FYSS7116 Integral Transformations (3 cr)

Open the course unit brochure on Sisu
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Physics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

Description

  • Sine and Cosine series, Fourier series, formation and convergence of these series, complex number representations

  • Fourier and Laplace transformations and inverse transformations

  • Dirac delta function and Green’s function

  • Solving differential equations using series and transformations 

Learning outcomes

After completing the course, student is expected to

  • Compute Fourier, sine and cosine series with real and complex coefficients for different functions.

  • Compute Fourier transformations and inverse Fourier transformations for different functions.

  • Present Dirac’s delta function in different forms and compute integrals containing delta functions.

  • Use Fourier transformations and Fourier series as a method for solving linear differential equations.

  • Form Laplace transformations and use these to solve linear differential equations with constant coefficients and also apply these to solve partial differential equations 

Description of prerequisites

  • Basic studies on Mathematics (option A or B)

  • MATA114 Differential equations (recommendation)

  • MATA200 Complex calculus tai FYSS7301 Complex Analysis (recommendation) 

Study materials

Lecture notes 

Literature

  • G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (5th ed., Academic Press 2001)

Completion methods

Method 1

Evaluation criteria:
Course is evaluated based on excercise and exam points. Passing course requires at least 50% of the total points, example weighting: excercises: 60%, exam 40%.
Time of teaching:
Period 5, Period 4
Select all marked parts

Method 2

Description:
This completion method is intended for students for whom method 1 is not possible for specific reasons (e.g. language, living elsewhere). Contact the teacher before enrolling to the course via this completion method.
Evaluation criteria:
Course is evaluated based on excercise and exam points. Passing course requires at least 50% of the total points, example weighting: excercises: 60%, exam 40%.
Select all marked parts
Parts of the completion methods
x

Teaching (3 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Course is evaluated based on excercise and exam points. Passing course requires at least 50% of the total points, example weighting: excercises: 60%, exam 40%.
Language:
Finnish
Study methods:

Lectures, excercises, exam.

Teaching

x

Independent study (3 cr)

Type:
Independent study
Grading scale:
0-5
Evaluation criteria:
Course is evaluated based on excercise and exam points. Passing course requires at least 50% of the total points, example weighting: excercises: 60%, exam 40%.
Language:
English, Finnish
Study methods:

Independent studying, exercises, exam. 

Teaching