PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
MAT 606	MATHEMATICAL ANALYSIS	3 + 0	1st Semester	7,5

COURSE DESCRIPTION

Course Level	Master's Degree
Course Type	Compulsory
Course Objective	To examine differential and integral calculus in n-dimensional Euclidean space and to introduce basic analysis concepts on manifolds.
Course Content	R^n space topology, concept of compactness, continuous functions and differentiation, Riemann integral and differential forms in R^n , inverse and implict functions theorem, Stokes theorem for integral and differential forms on manifolds.
Prerequisites	No the prerequisite of lesson.
Corequisite	No the corequisite of lesson.

COURSE LEARNING OUTCOMES

1	Knows linear, inner product and normed linear spaces.
2	Learns the topological structure of R^n space.
3	Learns the concepts of compactness and convergence in R^n space.
4	Understands the differentiation and differential concepts in R^n space.
5	Knows the Riemann integral and the Lebesgue Theorem.
6	Calculates applications of multiple integrals.
7	Knows the vector fields on the manifold.
8	Applies the Stokes theorem on the manifold.
9	Calculates line and surface integrals.

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			5		5
LO 002		4		5	4	4
LO 003	5				4		4	4
LO 004		4		4		4
LO 005	5		4	5	4
LO 006		4			5	5
LO 007	4	5			5
LO 008	5				4		5	5
LO 009		4	4	4
Sub Total	23	21	13	18	26	18	9	14
Contribution	3	2	1	2	3	2	1	2

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	İSMAİL YASLAN

Course Details

Course Code	Course Title	L+P Hour	Course Code	Language Of Instruction	Course Semester	Mode of Delivery
MAT 606	MATHEMATICAL ANALYSIS	3 + 0	1	Turkish	2025-2026 Fall	Face to Face

Course Coordinator	E-Mail	Phone Number	Course Location	Attendance
Prof. Dr. İSMAİL YASLAN	iyaslan@pau.edu.tr		FEN A0316	%

Goals		To examine differential and integral calculus in n-dimensional Euclidean space and to introduce basic analysis concepts on manifolds.
Content		R^n space topology, concept of compactness, continuous functions and differentiation, Riemann integral and differential forms in R^n , inverse and implict functions theorem, Stokes theorem for integral and differential forms on manifolds.

Topics

Materials

Materials are not specified.

Resources

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