# Computational Methods for Scientific Applications

5 credits

Syllabus, Master's level, 1TD047

Code
1TD047
Education cycle
Second cycle
Main field(s) of study and in-depth level
Computational Science A1N, Computer Science A1N
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 9 February 2023
Responsible department
Department of Information Technology

## Entry requirements

A Bachelor's degree, equivalent to a Swedish Kandidatexamen, from an internationally recognised university, and 15 credits in mathematics and/or statistics as well as participation in 5 credits programming (Python recommended). Proficiency in English equivalent to the Swedish upper secondary course English 6.

## Learning outcomes

On completion of the course, the student should be able to:

• describe the key concepts covered in the course and perform tasks that require knowledge about these concepts;
• explain and be able to use algorithms for solving least squares problems, ordinary differential equations and for Monte Carlo simulations;
• analyze computational algorithms in order to investigate algorithmic properties such as accuracy;
• discuss suitable methods and algorithms given a application problem and the properties of the algorithms;
• given a mathematical model, solve problems in science and engineering by structuring the problem, choose appropriate numerical method and generate solution using software and by writing programming code;
• explain, summarise, evaluate and discuss solution methods and results.

## Content

Fundamentals in computational science: representation pf floating point numbers, IEEE floating point standard, overflow/underflow, machine epsilon, rounding errors and its effect on computations. Programming for computations in Python (numPy). Big-O notation.

Bisic methods för data analysis: regression analysis, least squares approximations, and solutions to overdermined equation systems. Ordinary differetial equations and numerical solutions to initial value problems using commonly used numerical methods.

Monte Carlo methods and methods based on stochastic simulation: stochastic in comparison with deterministic methods. Brownian motion, Markov processes. Gillespes algorithm.

Important key concepts in the course include, e.g., rounding errors, machine psilon, overflow and underflow, cancellation, floating point number, accuracy and order of accuracy, discretization and discretization errors, stability and instability, adaptivity, stochastic / deterministic model and method.

## Instruction

Laboratory work, lectures, problem solving classes.

## Assessment

Assignments (2 credits) and final written exam (3 credits).