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Visual differential geometry and for...

Needham, Tristan,

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Visual differential geometry and forms : = a mathematical drama in five acts /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Visual differential geometry and forms :/ Tristan Needham.
其他題名:	a mathematical drama in five acts /
作者:	Needham, Tristan,
出版者:	Princeton, NJ :Princeton University Press, : c2021. ,
面頁冊數:	xxviii, 501 p. :ill. ;26 cm.
標題:	Differential forms. -
ISBN:	9780691203706

Visual differential geometry and forms : = a mathematical drama in five acts /
Needham, Tristan,

Visual differential geometry and forms :a mathematical drama in five acts /Tristan Needham. - Princeton, NJ :Princeton University Press,c2021. - xxviii, 501 p. :ill. ;26 cm.

Includes bibliographical references (p. 485-489) and index.

Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton's geometrical methods to provide geometrical explanations ofthe classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four actsinclude: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss's famous Theorema Egregium; a complete geometrical treatmentof the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein's field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The finalact elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell's equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan's method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms.Six of the seven chapters of Act V can be read completely independently from the rest of the book

ISBN: 9780691203706US45Subjects--Topical Terms:

532741
Differential forms.

LC Class. No.: QA641 / .N44 2021

Dewey Class. No.: 515.37

Visual differential geometry and forms : = a mathematical drama in five acts /
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300 $a xxviii, 501 p. : $b ill. ; $c 26 cm.
504 $a Includes bibliographical references (p. 485-489) and index.
520 8 $a Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton's geometrical methods to provide geometrical explanations ofthe classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four actsinclude: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss's famous Theorema Egregium; a complete geometrical treatmentof the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein's field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The finalact elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell's equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan's method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms.Six of the seven chapters of Act V can be read completely independently from the rest of the book
650 # 0 $a Differential forms. $3 532741
650 # 0 $a Geometry, Differential. $3 523835