Differential Geometry of Curves and Surfaces (Hardcover)
暫譯: 曲線與曲面的微分幾何 (精裝版)

Banchoff, Thomas F., Lovett, Stephen

Differential Geometry of Curves and Surfaces (Hardcover)
  • 出版商: CRC
  • 出版日期: 2022-08-05
  • 售價: $2,900
  • 貴賓價: 9.5 折 $2,755
  • 語言: 英文
  • 頁數: 368
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 103228109X
  • ISBN-13: 9781032281094

    • 海外代購書籍(需單獨結帳)

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商品描述

Through two previous editions, the third edition of this popular and intriguing text takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces.

Requiring only multivariable calculus and linear algebra, it develops students' geometric intuition through interactive graphics applets. Applets are presented in Maple workbook format, which readers can access using the free Maple Player.

The book explains the reasons for various definitions while the interactive applets offer motivation for definitions, allowing students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. Investigative project ideas promote student research.

At users of the previous editions' request, this third edition offers a broader list of exercises. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress. The authors also add hints to motivate students grappling with the more difficult exercises.

This student-friendly and readable approach offers additional examples, well-placed to assist student comprehension. In the presentation of the Gauss-Bonnet Theorem, the authors provide more intuition and stepping-stones to help students grasp phenomena behind it. Also, the concept of a homeomorphism is new to students even though it is a key theoretical component of the definition of a regular surface. Providing more examples show students how to prove certain functions are homeomorphisms.

商品描述(中文翻譯)

透過前兩版的經驗，這本受歡迎且引人入勝的書籍第三版採取了分析/理論與視覺/直觀的方式來探討曲線和曲面的局部及全球性質。

本書僅需多變數微積分和線性代數，透過互動圖形小程式來培養學生的幾何直覺。小程式以 Maple 工作簿格式呈現，讀者可以使用免費的 Maple Player 來訪問。

本書解釋了各種定義的原因，而互動小程式則提供了定義的動機，讓學生能進一步探索範例，並對複雜定理提供視覺上的解釋。在小程式中改變參數曲線和參數曲面的能力，讓學生能深入探討這些概念，超越靜態文本所能提供的範疇。調查性專案的想法促進了學生的研究。

應前版用戶的要求，這第三版提供了更廣泛的練習題列表。增加了更多基礎練習，並將一些具有挑戰性的問題移至練習集的後面，以確保學生能夠逐步進步。作者還增加了提示，以激勵學生解決更困難的練習題。

這種對學生友好且易讀的方法提供了額外的範例，恰當地幫助學生理解。在高斯-博內定理的呈現中，作者提供了更多的直覺和基礎，幫助學生掌握其背後的現象。此外，雖然同胚的概念是正規曲面定義中的一個關鍵理論組成部分，但對學生來說仍然是新的。提供更多範例展示了如何證明某些函數是同胚。

作者簡介

Thomas F. Banchoff is a geometer and a professor at Brown University. Dr. Banchoff was president of the Mathematical Association of America (MAA) from 1999 to 2000. He has published numerous papers in a variety of journals and has been the recipient of many honors, including the MAA's Deborah and Franklin Tepper Haimo Award and Brown's Teaching with Technology Award. He is the author of several books, including Linear Algebra Through Geometry with John Wermer and Beyond the Third Dimension.

Stephen Lovett is an associate professor of mathematics at Wheaton College. Dr. Lovett has taught introductory courses on differential geometry for many years, including at Eastern Nazarene College. He has given many talks over the past several years on differential and algebraic geometry as well as cryptography. In 2015, he was awarded Wheaton's Senior Scholarship Faculty Award. He is the author of Abstract Algebra: Structures and Applications, Differential Geometry of Manifolds, Second Edition, A Transition to Advanced Mathematics with Danilo Dedrichs (forthcoming), all published by CRC Press.

作者簡介(中文翻譯)

托馬斯·F·班喬夫是幾何學家，也是布朗大學的教授。班喬夫博士曾於1999年至2000年擔任美國數學協會（MAA）會長。他在多個期刊上發表了大量論文，並獲得了許多榮譽，包括MAA的德博拉與富蘭克林·泰珀·海莫獎以及布朗大學的科技教學獎。他是幾本書的作者，包括與約翰·維爾默（John Wermer）合著的《透過幾何學的線性代數》（Linear Algebra Through Geometry）和《超越第三維度》（Beyond the Third Dimension）。

史蒂芬·洛維特是惠頓學院的數學副教授。洛維特博士多年來教授微分幾何的入門課程，包括在東方納撒尼爾學院（Eastern Nazarene College）。在過去幾年中，他就微分幾何、代數幾何以及密碼學發表了許多演講。2015年，他獲得惠頓學院的高年級獎學金教職員獎。他是《抽象代數：結構與應用》（Abstract Algebra: Structures and Applications）、《流形的微分幾何，第二版》（Differential Geometry of Manifolds, Second Edition）以及與丹尼洛·德德里希斯（Danilo Dedrichs）合著的《過渡到高級數學》（Transition to Advanced Mathematics，待出版）的作者，這些書籍均由CRC Press出版。

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