ECTS - Mathematical Methods in Physics
Mathematical Methods in Physics (PHYS503) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematical Methods in Physics | PHYS503 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture. |
| Course Lecturer(s) |
|
| Course Objectives | The main objective of this course is to familiarize students with some mathematical methods which are important for solving advanced problems in theoretical physics. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Functions of complex variables, Cauchy?s integral theorem, differential equations, Sturm-Liouville theory, Bessel functions, Legendre functions, special functions. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Complex Algebra, Cauchy-Riemann Conditions | Chapter 6 |
| 2 | Cauchy’s Integral Theorem Cauchy’s Integral Formula | Chapter 6 |
| 3 | Laurent Expansion Mapping | Chapter 6 |
| 4 | Singularities Calculus of Residues | Chapter 7 |
| 5 | Calculus of Residues Dispersion Relations | Chapter 7 |
| 6 | Partial Differential Equations First-Order Differential Equations Separation of Variables | Chapter 8 |
| 7 | Singular points Series Solutions – Frobenius’s Method | Chapter 8 |
| 8 | A Second Solution Nonhomogeneous Equation – Green’s Function Numerical Solutions | Chapter 8 |
| 9 | Midterm | |
| 10 | Self-Adjoint ODEs Hermitian Operators | Chapter 9 |
| 11 | Gram-Schmidt Orthogonalization Completeness of Eigenfunctions Green’s Function – Eigenfunction Expansion | Chapter 9 |
| 12 | Bessel Functions of the First Kind Jv (x) Orthogonality Neumann Functions, Bessel Functions of the Second Kind | Chapter 11 |
| 13 | Hankel Functions Modified Bessel Functions Iv(x) and Kv(x) Asymptotic Expansions Spherical Bessel Functions | Chapter 11 |
| 14 | Generating Function Recurrence Relations Orthogonality Associated Legendre Functions | Chapter 12 |
| 15 | Hermite Functions Laguerre Functions | Chapter 12 |
| 16 | Final Exam |
Sources
| Course Book | 1. George B. Arfken, Mathematical Methods for Physicists, Academis Press, 5th Edition |
|---|---|
| Other Sources | 2. HILDEBRAND F.B., Advanced Calculus for Applications, Prentice-Hall Inc. (1976) |
| 3. Brown J. W., Churchill R. V., Complex Variables and Applications, CGraw-Hill (1996) | |
| 4. BAYIN S., Mathematical Methods in Science and Engineering, Wiley-Interscience (2006) |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 6 | 40 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 25 |
| Final Exam/Final Jury | 1 | 35 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | 65 |
|---|---|
| Percentage of Final Work | 35 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | X |
| 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 | Acquiring core knowledge of theoretical and mathematical physics together with their research methodologies. | X | ||||
| 2 | Gaining a solid understanding of the physical universe together with the laws governing it. | X | ||||
| 3 | Developing a working research skill and strategies of problem solving skills in theoretical, experimental, and/or simulation physics. | X | ||||
| 4 | Developing and maintaining a positive attitude toward critical questioning, creative thinking, and formulating new ideas both conceptually and mathematically. | X | ||||
| 5 | Ability to sense, identify, and handle the problems in theoretical, experimental, or applied physics, or in real-life industrial problems. | X | ||||
| 6 | Ability to apply the accumulated knowledge in constructing mathematical models, determining a strategy for its solution, making necessary and appropriate approximations, evaluating and assessing the correctness and reliability of the procured solution. | X | ||||
| 7 | Ability to communicate and discuss physical concepts, processes, and the newly obtained results with the colleagues all around the world both verbally and in written form as proceedings and research papers. | X | ||||
| 8 | Reaching and excelling an advanced level of knowledge and skills in one or more of the disciplines offered. | X | ||||
| 9 | An ability to produce, report and present an original or known scientific body of knowledge. | X | ||||
| 10 | An ability to make methodological scientific research. | X | ||||
| 11 | An ability to use existing physics knowledge to analyze, to determine a methodology of solution (theoretical/mathematical/experimental) and to solve a problem. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 2 | 28 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 6 | 4 | 24 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 10 | 10 |
| Prepration of Final Exams/Final Jury | 1 | 15 | 15 |
| Total Workload | 125 | ||