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DIFFERENTIABLE GEOMETRY (M2, Lang)

Lecture Topic : (Pure Math) DIFFERENTIABLE GEOMETRY (M2, Lang)

Prerequisites : Differential Geometry in 3D (Sen, M1); Manifold Theory (M1); Differential Forms (M1);

Recommended Text(s) :

“Fundamentals of Differential Geometry”, Graduate Texts in Mathematics (GTM) No. 191, Serge Lang, Springer, 1999.

Approx price new on Amazon.com (hard copy) : $52

Approx price second hand on Amazon.com (hard copy) : $40

Availability free on eMule.com (e-format) : Yes

eMule search key word(s) : Lang, Differential Geometry

Lectures and Links :

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Lecture 1  (link)

Ch.1   Differential Calculus

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Lecture 2  (link)

Ch.2   Manifolds

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Lecture 3  (link)

Ch.3   Vector Bundles

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Lecture 4 (link)

Ch.4   Vector Fields and Differential Equations

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Lecture 5  (link)

Ch.5   Operations on Vector Fields and Differential Forms

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Lecture 6  (link)

Ch.6   The Theorem of Frobenius

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Lecture 7  (link)

Ch.7   Metrics

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Lecture 8  (link)

Ch.8   Covariant Derivatives and Geodesics

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Lecture 9  (link)

Ch.9   Curvature

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Lecture 10  (link)

Ch.10   Jacobi Lifts and Tensorial Splitting of the Double Tangent Bundle

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Lecture 11  (link)

Ch.11   Curvature and the Variation Formula

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Lecture 12  (link)

Ch.12   An Example of Seminegative Curvature

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Lecture 13  (link)

Ch.13   Automorphisms and Symmetries

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Lecture 14  (link)

Ch.14   Immersions and Submersions

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Lecture 15  (link)

Ch.15   Volume Forms

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Lecture 16  (link)

Ch.16   Integration of Differential Forms

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Lecture 17  (link)

Ch.17   Stokes Theorem

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Lecture 18  (link)

Ch.18   Applications of Stokes Theorem

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Lecture 19  (link)

Appendix :  The Spectral Theorem

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