Information Package / Course Catalogue - Adnan Menderes University

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

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Differential Geometry I

Course Code	: MAT328
Course Type	: Required
Couse Group	: First Cycle (Bachelor's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 2
Prt.	: 2
Credit	: 3
Lab	: 0
ECTS	: 6

Objectives of the Course

The fundamental knowledges that are needed during students undergraduate and graduate education on differential geometry are taught.

Course Content

Euclidean space, differentiable functions, directional derivative , tangent map, vector fields, cotangent vector fields, covariant derivative, curves , Frenet vector fields.

Name of Lecturer(s)

Lec. Dilek AÇIKGÖZ KAYA

Learning Outcomes

1.	To be able to define basic concepts of differential geometry
2.	To be able to apply derivatives, directional derivatives and the tangent map using the concepts of differentiable functions.
3.	To be able to explain vector fields and 1-forms and perform basic operations on these structures.
4.	To be able to compute the gradient, divergence, and curl of a vector field and interpret their geometric and physical meanings.
5.	To be able to understand curves and the fundamental concepts related to curves
6.	To be able to calculate the Frenet frames of a curve

Recommended or Required Reading

1.	Eğrilerin ve Yüzeylerin Diferensiyel Geometrisi, Prof. Dr. Cumali Ekici
2.	Elementary Differential Geometry, Barret O’Neill
3.	Diferansiyel Geometri(Differential Geometry), Prof Dr. Arif Sabuncuoğlu

Weekly Detailed Course Contents

Week 1 - Theoretical & Practice

Affine space and Euclidean Space

Week 2 - Theoretical & Practice

Differentiable functions

Week 3 - Theoretical & Practice

Tangent vectors and tangent space

Week 4 - Theoretical & Practice

Directional derivatives and tangent map

Week 5 - Theoretical & Practice

Tangent map

Week 6 - Theoretical & Practice

Vector fields

Week 7 - Theoretical & Practice

Gradient, divergence, rotational function

Week 8 - Theoretical & Practice

Lie operator(Midterm Exam)

Week 9 - Theoretical & Practice

1-forms

Week 10 - Theoretical & Practice

Curves, tangent space at a point on the curve, velocity vector of a curve, reparametrization

Week 11 - Theoretical & Practice

Covariant derivative

Week 12 - Theoretical & Practice

Serret-Frenet vectors

Week 13 - Theoretical & Practice

Curvature and torsion of a curve

Week 14 - Theoretical & Practice

The circle of curvature, the sphere of curvature,

Week 15 - Theoretical & Practice

Serret-Frenet frame for arbitrary speed curves

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Midterm Examination	1	%40
Final Examination	1	%60

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	0	2	28
Lecture - Practice	14	0	2	28
Reading	14	2	1	42
Individual Work	14	0	2	28
Midterm Examination	1	7	2	9
Final Examination	1	13	2	15
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	5		3		5				5	3		5	5
OÇ-2	5		3		5				5	3		5	5
OÇ-3
OÇ-4	5		3		5				5	3		5	5
OÇ-5	5		3		5				5	3		5	5
OÇ-6

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