Title

Title
Bienvenue sur Biblio-Sciences, site communautaire principalement destiné aux étudiants, élèves et à toute autre personne désirant trouver des documents numériques dans un but académique, ludique ou autre. Explorez Biblio-Sciences où chaque livre est une aventure scientifique qui commence. La connaissance n'attend que vous !

Search

Rechercher des livres par catégories

togglesFiltrer

Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts
























Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts


Author(s):
Tristan Needham



Collection:


Publisher:
Princeton University Press


Year:
July 13, 2021


Language:
English


Pages:
531 pages


Size:
24.8 MB


Extension:
PDF






[tab]

[content title="Description"]

An inviting, intuitive, and visual exploration of differential geometry and forms

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 of the 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 acts include: 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 treatment of 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 final act 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.

Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

[/content]

[content title="Content"] [/content]

[content title="About the author(s)"]Tristan Needham is professor of mathematics at the University of San Francisco. He is the author of Visual Complex Analysis. [/content]

[/tab]




Download (pdf, 24.8 MB)






[facebook src="bibliosciencesorg"/]






Mots-Clés:
Télécharger Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts EBOOK PDF EPUB DJVU. Download Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts EBOOK PDF EPUB DJVU.



Books›Science & Math›Mathematics
Page précédente Accueil Page suivante

Post Share Buttons

LITTERATURE ET LANGUES

Les plus populaires Voir la suite

Popup

Sciences et Techniques

Sciences et TechniquesVoir la suite

Sciences Humaines et Sociales

Sciences Humaines et SocialesVoir la suite

ECONOMIE FINANCES ET ENTREPRISESVoir la suite

LITTERATURE ET LANGUESVoir la suite

ARTS CULTURE LOISIRS ET ACTUALITESVoir la suite

RELIGIONVoir la suite