CANKIRI KARATEKIN UNIVERSITY Bologna Information System


  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Differential Geometry I MATH307 FALL 4+0 C 5
    Learning Outcomes
    1-Explains the basic concepts of geometry.
    2-Comments on the notions of manifold and differentiation.
    3-Describes the basic notions about the theory of curves.
    Prerequisites -
    Language of Instruction English
    Responsible Dr. Gül UĞUR KAYMANLI
    Instructors -
    Assistants -
    Resources R1. Ekici, C. (2021). Eğrilerin ve Yüzeylerin Geometrisi. Eskişehir Osmangazi Üniversitesi, Eskişehir.
    Supplementary Book SR1. Block, E. D. (1996). A First Course in Geometric Topology and Differential Geometry. Birkhauser, Boston. SR2. O`Neil, B. (2006). Elementary differential geometry. Revised second edition. Elsevier/Academic Press, Amsterdam. SR3. do Carmo, M. P. ( 2016). Differential geometry of curves & surfaces. Dover Publications, Mineola, NY. SR4. Pressley, A. (2010). Elementary differential geometry. Second edition. Springer Undergraduate Mathematics Series, Springer, Berlin. SR5. Hacısalihoğlu, H. H. (1998). Diferensiyel Geometri Cilt : 1 (3. Baskı). Hacısalihoğlu Yayınları, Anakara. SR6. Sabuncuoğlu, A. (2010). Diferensiyel Geometri (4. Baskı). Nobel Akademik Yayıncılık, Ankara.
    Goals To teach basic notions and results of surfaces in classical differential geometry, and to provide necessary substructure to students who wish to study for a master degree in this area.
    Content Geometries and same related notions, affine space and Euclidean space; Topological manifold, diffeomorphism, differentiable manifold; Tangent vectors, tangent spaces and vector fields; Directional derivative, covariant derivative; Integral curve; Lie operator; Gradient divergence rotational function and the differential of a transformation; Curves and change of parameter; Serret-Frenet vectors; The osculating planes of a curve, curvatures and its geometric meanings; Curvature centers, osculating spheres; Some frame fields; Parallel curve pairs and involute evolute curve pair; Bertrand curve pair and Mannheim curve pair.
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