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:
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