FYSA1130 Numerical Methods in Physics (4 cr)

Open the course unit brochure on Sisu
Study level:
Intermediate studies
Grading scale:
0-5
Language:
Finnish
Responsible organisation:
Department of Physics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

Description

  • Integrated development environment (Spyder), debugging, good practices in development

  • Numerical integrals and derivatives.

  • Solving linear and non-linear equations numerically.

  • Solve ordinary- and partial differential equations numerically.

  • Differences between boundary-, initial- and eigenvalue problems.

  • Numerical optimization and fitting

  • Limitations of numerics and estimating errors 

Learning outcomes

Upon completion of the course the student is able to

  • use a modern development tool for numerical problems

  • calculate numerical derivatives and integrals

  • solve simultanous linear and non-linear equations numerically

  • solve ordinary differential equation numerically

  • solve elliptic partial differential equation numerically

  • deal with boundary-, initial- and eigenvalue problems.

  • use different methods for non-linear optimization

  • fit linear and non-linear models to data.

  • Assess the accuracy and precision of numerical solutions 

Additional information

  • Own laptop for use during the lectures and during the exam is highly recommended but not mandatory.

  • Uses a web platform, such as TIM, where Python code can be run and returned for evaluation. 

Description of prerequisites

  • Reasonable knowledge of high school level physics and mathematics

  • Some familiarity with concepts relating to differential equations

  • Basic level Python programming skills

  • Familiarity with NumPy, SciPy and matplotlib libraries 

Study materials

  • Lecture notes, course TIM-pages

  • Python language documentation

  • NumPy, SciPy and matplotlib documentation 

Literature

  • Newman, Computational Physics

Completion methods

Method 1

Evaluation criteria:
Harjoitustehtävät ja tentti (esim. harjoitustehtävät 50 %, tentti 50 %).
Time of teaching:
Period 3
Select all marked parts

Method 2

Description:
This method is intended for students for whom method 1 is not possible for specific reasons (e.g. language, living elsewhere). The course lecturer must be contacted before enrolling on the course.
Evaluation criteria:
A scheduled home exam and the ability to explain the solutions in an assessment discussion.
Time of teaching:
Period 5, Period 4, Period 2, Period 1
Select all marked parts

Method 3

Description:
This method is intended for students for whom method 1 is not possible for specific reasons (e.g. language, living elsewhere). The course lecturer must be contacted before enrolling on the course.
Evaluation criteria:
Acceptable completion of the project.
Select all marked parts
Parts of the completion methods
x

Teaching (4 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
<p>Harjoitustehtävät ja tentti (esim. harjoitustehtävät 50 %, tentti 50 %).</p>
Language:
Finnish
Study methods:

Luennot, harjoitustehtävät, ohjaukset ja tentti. 

Teaching

x

Independent study (4 cr)

Type:
Independent study
Grading scale:
0-5
Evaluation criteria:
A scheduled home exam and the ability to explain the solutions in an assessment discussion.
Language:
English, Finnish
Study methods:

Self-study, home exam and an assessment discussion. 

Teaching

x

Independent study (4 cr)

Type:
Independent study
Grading scale:
0-5
Evaluation criteria:
Acceptable completion of the project
Language:
English, Finnish
Study methods:

Self-Study, project work. 

Teaching