SF1544 Numerical Methods, Basic Course IV 6.0 credits

Numeriska metoder, grundkurs IV

  • Education cycle

    First cycle
  • Main field of study

    Technology
  • Grading scale

    A, B, C, D, E, FX, F

Course offerings

Autumn 19 CTFYS2,CLGYM for programme students

Autumn 18 CTFYS2,CLGYM for programme students

Intended learning outcomes

The course gives an overview of numerical methods for simulation of technical and scientific processes based on mathematical models. The general aim is that you should be able to solve simple such problems by means of numerical methods and be able to assess the reliability of the numerical solution. You also should be able to explain a method's advantages and disadvantages by analysing it regarding some important theoretical concepts. The course should furthermore give you an experience to use software suited for calculations and numerical problem-solving, as e.g. Matlab.

You should more specific after the course be able to

1. For a general problem formulation refine and classify the mathematical sub problems that need to be solved.

2. Choose appropriate numerical methods for the mathematical standard problem that are included in the course (see below), and explain how and why the methods work.

3. Implement the methods in an appropriate programming language, e.g. Matlab, and estimate reliability and parameter sensitivity in the numerical solution.

4. Evaluate and analyse the advantages and limitations of numerical methods by

• deciding the order of accuracy/sped of convergence of a method and explaining how this controls the size of the error

• deciding the complexity of a method and explaining how it influences the computational cost

• explaining how the condition of a problem influences the reliability in a numerical solution and deciding the condition for simple problems

• explaining the importance of stability of methods for differential equations.

Course main content

Numerical methods for various types of linear systems of equations (full, triangular, banded), the least squares method for inconsistent systems, nonlinear equations (scalar and system), eigenvalue problem, integration, derivation, interpolation and initial and boundary value problems for ODE. Basic technologies for numerical methods, as iteration, linearisation, discretisation and extrapolation, and theoretical concepts as order of accuracy, speed of convergence, complexity, condition and stability.

Disposition

Lectures, exercises laboratory

Eligibility

For KTH students: compulsory courses in Mathematics given during the first year of the curriculum of CTFYS or CLGYM and, additionally, a course in Computer Science/Programming.

For non-program students: basic university qualification and 15 credits in mathematics and 6 credits computer science or programming techniques.

Literature

Announced no later than 4 weeks before the start of the course on the course web page

Examination

  • LABA - Laboration Work, 1.5, grading scale: P, F
  • LABB - Laboration Work, 1.5, grading scale: P, F
  • TEN1 - Written Examination, 3.0, grading scale: A, B, C, D, E, FX, F
  • LABA - Laboratory sessions, 1.5 credits, grading scale: P, F
  • LABB - Laboratory sessions, 1.5 credits, grading scale: P, F
  • TEN1 - Examination, 3.0 credits, grading scale: A, B, C, D, E, FX, F

In this course, the code of honour of the school is applied, see: http://www.sci.kth.se/institutioner/math/avd/na/utbildning/hederskodex-for-studenter-och-larare-vid-kurser-pa-avdelningen-for-numerisk-analys-1.357185

Requirements for final grade

A written examination (TEN1; 3 credits).
Laboratory assignments (LABA; 1.5 credits).
Laboratory assignments (LABB; 1.5 credits).

Offered by

SCI/Mathematics

Contact

Mattias Sandberg (msandb@kth.se)

Examiner

Mattias Sandberg <msandb@kth.se>

Add-on studies

SF2520 Applied Numerical Methods

SF2521 Numerical Solutions of Differential Equations

SF2561 The Finite Element Method

SF2568 Parallel Computations for Large- Scale Problems

Version

Course syllabus valid from: Autumn 2016.
Examination information valid from: Autumn 2012.