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MATHEMATICAL METHODS IN PHYSICS

Course Code: 
PHYS 206
Semester: 
Spring
Course Type: 
Core
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