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MATH0006-1

Numerical Analysis (first part)

[ version française ]

Duration :20h Th, 40h Pr
Credits/ECTS :
2nd year of a Bachelor's degree in engineering sciences, civil ingineer in architecture orientation5
2nd year of a Bachelor's degree in civil ingeneering sciences, civil ingeneer orientation5
2nd year of a Bachelor's degree in computers sciences6
3rd year of the 5 year degree in civil engineering in geology for "licenciés" in geological and mineralogical sciences5
Holder(s) :François‑Xavier Litt
Course contents : Numerical problems and algorithms, numerical instability.
Numbering systems, condition numbers, estimation and control of the errors.
Linear systems: Gauss method, LU decomposition, particular systems, analysis of errors, iterative methods.
Least squares: normal equations, orthogonalisation.
Singular values.
Eigenvalues: power method, Jacobi method, QR algorithm.
Nonlinear equations: Picard iteration, first order methods, Newton-Raphson method, polynomial equations.
Systems of nonlinear equations.
Practical works on computers with MATLAB.
Course objective : To give students basic notions for scientific computing.
Prerequisites : Knowledge of mathematical analysis and linear algebra.

Workshops : During the first semester:
Practical lessons during the 10 first thursdays of the semester from 10:30 to 12:30 in small working groups. These groups shall be formed during the first lecture.
By groups also, 5 two hours laboratories. A test will be given during the fifth laboratory.
The schedule of the laboratories will be announced at the beginning of the semester.

Organization : Organization : During the first semester:
Lectures during tht 10 first thursdays of the semester from 8:30 to 10:30 for the whole students at once.
Working lessons and laboratories as above.


Written notes :
  • Working books:
    Analyse numérique, première partie, F.X. Litt; for sale at AEES.
    Analyse numérique, première partie, Manuel d'exercices, C. Bernard et al.; for sale at AEES.
    Analyse numérique, première partie, Manuel de laboratoire, F.X. Litt; for sale at AEES.
  • Recommended readings: see list in the first of the working books.
Assessment : 1st session: laboratory: 20%, written exam: 80%, no oral exam.
2nd session: written exam: 100%, no oral exam.

The written exam has two parts of equal importance for the grade:
  • exercices, at closed book (a calculator is absolutely necessary), lasting 2:30.
  • QCM with certainty coefficients, at closed book, on the theory, lasting 1:30.

    These two parts cannot be dissociated, no grade is ever given for just one part alone.
Contacts : Teacher : F.X.Litt, Institut Montefiore, B28, Sart Tilman, 4000 Liège; Tél. 04/366.26.92 ; Fax 04/366.28.74 ; e-mail FX.Litt@ulg.ac.be.

Secretary : M.T.Ratz, Tél 04/366.26.81; e-mail MT.Ratz@ulg.ac.be.

Assistants : D. Detry, V. Leroy, C. Thiernesse.

Teaching assistants: C. Bastin, M. Dumont, V.A. Huynh-Thu, T. Zangerle.

NB: Modification to these lists of assistants and teaching assistants can occur during the academic year.
Remarks :
  • Every attributed grade (even partial, i.e. laboratory or oral exam) can be maintained.
  • The students following this course as "free auditors" must always (even if the written exam is taken in September) have done the laboratories.




ULg : Students and Studies Administration - Academic Affairs
Contact : Monique Marcourt, direction A.E.E.
Date of data : 18/05/2007
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