Master’s studies

# Syllabus for Scientific Computing, Bridging Course

Beräkningsvetenskap, bryggningskurs

## Syllabus

• 5 credits
• Course code: 1TD045
• Education cycle: Second cycle
• Main field(s) of study and in-depth level: Computer Science A1N, Computational Science A1N, Mathematics A1N
• Grading system: Fail (U), Pass (G)
• Established: 2013-03-21
• Established by: The Faculty Board of Science and Technology
• Revised: 2015-04-27
• Revised by: The Faculty Board of Science and Technology
• Applies from: week 50, 2014
• Entry requirements: 120 credits in science/engineering including 30 credits in mathematics, 5 credits in computer programming and 5 credits in scientific computing.
• Responsible department: Department of Information Technology

## Learning outcomes

To pass, the student should be able to

• describe the key concepts covered in the course (see Content) and perform tasks that require knowledge about these concepts;
• in general terms explain the ideas behind, and be able to use algorithms for solving linear systems, ordinary differential equations and for Monte Carlo simulations;
• analyse properties of the computational algorithms and mathematical models using the analytical tools presented in the course;
• discuss suitable methods and algorithms given a application problem;
• 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;
• present, explain, summarise, evaluate and discuss solution methods and results.

## Content

Solutions to linear systems of equations using LU-decomposition. Matrix and vector norms. The concepts sensitivity, conditioning, stable/non-stable algorithm. Solutions to ordinary differential equations (initial value problems). Adaptivity. Stability. Explicit and implicit methods. The concepts of discretisation and discretisation (truncation) error. Floating point representation and the IEEE floating-point standard, machine epsilon and roundoff error. Monte Carlo methods and methods based on stochastic simulation. MATLAB and programming in MATLAB
Key concepts covered in the course: discretisation and discretisation error, machine epsilon, roundoff error, condition and condition number, accuracy and order of accuracy, efficiency, stability, adaptivity.

## Instruction

Laboratory work, lectures, problem and problem solving classes.

Mini projects.

## Other directives

The aim of the Scientific Computing, bridging course is to provide students with the knowledge required for the study of higher courses in Scientific Computing or Computational Science. The course assist in bridging the gap between previous Scientific Computing studies and the level needed at the Master in Computational Science. As a prerequisite this course can replace Scientific computing I and II.