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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS LME 5001 DIFFERENTIAL GEOMETRY ELECTIVE 2 0 0 4

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR SÜHA YILMAZ

Offered to

Mathematics Teacher Education

Course Objective

To introduce some of the main ideas of differential geometry of curves and surfaces in 3-dimensional space, to reinforce their advanced calculus and linear algebra knowledge giving a good opportunity to exhibit their interplay through application to geometry.

Learning Outcomes of the Course Unit

1   1.To comprehent the main ideas of differential geometry of curves and surfaces. 2   2.To be able to find invariants of curves by applying Frenet Formulas. 3   3.To be able to evaluate curvatures of a surface by using shape operator 4   4.To be able use apply their advance calculus and linear algebra knowledge to explore geometry. 5   5.To be able use apply concepts and subjects of differential geometry to other disciplines and real life situations.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 1.WEEK:Three dimensional space vectors and vector fields 11.WEEK:Gauss and mean curvature functions, Meusnier Theorem. 2 2.WEEK:Directional derivative, Differential forms. 12.WEEK:Special curves on the surface. 3 3.WEEK :Transformations and derivative transformations between Euclidean spaces; Dot product. 13.WEEK:Gauss transformation, rotating surfaces. 4 4.WEEK:Curves in space; Parameter exchange. 14.WEEK:Regle surfaces. 5 5.WEEK:Serret-Frenet formulas. 15.WEEK:Final exam. 6 6.WEEK:Covariant derivative; Roof areas, vineyard forms.Covariant derivative; Roof areas, vineyard forms. 7 7.WEEK:Shape operator 8 8.WEEK:Course overview,evaluation,Midterm examination. 9 9.WEEK:Normal curvatures 10 10.WEEK:Main forms

Recomended or Required Reading

O'Neill, B. 1966; Elementary Differential Geometry, Academic Press, New York and London Gray, A. 1999; Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press Hacısalihoğlu, H.H. 1983; Differential Geometry, Inönü University, Science-Ed. Faculty Publications, No: 2,

Planned Learning Activities and Teaching Methods

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Midterm 2 FN Semester final exam 3 BNS BNS Student examVZ * 0.40 + Student examFN * 0.60 4 BUT Make-up note 5 BBN End of make-up grade Student examVZ * 0.40 + Student examBUT * 0.60 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

Prof.Dr.Süha Yılmaz Tel:02323012335 email:suha.yilmaz@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 7 1 Field Study 9 1 Group session 5 1 Procedural skills practice 5 1 Preparations before/after weekly lectures 13 3 Preparation for midterm exam 10 2 Preparation for midterm exam 10 2 Final 1 1 Midterm 1 1 TOTAL WORKLOAD (hours) 0

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 PO.14 PO.15 PO.16 PO.17 PO.18 LO.1 5 4 2 3 1 1 2 LO.2 5 4 2 3 1 1 2 LO.3 5 4 2 3 1 2 LO.4 5 4 5 3 1 2 LO.5 5 4 5 3 1 2