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Course Information

Course Name
Turkish Manifoldlar Üzerinde Integral Hesabı
English Integration on Manifold
Course Code
MAT 508E Credit Lecture
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 n-dimensional 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 n-dimensional 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 n-dimensional real spaces;
III. Integration on chains and Stokes’ theorem on n-dimensional real spaces;
IV. Integration on manifolds;
V. Stokes’, Green’s and divergence theorems on manifolds.
Required Facilities
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..
Other References
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