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 3 0 0 3 5
Pre-requisite Course(s)
N/A
Course Language English
Course Type N/A
Course Level Natural & Applied Sciences Master's Degree
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture.
Course Coordinator
Course Lecturer(s)
  • Asst. Prof. Dr. Mehmet Işık
Course Assistants
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;
  • To understand and apply differential and integral calculations of complex functions
  • To understans and solve partial and first order differential equations
  • To understand and apply Frobenius method
  • To understand the properties of Bessel function and apply this function in physics
  • To understand the properties of Legendre function and apply this function in physics
  • To understand the properties of Hermite and Laguerre functions and apply this function in physics
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