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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 (hard copy) : $52

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

Availability free on (e-format) : Yes

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

Lectures and Links :


Lecture 1  (link)

Ch.1   Differential Calculus


Lecture 2  (link)

Ch.2   Manifolds


Lecture 3  (link)

Ch.3   Vector Bundles


Lecture 4 (link)

Ch.4   Vector Fields and Differential Equations


Lecture 5  (link)

Ch.5   Operations on Vector Fields and Differential Forms


Lecture 6  (link)

Ch.6   The Theorem of Frobenius


Lecture 7  (link)

Ch.7   Metrics


Lecture 8  (link)

Ch.8   Covariant Derivatives and Geodesics


Lecture 9  (link)

Ch.9   Curvature


Lecture 10  (link)

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


Lecture 11  (link)

Ch.11   Curvature and the Variation Formula


Lecture 12  (link)

Ch.12   An Example of Seminegative Curvature


Lecture 13  (link)

Ch.13   Automorphisms and Symmetries


Lecture 14  (link)

Ch.14   Immersions and Submersions


Lecture 15  (link)

Ch.15   Volume Forms


Lecture 16  (link)

Ch.16   Integration of Differential Forms


Lecture 17  (link)

Ch.17   Stokes Theorem


Lecture 18  (link)

Ch.18   Applications of Stokes Theorem


Lecture 19  (link)

Appendix :  The Spectral Theorem


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