Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

Person Responsible for Information Package

Prof. Adnan MELEKOĞLU

Prof. Hülya İNCEBOZ

Prof. İnci EGE

Prof. Semra DOĞRUÖZ

Assoc. Prof. Berna ARSLAN

Assoc. Prof. Emrah YILDIRIM

Assoc. Prof. Korhan GÜNEL

Ins. Nihal GÜNEL

Lec. Ahmet GENÇ

Lec. Dilek AÇIKGÖZ KAYA

Lec. Erdal ÖZYURT

Lec. Muhammet Ali OKUR

Lec. Okan ARSLAN

Lec. Rıfat AŞLIYAN

Lec. Sibel KOÇER

Res. Assist. İclal GÖR

Res. Assist. Mehmet Soner PEHLİVAN

Curves and Surfaces

Course Code	: MAT455
Course Type	: Area Elective
Couse Group	: First Cycle (Bachelor's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 6

Objectives of the Course

The purpose of this course is to learn some theories and applications of differential geometry and also the main theories of the differential geometry of curves and surfaces with using the basic concepts and the techniques of differential geometry.

Course Content

Basic Concepts, Differential Geometry of Curves, The Curvatures of a curve, Geometric Meaning of Curves, Surfaces, Some Examples About Surfaces, The Curvatures of a Surface.

Name of Lecturer(s)

Learning Outcomes

1.	Ability to learn the theories of curves
2.	Ability to do some applications with curves
3.	Ability to interpret curves geometrically
4.	Ability to understand the concept of the surface and the parameters
5.	Ability to calculate the curvatures of a surface

Recommended or Required Reading

1.	Pressley, A., Elemetary Differential Geometry
2.	Ekici, C., Eğrilerin ve Yüzeylerin Diferensiyel Geometrisi
3.	Montiel S., Ros A., Curves and Surfaces
4.	O’Neil, B., Elementary Differential Geometry

Weekly Detailed Course Contents

Week 1 - Theoretical

Curves

Week 2 - Theoretical

Arc Length, Curves Parametrized by Arc Lenght

Week 3 - Theoretical

The Curvatures of a Curve

Week 4 - Theoretical

Plane and Space Curves

Week 5 - Theoretical

Surfaces

Week 6 - Theoretical

Smooth Surfaces and Smooth Maps

Week 7 - Theoretical

The Tangents, The Differantiations, Normals and Orientation

Week 8 - Theoretical

Some Examples of Surfaces (MIDTERM EXAM)

Week 9 - Theoretical

Arc Length of A Curve on a Surface, I. Fundamental Form

Week 10 - Theoretical

The Curvature of a Surface, II. Fundamental Form

Week 11 - Theoretical

Gauss and Weingarten Maps

Week 12 - Theoretical

Normal and Geodesic Curvatures

Week 13 - Theoretical

Covariant Derivative

Week 14 - Theoretical

Gauss Curvature and The Mean Curvature

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Assignment	1	%5
Term Assignment	1	%5
Midterm Examination	1	%30
Final Examination	1	%60

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	0	3	42
Assignment	1	0	5	5
Term Project	1	0	9	9
Individual Work	14	0	4	56
Midterm Examination	1	16	2	18
Final Examination	1	18	2	20
TOTAL WORKLOAD (hours)				150

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12	PÇ-13	PÇ-14	PÇ-15	PÇ-16	PÇ-17	PÇ-18
OÇ-1	3	2	3	4		2	2			2	2				2
OÇ-2	3	4	4	3	4	4	3		3	4	2	3			4
OÇ-3	3	3	4	4						3
OÇ-4	4		4	3	3	4	4			4	3				5
OÇ-5	4	4	4	4	3	4	4		4	3		2	2	3	4