PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
MAT 559	APPLIED DIFFERENTIAL GEOMETRY II	3 + 0	1st Semester	7,5

COURSE DESCRIPTION

Course Level	Master's Degree
Course Type	Elective
Course Objective	Teaching of computer modeling and simulation of mechanical systems.
Course Content	Minimal Surfaces and Modeling of Minimal Surface’s Properties with Computer Programming, Isothermal Coordinates and Applications, Björling Problem and Computer Applications, Manifolds, Covariant Derivatives, Cristoffel Symbols, Curvatures and Computer Applications, Mechanical Systems and Computer Applications of Mechanical Systems.
Prerequisites	No the prerequisite of lesson.
Corequisite	No the corequisite of lesson.

COURSE LEARNING OUTCOMES

1	Identifies the Minimal Surfaces and Modeling of Minimal Surface’s Properties with Computer Programming.
2	Learns the Isothermal Coordinates and Applications, Björling Problem and Computer Applications.
3	Knows the Manifolds, Covariant Derivatives, Cristoffel Symbols, Curvatures and Computer Applications.
4	Realizes the Mechanical Systems and Computer Applications of Mechanical Systems.

COURSE'S CONTRIBUTION TO PROGRAM

	PO 01	PO 02	PO 03	PO 04	PO 05	PO 06	PO 07	PO 08
LO 001	4			5				4
LO 002	5		4	4				5
LO 003	4		5	4				4
LO 004	5		4	5				5
Sub Total	18		13	18				18
Contribution	5	0	3	5	0	0	0	5

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
Final examination	1	35	35
Midterm	1	15	15
Total Work Load ECTS Credit of the Course			195 7,5

COURSE DETAILS

Select Year

Course Details

Course Code	Course Title	L+P Hour	Course Code	Language Of Instruction	Course Semester	Mode of Delivery
MAT 559	APPLIED DIFFERENTIAL GEOMETRY II	3 + 0	1	Turkish	2025-2026 Spring	Face to Face

Course Coordinator	E-Mail	Phone Number	Course Location	Attendance
Prof. Dr. CANSEL AYCAN ÖZDEMİR	c_aycan@pau.edu.tr		FEN B0318	%70

Goals		Teaching of computer modeling and simulation of mechanical systems.
Content		Minimal Surfaces and Modeling of Minimal Surface’s Properties with Computer Programming, Isothermal Coordinates and Applications, Björling Problem and Computer Applications, Manifolds, Covariant Derivatives, Cristoffel Symbols, Curvatures and Computer Applications, Mechanical Systems and Computer Applications of Mechanical Systems.

Topics

Weeks	Topics
1	structure of manifold
2	system of frenets
3	frenet roofs
4	curvatures
5	tensors
6	christoffel symbols
7	mechanical systems
8	applications of mechanical systems
9	midterm exam
10	jet manifolds
11	jet bundles and its applications
12	minimal surfaces
13	trend lines, curvatures
14	fınal 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