Introduction à l’analyse complexe et au calcul numérique

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

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.

Cours co-requis

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)

Contacts

• 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

Campus

Solbosch

Method(s) of evaluation

• Other

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) ) .

Language(s) of evaluation

• french