PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
MAT 576	APPLIED DIFFERENTIAL GEOMETRY-I	3 + 0	2nd Semester	7,5

COURSE DESCRIPTION

Course Level	Master's Degree
Course Type	Elective
Course Objective	Teaching of various curved structures and their computer modeling.
Course Content	Curvatures in Euclid Space, Arclength parametrization, Frenet formulas, unit speed-nonunit speed Curvatures, Curvature and Torsion, plotting Curvatures in MAPLE, Surfaces, Linear Algebra on Surfaces, normal Curvature, plotting Surfaces in MAPLE, Curvatures, calculating Curvatures, Gaus Curvature, the properties of Curvature, calculating Curvatures with MAPLE, Curvatures on minimal Surfaces, harmonic functions, Constant Mean Curvature.
Prerequisites	No the prerequisite of lesson.
Corequisite	No the corequisite of lesson.

COURSE LEARNING OUTCOMES

1	Learns the Curvatures in Euclid Space, Arclength parametrization, Frenet formulas, unit speed-nonunit speed Curvatures, Curvature and Torsion, Knows the plotting Curvatures in MAPLE.
2	Knows the Surfaces, Linear Algebra on Surfaces, normal Curvature, plotting Surfaces in MAPLE.
3	Identifies the Curvatures, calculating Curvatures, Gaus Curvature, the properties of Curvature, can make calculating Curvatures with MAPLE.
4	Knows the Curvatures on minimal Surfaces, harmonic functions, Constant Mean Curvature.

COURSE'S CONTRIBUTION TO PROGRAM

	PO 01	PO 02	PO 03	PO 04	PO 05	PO 06	PO 07	PO 08
LO 001	4		4	5			5	4
LO 002	5		5				4	4
LO 003	4			4			4	5
LO 004	4		5	5			4	4
Sub Total	17		14	14			17	17
Contribution	4	0	4	4	0	0	4	4

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities	Quantity	Duration (Hour)	Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	7	98
Assignments	1	5	5
Mid-terms	1	15	15
Final examination	1	35	35
Total Work Load ECTS Credit of the Course			195 7,5

COURSE DETAILS

Select Year

	Course Term	No	Instructors
Details	2025-2026 Fall	1	CANSEL AYCAN ÖZDEMİR

Course Details

Course Code	Course Title	L+P Hour	Course Code	Language Of Instruction	Course Semester	Mode of Delivery
MAT 576	APPLIED DIFFERENTIAL GEOMETRY-I	3 + 0	1	Turkish	2025-2026 Fall	Face to Face

Course Coordinator	E-Mail	Phone Number	Course Location	Attendance
Prof. Dr. CANSEL AYCAN ÖZDEMİR	c_aycan@pau.edu.tr		FEN B0318	%

Goals		Teaching of various curved structures and their computer modeling.
Content		Curvatures in Euclid Space, Arclength parametrization, Frenet formulas, unit speed-nonunit speed Curvatures, Curvature and Torsion, plotting Curvatures in MAPLE, Surfaces, Linear Algebra on Surfaces, normal Curvature, plotting Surfaces in MAPLE, Curvatures, calculating Curvatures, Gaus Curvature, the properties of Curvature, calculating Curvatures with MAPLE, Curvatures on minimal Surfaces, harmonic functions, Constant Mean Curvature.

Topics

Weeks	Topics
1	topological manifolds
2	differentiable manifolds
3	product and quotient manifoldscotangent space, covector, 1-forms
4	tangent vectors and tangent space, lie algebra and lie bracket
5	tensors and tensor algebra
6	covariant, contravariant and mixed tensors
7	middterm exam
8	Riemannian metric and Riemannian manifolds
9	Complex manifolds and properties
10	frenet vectors, torsions and curvatures
11	surfaces theory and their properties
12	jeodesics,metrics and isometries
13	computer programming of curves and surfaces
14	final exam

Materials

Materials are not specified.

Resources

Resources	Resources Language
yüksek diferensiyel geometriye giriş, H.H. Hacısalihoğlu	Türkçe

Course Assessment

Assesment Methods	Percentage (%)	Assesment Methods Title
Final Exam	50	Final Exam
Midterm Exam	50	Midterm Exam

L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes

Prospective Student