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 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.
Pre-requisite(s)
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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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