Mathematics (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH372

Course Name:

Differential Geometry

Semester:

Spring

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Araş. Gör. GAMZE AKAR UYSAL

Course Lecturer(s):

Prof. Dr. Selçuk Demir

Course Assistants:

Course Objective and Content

Course Objectives:	The course aims to introduce the concepts of differential geometry and to study the curves and surfaces in 3 dimensional Euclidean space.
Course Content:	The content of the course consists concepts and methods of differential geometry and some significant results related to curves and surfaces in 3 dimensional eulidean space.

Learning Outcomes

The students who have succeeded in this course;
1) will be able to do calculus on Euclidean spaces,
2) will be able to understand notions of tangent vector, directional derivative, vector field, differential forms, and geometric transformations.
3) will be able to understand the notions of the curvature and torsion of a curve in 3 dimensional Euclidean space.
4) will be able to know the basic concepts of surfaces and will be able to do calculus on surfaces.

Course Flow Plan

Week	Subject	Related Preparation
1)	Euclidean space, tangent vectors, directional derivative, vector fields.
2)	The curves in 3 dimensional Euclidean space, velocity, acceleration.
3)	1-forms, differential forms, differential operator d, wedge product.
4)	Mappings, derivative map, the Jacobian matrix.
5)	The curves, speed function, arc length, reparametrizations, vector fields on curves.
6)	The Frenet formulas for unit speed curves, the curvature and the torsion.
7)	Circular, spherical, planar curves. Curvature center and the curvature radius.
8)	Midterm Exam
9)	The arbitrary speed curves. The velocity, the acceleration and their geometric interpretations.
10)	The Frenet formulas for arbitrary speed curves. Spherical image curve.
11)	The cylindrical helix. The classification of curves by their curvatures and torsions.
12)	Calculus on surfaces. The definition of a surface. Patches.
13)	Proper patches. Monge patches. The surfaces given by the implicit functions.
14)	Cylinders, spheres, and surface of revolutions.

Sources

Course Notes / Textbooks:	ders notları
References:	B. O'Neill, Elementary Differential Geometry, Academic Press.

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.	2
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4)	Have the ability to think analytically and use the time effectively in the process of deduction.	3
5)	Have the ability to search the literature, understand and interpret scientific articles.
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.	3
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.	3

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Application	13	0			0
Study Hours Out of Class	13	0	3		39
Midterms	1	0	15		15
Final	1	0	25		25
Total Workload					118