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MAT 508E
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Course Information
Course Name
Turkish
Manifoldlar Üzerinde Integral Hesabı
English
Integration on Manifold
Course Code
MAT 508E
Credit
Lecture
(hour/week)
Recitation
(hour/week)
Laboratory
(hour/week)
Semester
1
3
3


Course Language
English
Course Coordinator
Elif Canfes
Course Objectives
1. To recall the basic definitions and theorems of manifold theory;
2. To introduce the orientations on manifolds;
3. To teach the concept of integration on ndimensional real spaces;
4. To apply the concept of integration to chains and manifolds.
Course Description
Basic definitions: manifolds, charts, atlases, vector fields, tensors and forms. Orientation on manifolds. Inverse function theorem and implicit function theorem. Integration on ndimensional real spaces. Integration on chains. Integration on manifolds.
Course Outcomes
Ph.D. students who successfully pass this course gain knowledge, skills and competency in the following subjects;
I. Orientation and orientability on manifolds;
II. Measure, partition of unity and integration on ndimensional real spaces;
III. Integration on chains and Stokes’ theorem on ndimensional real spaces;
IV. Integration on manifolds;
V. Stokes’, Green’s and divergence theorems on manifolds.
Prerequisite(s)
Required Facilities
Other
Textbook
1. Spivak, M.(1968). Calculus on Manifolds, Westview Press.
2. Boothby, W.M. (1975). An Introduction to Differential Manifolds and Riemannian Geometry, Academic Press Inc.
3. Munkres , J. R (1991). Analysis on Manifolds, Westview Press.
4. Dubrovin, B.A. , Fomenko, A.T.ve Novikov, S.P.(1984). Modern geometry, methods and applications, Springer Verlag.
5. Warner, F.W ,(1983). Foundation of differentiable manifolds and Lie groups, Springer Verlag..
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