COURSE UNIT TITLE

: DIFFERENTIAL GEOMETRY

DEGREE PROGRAMMES

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

The aim of this course is 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 be able to comprehend 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
2 2.WEEK:Directional derivative, Differential forms.
3 3.WEEK :Transformations and derivative transformations between Euclidean spaces; Dot product.
4 4.WEEK:Curves in space; Parameter exchange.
5 5.WEEK:Serret-Frenet formulas.
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
11 11.WEEK:Gauss and mean curvature functions, Meusnier Theorem.
12 12.WEEK:Special curves on the surface.
13 13.WEEK:Gauss transformation, rotating surfaces.
14 14.WEEK:Regle surfaces.
15 15.WEEK: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; Differential Geometry, Inönü University, Science-Ed. Faculty Publications, No: 2,

Planned Learning Activities and Teaching Methods

Lecture, Question-answer

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,Hasan Ali Yücel Building,420 Room.
Tel:02323012335
email:suha.yilmaz@deu.edu.tr

Office Hours

Wednesday,16:00.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 2 26
Preparations before/after weekly lectures 13 2 26
Preparation for midterm exam 1 15 15
Preparation for midterm exam 1 20 20
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 91

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.15423112
LO.25423112
LO.3542312
LO.4545312
LO.5545312

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

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