Manifolds, Vector Fields, and Differential Forms: An Introduction to Differential Geometry (Paperback)
暫譯: 流形、向量場與微分形式：微分幾何入門（平裝本）
Gross, Gal, Meinrenken, Eckhard
- 出版商: Springer
- 出版日期: 2023-04-26
- 售價: $2,130
- 貴賓價: 9.5 折 $2,024
- 語言: 英文
- 頁數: 343
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031254082
- ISBN-13: 9783031254086
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相關分類:
工程數學 Engineering-mathematics
海外代購書籍(需單獨結帳)
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相關主題
商品描述
This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate level references, the text relies on a minimal set of prerequisites: a solid grounding in linear algebra and multivariable calculus, and ideally a course on ordinary differential equations. Manifolds are introduced intrinsically in terms of coordinate patches glued by transition functions. The theory is presented as a natural continuation of multivariable calculus; the role of point-set topology is kept to a minimum.
Questions sprinkled throughout the text engage students in active learning, and encourage classroom participation. Answers to these questions are provided at the end of the book, thus making it ideal for independent study. Material is further reinforced with homework problems ranging from straightforward to challenging. The book contains more material than can be covered in a single semester, and detailed suggestions for instructors are provided in the Preface.
商品描述(中文翻譯)
這本教科書作為現代微分幾何的入門，適合高年級本科生和碩士生閱讀。它特別強調動機和理解，同時培養對更抽象概念的堅實直覺。與研究生級別的參考書相比，這本書依賴於最少的先備知識：對線性代數和多變數微積分的扎實基礎，理想情況下還應修過常微分方程的課程。流形以內在的方式介紹，通過過渡函數將坐標片段粘合在一起。理論被呈現為多變數微積分的自然延續；點集拓撲的角色保持在最低限度。
書中穿插的問題促使學生積極學習，並鼓勵課堂參與。這些問題的答案在書末提供，因此非常適合獨立學習。教材還通過從簡單到具有挑戰性的作業題目進一步加強。這本書的內容超過一個學期所能涵蓋的範圍，並在前言中提供了詳細的教學建議。
作者簡介
Gal Gross is a Ph.D. student in mathematics at the University of Toronto, working in combinatorics and algebra with a special interest in additive combinatorics. Gross' other mathematical interests include differential geometry, set theory and foundational questions.
Eckhard Meinrenken is a professor of mathematics at the University of Toronto, working in the fields of differential geometry and mathematical physics. His contributions include a proof of the Guillemin-Sternberg conjecture in symplectic geometry and the development, with Alekseev and Malkin, of the theory of group-valued momentum maps. In 2002 he was an invited speaker at the ICM in Beijing, and in 2008 he was elected Fellow of the Royal Society of Canada. Meinrenken's book Clifford Algebras and Lie Theory was published (c) 2013 in Springer's Ergebnisse series
作者簡介(中文翻譯)
Gal Gross 是多倫多大學的數學博士生，專注於組合數學和代數，特別對加法組合數學有興趣。Gross 的其他數學興趣包括微分幾何、集合論和基礎問題。
Eckhard Meinrenken 是多倫多大學的數學教授，專注於微分幾何和數學物理領域。他的貢獻包括在辛幾何中對 Guillemin-Sternberg 猜想的證明，以及與 Alekseev 和 Malkin 共同發展的群值動量映射理論。2002 年，他在北京的國際數學家大會（ICM）上擔任邀請演講者，並於 2008 年當選為加拿大皇家學會院士。Meinrenken 的著作 Clifford Algebras and Lie Theory 於 2013 年在 Springer 的 Ergebnisse 系列中出版。
