CANKIRI KARATEKIN UNIVERSITY
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  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    COMPLEX ANALYSIS II MAT302 SPRING 4+0 Fac./ Uni. C 8
    Learning Outcomes
    1-To be able to describe the relationship between vector and directional derivative
    2-To be able to explain the concepts of vector field and cotangent vector field
    3-To be able to explain basic notions of curves
    4-To be able to explain basic notions of surfaces
  • ECTS / WORKLOAD
  • ActivityPercentage

    (100)

    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14456
    Classroom study (Pre-study, practice)148112
    Assignments102816
    Short-Term Exams (exam + preparation) 102816
    Midterm exams (exam + preparation)3011212
    Project0000
    Laboratory 0000
    Final exam (exam + preparation) 5011616
    Other 0000
    Total Workload (hours)   228
    Total Workload (hours) / 30 (s)     7,6 ---- (8)
    ECTS Credit   8
  • Course Content
  • Week Topics Study Metarials
    1 Tangent plane and directional derivative
    2 Differential of a map
    3 Vector field and cotangent vector field
    4 The definition of a curve and its parametric representations; velocity vector and its length, unit-speed curves
    5 The derivative of a vector field along a curve
    6 Covariant derivative in the Euclidean space
    7 Tangent, normal, and binormal vectors; the notion of curvature and its geometric interpretation
    8 Osculating, rectifying, and normal planes; the notion of torsion and its geometric interpretation
    9 Non-unit-speed curves; the fundamental theorem of curves
    10 The definition and examples of surface; Monge surface and the notion of regular value
    11 The parametric curves on a surface; normal vector and tangent space of a surface
    12 Smooth functions on a surface and directional derivative
    13 A vector field on a surface
    14 Covariant derivative on a surface
    Prerequisites -
    Language of Instruction Turkish
    Course Coordinator Assist. Prof. Dr. Süleyman CENGİZ
    Instructors -
    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. Diferensiyel Geometri Cilt : 2 (3. Baskı), H.Hilmi Hacısalihoğlu, Hacısalihoğlu Yayınları, Anakara, 2000 5. Çözümlü Diferensiyel Geometri Problemleri Cilt : 1 (2. Baskı), H.Hilmi Hacısalihoğlu, Ertuğrul Özdamar, Cengizhan Murathan, Esen İyigün, Hacısalihoğlu Yayınları, Anakara, 2005 6. Çözümlü Diferensiyel Geometri Problemleri Cilt : 2, H.Hilmi Hacısalihoğlu, Yusuf Yaylı, Nejat Ekmekçi, Cengizhan Murathan, Ertuğrul Özdamar, Hacısalihoğlu Yayınları, Anakara, 1996 7. A First Course in Geometric Topology and Differential Geometry, Ethan D. Block, Birkhauser, Boston, 1996 8. Elementary Differential Geometry (Springer Undergraduate Mathematics Series) (2nd Edition), Andrew Pressley, Springer-Verlag, London, 2010
    Document -
    Goals To teach the basic notions and theorems of curves and surfaces in R^3, to consolidate and to relate basic knowledge learned in analysis and linear algebra courses by applying them to geometry
    Content Tangent plane and directional derivative; Differential of a map; Vector field and cotangent vector field; The definition of a curve and its parametric representations; Velocity vector and its length, unit-speed curves; The derivative of a vector field along a curve; Covariant derivative in the Euclidean space; Tangent, normal, and binormal vectors; The notion of curvature and its geometric interpretation; Osculating, rectifying, and normal planes; The notion of torsion and its geometric interpretation; Non-unit-speed curves; The fundamental theorem of curves; The definition and examples of surface; Monge surface and the notion of regular value; The parametric curves on a surface; Normal vector and tangent space of a surface; Smooth functions on a surface and directional derivative; A vector field on a surface; Covariant derivative on a surface
  • 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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