CANKIRI KARATEKIN UNIVERSITY
Bologna Information System


  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    INTRODUCTION TO DIFFERANTIAL GEOMETRY MAT307 FALL 4+0 C 6
    Learning Outcomes
    1-To describe the relationship between vector and directional derivative
    2-To explain the concepts of vector field
    3-To explain basic notions of curves
  • ECTS / WORKLOAD
  • ActivityPercentage

    (100)

    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14456
    Classroom study (Pre-study, practice)14570
    Assignments102612
    Short-Term Exams (exam + preparation) 102612
    Midterm exams (exam + preparation)3011414
    Project0000
    Laboratory 0000
    Final exam (exam + preparation) 5011616
    Other 0000
    Total Workload (hours)   180
    Total Workload (hours) / 30 (s)     6 ---- (6)
    ECTS Credit   6
  • Course Content
  • Week Topics Study Metarials
    1 Affine space
    2 Euclidean space, Euclidean frame and coordination system
    3 Topolojic space, Metric space and relationship between E^n
    4 Differentiable functions
    5 Tangent plane and directional derivative
    6 Vector field
    7 The derivative transformation
    8 The definition of a curve and its parametric representations; velocity vector and its length, unit-speed curves
    9 Vector field along a curve
    10 Covariant derivative in the Euclidean space
    11 Serret-Frenet formulas of unit speed curves; curvatures and geometric comments
    12 Touching theory
    13 Serret- Frenet formulas of non-unit-speed curves
    14 Involute -Evolute, Bertnard curve pair and spherical indicatrix of a curve
    Prerequisites -
    Language of Instruction Turkish
    Course Coordinator Assist. Prof. Dr. Celallettin Kaya
    Instructors

    1-)Ufuk Öztürk

    Assistants -
    Resources Diferensiyel Geometri (4. Baskı), Arif Sabuncuoğlu, Nobel Akademik Yayıncılık, 2010.
    Supplementary Book [1] Çözümlü Diferensiyel Geometri Alıştırmaları (2. Baskı), Arif Sabuncuoğlu, Nobel Akademik Yayıncılık, 2012. [2] Diferansiyel Geometri : Eğriler ve Yüzeyler, P. Do. Carmo Manfredo, Çeviren : Belgin Korkmaz, TÜBA Ders Kitapları Dizisi, Sayı : 8, 2012. [3] Diferensiyel Geometri Cilt : 1 (3. Baskı), H.Hilmi Hacısalihoğlu, Hacısalihoğlu Yayınları, Anakara, 1998. [4] Çözümlü Diferensiyel Geometri Problemleri Cilt : 1 (2. Baskı), H.Hilmi Hacısalihoğlu, Ertuğrul Özdamar, Cengizhan Murathan, Esen İyigün, Hacısalihoğlu Yayınları, Anakara, 2005 [5] A First Course in Geometric Topology and Differential Geometry, Ethan D. Block, Birkhauser, Boston, 1996. [6] Elementary Differential Geometry (Springer Undergraduate Mathematics Series) (2nd Edition), Andrew Pressley, Springer-Verlag, London, 2010.
    Document Lecture notes
    Goals To teach the basic notions and theorems of curves and surfaces in R^3
    Content -
  • Program Learning Outcomes
  • Program Learning Outcomes Level of Contribution
    1 To have a grasp of theoretical and applied knowledge in main fields of mathematics 5
    2 To have the ability of abstract thinking 4
    3 To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps 5
    4 To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life 3
    5 To have the qualification of studying independently in a problem or a project requiring mathematical knowledge 3
    6 To be able to work compatibly and effectively in national and international groups and take responsibility -
    7 To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge 4
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge 4
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time 2
    10 To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally 4
    11 To be able to produce projects and arrange activities with awareness of social responsibility -
    12 To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level -
    13 To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results -
    14 To have the awareness of acting compatible with social, scientific, cultural and ethical values -
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