新引入微分几何，使用235幅作者自绘插图，运用牛顿的几何方法对经典结果提供几何解释。在第五幕中，本书特别向本科生介绍微分形式，以直观和几何的方式处理进阶主题。学习本书只需要基本的微积分和几何学知识，高等院校数学专业学生及数学研究者均可阅读。

　　作者简介

　　特里斯坦·尼达姆（Tristan Needham）

　　旧金山大学数学系教授，理学院副院长。牛津大学博士，导师为Roger Penrose（与霍金齐名的英国物理学家）。1995年被美国数学学会授予Carl B.Allendoerfer奖，他的研究领域包括几何、复分析、数学史、广义相对论。

Content introduction

Differential geometry and differential forms are presented visually in the form of a five-act mathematical play, including "The nature of Space," "Metrics," "curvature," "parallel mobility," and "Differential Forms." In the first four acts, classical geometry is reintroduced into differential geometry, using 235 author-drawn illustrations that provide geometric explanations of classical results using Newton's geometric methods. In Act 5, the book specifically introduces undergraduate students to differential forms, dealing with advanced topics in an intuitive and geometric manner. This book requires only a basic knowledge of calculus and geometry, and can be read by college mathematics majors and mathematics researchers.

About the author

Tristan Needham

Professor of Mathematics, Associate Dean of Science, University of San Francisco. He received a PhD from the University of Oxford under the guidance of Roger Penrose (a British physicist of Hawking's equal name). In 1995, he was awarded the Carl B.Allendoerfer Award by the American Mathematical Society for his research in geometry, complex analysis, the history of mathematics, and general relativity.