# Mathematical Methods in Physics

Course Code:
PHYS 206
Course Type:
Area Elective
P:
3
Lab:
2
Laboratuvar Saati:
0
Credits:
4
ECTS:
7
Course Language:
English
Course Objectives:
The aim of this course is to give the students the necessary mathematical background for solving more complicated problems in various fields of physics, in later courses and in industry.
Course Content:

Coordinate systems, vector calculus, differentiation, integration, infinite series, analysis of vectors, tensors, complex analysis, partial differential equations, integral transforms, nonlinear dynamics and chaos, probability theory.

Course Methodology:
1: Lecture, 2: Question-Answer, 5: Problem Solving, 14: Laboratory ; 15:Homework
Course Evaluation Methods:
A: Testing, B: Final, I:Laboratory

## Vertical Tabs

### Course Learning Outcomes

 Learning Outcomes Teaching Methods Assessment Methods 1- Learns more advanced mathematical methods and principles to be used for more complicated problems in later courses or in real life. 1, 5, 15 A, B, C 2- Exhibits a mathematical approach to the interdisciplinary phenomena by using the insight gained in the course. 1, 5, 15 A, B, C

### Course Flow

 Week Topics Study Materials 1 Coordinate systems, vector calculus Coordinate transformations, unit vectors, dot product, cross product. 2 Differentiation, integration Derivative, chain rule, elements of length, 3 Area, volume in cartesian, spherical and cylindrical systems, Dirac delta function 4 Infinite series Taylor and Fourier series, 5 Gamma, beta and error functions MIDTERM EXAM - 1 6 Analysis of vectors, tensors Solid angle, gradient, curl, divergence, 7 Laplacian, line integral, Stokes’ theorem, tensor analysis, metric tensor, numerical tensors 8 Complex analysis Complex arithmetic, complex functions, calculus of residues, conformal mapping 9 Partial differential equations     Laplace’s equation and its applications in cartesian, spherical and cylindrical systems, 10 Heat conduction, quantum harmonic oscillator, vibrating membrane 11 Integral transforms     Fourier transform, Laplace transform, Green’s function MIDTERM EXAM - 2 12 Nonlinear dynamics and chaos Stable and unstable fixed points, logistic map, 13 population dynamics, onset of chaos, bifurcation 14 Probability theory Average and standard deviation, Binomial, Gaussian and Poisson distributions

### Recommended Sources

 Textbook MATHEMATICAL METHODS FOR STUDENTS OF PHYSICS AND RELATED FIELDS S. HASSANI (2nd ed.) Additional Resources

### Material Sharing

 Documents Assignments Exams

### Assessment

 IN-TERM STUDIES NUMBER PERCENTAGE Mid-terms 2 50 Assignment 5 10 Total 100 CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE 40 CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE 60 Total 100

### Course’s Contribution to Program

 No Program Learning Outcomes Contribution 1 2 3 4 5 1 gains the ability to apply the knowledge in physics and mathematics X 2 gains the ability to construct an experimental setup, perform the experiment, analyze and interpret the results X 3 is supposed to have the education required for the measurements in scientific and technological areas X 4 is able to work in an interdisciplinary team X 5 is able to identify, formulate and solve physics problems X 6 is conscious for the professional and ethical responsibility X 7 is able to communicate actively and effectively X 8 is supposed to have the required education for the industrial applications and the social contributions of physics X 9 is conscious about the necessity of lifelong education and can implement it X 10 is supposed to be aware of the current investigations and developments in the field X 11 can make use of the techniques and the modern equipment required for physical applications X

### ECTS

 Activities Quantity Duration (Hour) Total Workload (Hour) Course Duration (Including the exam week: 14x Total course hours) 14 3 42 Hours for off-the-classroom study (Pre-study, practice) 14 7 98 Mid-terms 2 3 6 Assignment 4 8 32 Final examination 1 3 3 Total Work Load Total Work Load / 25 (h) 181 ECTS Credit of the Course 7.4 ECTS Credit of the Course 7