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    Hersteller: University Presses

    Visual Differential Geometry and Forms von Needham, Tristan

    A Mathematical Drama in Five Acts

    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.


    Autor Needham, Tristan
    Verlag University Presses
    Einband Kartonierter Einband (Kt)
    Erscheinungsjahr 2021
    Seitenangabe 584 S.
    Meldetext Lieferbar in ca. 10-20 Arbeitstagen
    Ausgabekennzeichen Englisch
    Abbildungen 235 b/w illus.
    Masse H25.4 cm x B17.8 cm
    Coverlag Princeton University Press (Imprint/Brand)
    ISBN 978-0-691-20370-6
    Kartonierter Einband (Kt)
    Lieferbar in ca. 10-20 Arbeitstagen
    978-0-691-20370-6
    Fr. 65.00
    Unsere Bestellmengen-Rabatte
    10+ /10%
    20+ /12.5%
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    Fr. 58.50
    Fr. 56.90
    Fr. 55.25

    Über den Autor Needham, Tristan

    Tristan Needham is professor of mathematics at the University of San Francisco. He is the author of Visual Complex Analysis.

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