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 M-573, Syllabus, Description and Links

 

MATH 573

Differentiable Manifolds

3 hours

Definition and examples of manifolds. Submanifolds, tangent and cotangent bundles, Vector fields, Differential forms, Tensors, Integration on manifolds.

 

573 ريض

المانيفولدات التفاضلية

3 ساعات

تعريف المانيفولد التفاضلي وأمثلة، المانيفولدات الجزئية، حزم المماسات والمماسات المرافقة، حقول المتجهات، الصيغ التفاضلية، حقول الممتدات، التكامل.

 

 Recommended Books:

 1) Y. Matsushima, Differentiable manifolds, Marcel Dekker, New York, 1972.

2) F.W. Warner, Foundations of differentiable manifolds and Lie groups, Scot Foresman and Company, 1971

 

M-573,  Course Description

 

Topic

 

No. of weeks

Smooth maps, regular and critical point, immersion and submersions, implicit function theorem, charts around critical and regular points.

 

3

 

Tangent and cotangent bundles, smooth vector fields, properties of smooth vector fields, Lie-algebra of smooth vector fields one parameter group of transformations, complete vector fields.

 

3

 

Local one parameter group of local transformations, .f-related vector fields, diffeomorphisms,. Partition of unity.

 

3

 

Differential forms, exterior differentiation of forms, effect of smooth maps on forms,.

 

3

 

Orientation, Volume form, Integration of differential froms with compact support.

 

3

  

For more details of the course click here.

Links:

http://en.wikipedia.org/wiki/Manifold

http://www.math.harvard.edu/theses/phd/bloom/ThesisXFinal.pdf

http://www.math.washington.edu/~arms/mpp07/t2sg.pdf

http://www2.maths.ox.ac.uk/~hitchin/hitchinnotes/hitchinnotes.html

http://math.ucsd.edu/~lindblad/250a/250a.html

http://mathworld.wolfram.com/SmoothMap.html

 

 MATH573

M-573final(1430).pdfM-573final(1430)شريف صادق دشموخ
M-573midterm(1430).pdfM-573midterm(1430)شريف صادق دشموخ
M-573IIsemesterfinal1429.pdfM-573IIsemesterfinal1429شريف صادق دشموخ
ModelanswersM-573secondmidterm.pdfModelanswersM-573secondmidtermشريف صادق دشموخ
M-573secondmidterm.pdfM-573secondmidtermشريف صادق دشموخ
Manifold - Wikipedia, the free encyclopedia.mhtManifold - Wikipedia, the free encyclopediaشريف صادق دشموخ
Chern'sintroduction to Geometry of curves.pdfChern'sintroduction to Geometry of curvesشريف صادق دشموخ
TangentbundleandVectorfields.pdfTangentbundleandVectorfieldsشريف صادق دشموخ
M-573(1429)Imidterm.pdfM-573(1429)Imidtermشريف صادق دشموخ
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