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Valid for year : 2013
 
TNCG19 Numerical Methods for Advanced Computer Graphics, 10 ECTS credits.
/Numerical Methods for Advanced Computer Graphics/

For:   ACG   MT  

 

Prel. scheduled hours: 80
Rec. self-study hours: 187

  Area of Education: Technology

Main field of studies: Media Technology

  Advancement level (G1, G2, A): A

Aim:
To provide the students with the mathematical skills necessary for coming courses in advanced computer graphics and image analysis. After the course the student shall be able to:
  • theoretically understand and also implement the following in at least one programming language (for example Matlab or C/C++),
  • Solving equations in one variable using different methods,
  • Analysing the error,
  • Doing interpolation and polynomial approximation, using for example, Lagrange polynomial, divided difference, Cubic spline and parametric curves,
  • Differentiating and integrating numerically using different methods,
  • Solving ordinary differential equations,
  • Solving linear systems using pivoting
  • Finding the determinant of a matrix, the inverse of a matrix, eigenvalues and eigenvectors, LU factorisation
  • Special types of matrices,
  • Solving linear systems by using iterative techniques, Finding the best polynomial representing a number of data points (or a function) by least squares method,
  • Understanding the difference between analogue and digital signals (images)
  • Understanding the Fourier Transform and its applications in image analysis


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus, Linear algebra

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Organisation:
The course consists of lectures, classes and laboratories.
Course contents:
Mathematical Preliminaries. Solutions of Equations in One Variable. Interpolation and Polynomial Approximation. Numerical Differentiation and Integration. Initial-Value Problems for Ordinary Differential Equations. Direct Methods for Solving Linear Systems. Iterative Techniques in Matrix Algebra. Approximation Theory. Digital Images. Fourier Transform.
Course literature:
Numerical Analysis, Richard L. Burden and J. Douglas Faires & Distributed material
Examination:
Written examination
Laboratory work
 6 ECTS
4 ECTS
 


Course language is English.
Department offering the course: ITN.
Director of Studies: Dag Haugum
Examiner: Sasan Gooran
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology
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Contact: TFK , val@tfk.liu.se
Last updated: 05/02/2013