ECTS - Applied Mathematics
Applied Mathematics (MATH463) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Applied Mathematics | MATH463 | Elective Courses | 4 | 0 | 0 | 4 | 8 |
| Pre-requisite Course(s) |
|---|
| MATH262 |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| 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 Lecturer(s) |
|
| 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;
|
| 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 | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | 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 | ||