Applied Mathematics (MATH463) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Applied Mathematics	MATH463		4	0	0	4	8

Pre-requisite Course(s)
Math 262 Ordinary Differential Equations

Course Language	English
Course Type	N/A
Course Level	Bachelor’s Degree (First Cycle)
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Discussion, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	The course is divided into two parts: Integral Equations and Calculus of Variations. In the first part, the course aims to present the basic elements of the calculus of variations. The approach is oriented towards the differential equation aspects. We will focus on variational problems that involve one and two independent variables. The fixed end-point problem and problems with constraints will be discussed in detail. Topics will also include Euler-Lagrange equation, the first and second variations, necessary and suffcient conditions for extrema, Hamilton's principle, and application to Sturm-Liouville problems and mechanics. In the second part, the course aims to introduce student the integral equations and their connections with initial and boundary value problems of differential equations. Topics will include mainly Fredholm and Volterra integral equations, the Green’s function, Hilbert-Schimidt theory, the Neumann series and Fredholm theory.
Course Learning Outcomes	The students who succeeded in this course; At the end of the course the students are expected to: 1- students are expected to know and understand various ideas, concepts and methods from applied mathematics and how these ideas may be used in, or are connected to, the fields of engineering and mathematics. 2 students will be able to apply various methods to solve a range of problems from applied mathematics and engineering - including: Integral equations, Green’s function and Calculus of Variations.
Course Content	Calculus of variations and applications, integral equations and applications.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	1. Week Maxima and minima of one variable and multivariable functions. The subject of calculus of variations. 2. Week The simplest case of variational problems. Necessary condition for the existence of an extremum: the Euler equation. Extremals. 3. Week Natural boundary conditions and transition conditions. Function spaces and functionals. 4. Week The concept of variation of functionals. A case of integrals depending on functions of two variables. 5. Week The more general case of variational problems. Variational problems with variable endpoints. 6. Week Application to Sturm-Liouville problems. Application to mechanics: Hamilton’s principle, Langrange’s equations, Hamilton’s canonical equations. 7. Week Basic Definitions.Fredholm and Volterra integral equations. 8. Week Midterm Exam 9. Week Relations between differential and integral equations. 10. Week The Green’s function. 11. Week Fredholm equations with separable kernels. 12. Week Hilbert-Schimidt theory. 13. Week Iterative methods for solving an integral equation of second kind. The Neumann series. 14. Week Fredholm theory.Singular integral equations. Special devices for solving some integral equations. 15. Week Methods for obtaining approximate solutions of integral equations. 16. Week Final Exam

Sources

Course Book	1. F. B. Hildebrand, Methods of Applied Mathematics, 2nd Edition, 1965, Prentice – Hall, Englewood Cliffs.
Other Sources	2. 1] I. M. Gelfand and S. V. Fomin, Calculus of Variations, 1963, Prentice – Hall, Englewood Cliffs. [2] W. V. Lovitt, Linear Integral Equations, 1924, McGraw – Hill, New York.

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	-	-
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	60
Final Exam/Final Jury	1	40
Toplam	3	100

Percentage of Semester Work
Percentage of Final Work	100
Total	100

Course Category

Core Courses	X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Acquiring the skills of understanding, explaining, and using the fundamental concepts and methods of economics
2	Acquiring the skills of macro level economic analysis
3	Acquiring the skills of micro level economic analysis
4	Understanding the formulation and implementation of economic policies at the local, national, regional, and/or global level
5	Learning different approaches on economic and related issues
6	Acquiring the quantitative and/or qualitative techniques in economic analysis					X
7	Improving the ability to use the modern software, hardware and/or technological devices
8	Developing intra-disciplinary and inter-disciplinary team work skills					X
9	Acquiring an open-minded behavior through encouraging critical analysis, discussions, and/or life-long learning
10	Adopting work ethic and social responsibility
11	Developing the skills of communication.
12	Improving the ability to effectively implement the knowledge and skills in at least one of the following areas: economic policy, public policy, international economic relations, industrial relations, monetary and financial affairs.			X

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	16	3	48
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	25	50
Prepration of Final Exams/Final Jury	1	35	35
Total Workload			133