COURSE UNIT TITLE

: ELECTIVE LLL DIFFERENTIAL GEOMETRY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
OMT 3021 ELECTIVE LLL DIFFERENTIAL GEOMETRY ELECTIVE 3 0 0 4

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR ŞUUR NIZAMOĞLU

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   To comprehent the main ideas of differential geometry of curves and surfaces.
2   To be able to find invariants of curves by applying Frenet Formulas.
3   To be able to evaluate curvatures of a surface by using shape operator
4   To be able use apply their advance calculus and linear algebra knowledge to explore geometry.
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 Vectors and vector fields in three dimensional space
2 Directional derivative, Differential forms
3 Maps between Euclidean space and their derivative maps, Dot product
4 Curves in the space, Change of parameter
5 Frenet formulas
6 Covariant derivative, Frame Fields
7 Connection forms
8 Midterm
9 Shape operator
10 Normal curvatures
11 Fundamental forms
12 Gaussian and mean curvatures
13 Special curves on a surface
14 Gauss map, Rotational surfaces, ruled surfaces
15 Final Exam

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; Diferansiyel Geometri, Inönü Üniversitesi, Fen-Ed. Fakültesi Yayınları, No:2,

Planned Learning Activities and Teaching Methods

Lecture, discussion, question-answer, problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FINS FINAL EXAM
3 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 +FINS * 0.60
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST* 0.60

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)

suur.noglu@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Preparation for midterm exam 1 10 10
Preparation for final exam 1 15 15
Preparations before/after weekly lectures 13 2 26
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 107

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15PO.16PO.17PO.18
LO.1553
LO.2553
LO.3553
LO.4553
LO.55

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

Copyright 2012 DEÜ. BİD

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