*Conducted in terms:*2020L, 2021L

*ECTS credits:*5

*Language:*Polish

*Organized by:*Faculty of Mathematics, Informatics, and Mechanics

*Related to study programmes:*

# Scientific computations 1000-712ONA

1. Number representation, coputer arithmetic, numerical stability of algorithms

2. Vectors and matrices - representation and basic operations

3. Vector functions, combining functions, plotting one and multidimensional data

4. Systems of Linear Equations - Gauss elimination

5. Eigen values and eigenvectors

6. Linear Least squares

7. Polynomials as a vector space, interpolation.

8. Approximating functions with polynomials and splines

9. basic signal processing, filters, smoothing of data

10. FIlters for 2d and 3d signal processing - pixel and voxel images.

11. Basics of data compression - lossless and lossy compression

12. Numerical differentiation (polynomials, numerical differentiation)

13. Numerical integration - numerical quadratures

14. Symbolic computations

## Type of course

## Prerequisites (description)

## Course coordinators

## Learning outcomes

Effects of teaching:

Knowedge and abilities: the student:

- understands the basics of computer arithmetic representation and problems associated with it

- Knows methods to solve non-linear equation problem;

- Understands the direct method of solving a system of linear equations probem by the LU decomposition

- Knows the definition of the linear least squares problem, its solution by the QR decomposition and its application to curve fitting

- knows the power iteration and inverse iteration methods for solving the eigenvalue problem

- Knows the definition of the Lagrange and Hermite interpolation problems

- knows the bases of polynomial vector space proposed by Lagange, and Newton .

- Knows the definition of linear and cubic splines for the purpose of interpolation

- Can perform all of the discussed operations on matrices in python programming language

- knows the basic python operations needed to present data graphically using line graphs, bar charts, boxplots, heatmaps and histigrams

- understands the basic notions of computer image representation and analysis

Social competences:

1. understands the role of numerical sicentific computing in modeling of pehnomena in physical and biological world.

2. understands the ethical implications of proper data visualisation

## Assessment criteria

writen test,

programming assignments,

Written exam

## Bibliography

A primer on scientific programming with python, Lagtangen

Scientific Programming, Barone, Marinari, Organtini, Ricci-Tersenghi

Numerical Recipes, Press Teukolsky, Veterling, Flannery

## Additional information

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
the following study programmes:

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: