MATH 410 | Course Introduction and Application Information - Department of Mathematics

Course Name

Linear Integral Equations

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 410	Fall/Spring	3	0	3	6

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	First Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	-
National Occupation Classification	-
Course Coordinator	-
Course Lecturer(s)	Dr. Öğr. Üyesi JAMİLA KALANTAROVA
Assistant(s)	Araş. Gör. Gökçe ÖZALTUN Araş. Gör. Ayşe BELER

Course Objectives

This course aims to provide solutions to common problems in applied mathematics, theoretical mechanics and mathematical physics.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	will be able to analyze integral operator and functional issues.
2	will be able to calculate Green functions, Fredholm and Volterra integral equations and variations.
3	will be able to analyze applied math problems.
4	will be able to solve ordinary and partial differential equations using Green's functions.
5	will be able to solve typical problems in linear integral equations and calculus of variations.

Course Description

In this course, basic issues of Green's functions will be discussed. Solution applications of ordinary differential equations, Fredholm and Volterra equations of 1st and 2nd type, separable kernel and Fredholm equations will be studied.

Course Category	Core Courses
	Major Area Courses
	Supportive Courses	X
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Definition of integral equation, Fredholm integral equations, singular integral equations, types of core function	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 1
2	Integral equations, Separable kernel, Fredholm alternative	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 1
3	An approximate method	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 2
4	Sequential approximation method	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 2
5	Volterra integral equation	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 3
6	Fredholm solution method	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 4
7	Fredholm's first theorem	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 4
8	Fredholm's second theorem	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 4
9	Fredholm's third theorem	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 5
10	Initial value problems	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 9
11	Boundary value problems	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 9
12	Green's function approximation	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 6
13	Applications to partial differential equations	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 9
14	Symmetrical kernels	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925 Chapter 10
15	Semester Review
16	Final Exam

Course Notes/Textbooks	“Linear Integral Equations” by Rainer Kress, Springer Verlag, 3rd Edition, 2014. ISBN-13: 978-1461495925
Suggested Readings/Materials	None

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5
Participation	-	-
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	2	60
Final Exam	1	40
Total

Weighting of Semester Activities on the Final Grade	2	60
Weighting of End-of-Semester Activities on the Final Grade	1	40
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	2	30	60
Final Exam	1	30	30
		Total	180

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.		-	-	-	-	X
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.		-	-	-	X	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.		-	X	-	-	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.		-	-	X	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.		-	-	-	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.		-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.		-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.		-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.		-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.		-	-	-	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.		-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.		-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.		-	-	-	-	-