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Introduction à l’analyse complexe et au calcul numérique

academic year

Course teacher(s)

Artem NAPOV (Coordinator) and Michel KINNAERT

ECTS credits


Language(s) of instruction


Course content

Numerical computing

  • Floating point representation and arithmetic.

  • Systems of linear equations.

  • Nonlinear equations and systems of nonlinear equations.

  • Interpolation and approximation of functions.

  • Numerical integration.

  • differential equations and systems of differential equations: initial value problems.

Complex analysis

  • Fourier Series

  • Fourier and Laplace Transforms

  • Resolution of ordinary differential equations by Laplace transform

  • Linear time-invariant systems and transfer function

  • Impulse, unit step and frequency responses of a linear time-invariant system

Objectives (and/or specific learning outcomes)

Numerical computing: present and study basic numerical methods for the solution of considered numerical problems. Explore practical aspects with the help of GNU Octave software.

Complex analysis: Study Fourier and Laplace transforms and their applications; introduce the basic notions of the theory of signals and systems.

Prerequisites and Corequisites

Cours co-requis

Teaching methods and learning activities

Numerical computing: theory is exposed during the lectures; students explore the practical aspects during the class hours (using Octave software in a computer laboratory).

Complex analysis: theory lectures and exercises sessions

References, bibliography, and recommended reading

Numerical computing

  • A Quarteroni, R Sacco, F Saleri, Méthodes numériques: algorithmes, analyse et applications, Springer

  • Lloyd N. Trefethen et David Bau, III, Numerical Linear Algebra, SIAM

  • Uri Ascher et Chen Greif, A First Course in Numerical Methods, SIAM

Complex analysis: A.V. Oppenheim et A.S. Willsky, Signals and systems, 2e édition, Prentice-Hall (1997)

Other information


  • Artem Napov

    office : campus Solbosch, building D, office DB3.141 ; e-mail : artem.napov@ulb.be

  • Michel Kinnaert

    office : campus Solbosch, building L, door E, level 2 (SAAS) ; email : michel.kinnaert@ulb.ac.be




Method(s) of evaluation

  • Other


Single exam organized in two parts (in computer room):

  • Numerical computing: exam with a written part and a part on computers covering the theoretical and (mostly) practical aspects of the course

  • Written exam covering theory and exercises

Mark calculation method (including weighting of intermediary marks)

Both parts are graded on a scale from 0 to 20 using half-integer grades.

  • If both partial grades are greater than or equal to 8/20, the global grade is the (rounded) arithmetic mean of the two partial grades ( n = round ( (n1+n2)/2 ) ) .

  • If at least one of the partial grades is less than 8/20, the global grade is the smallest of the two partial grades ( n = min(n1,n2) ) .

The report from one session to another, and from one year to another, is accepted only for grades greater than or equal to 10.

Language(s) of evaluation

  • french