Mathematics
Prof. Claude Lamoureux (Year 1 ñ Lectures: 24 hours; Required Sections: 24 hours)
Integration. Measure theory. Lebesgue integral. Monotone and dominated convergence theorems. Density theorems. Fixed point and contraction mapping theorems in LP(m) and Sobolev spaces.
Real Analysis. Discrete and continuous representations in usual function spaces. Hilbert spaces. Fourier and Laplace transforms.
Complex Analysis. Holomorphic functions. Singularities. Representation of solutions and classical functions.
Operator Theory. Integral equations. Fredholm theorems and Hilbert spectral theory.
Distributions. Dí, Sí, Dí(Gn), Dí+.
Introduction to Mathematica.
Probability and Statistics
Prof. Thérèse Phan
(Year 1 ñ Lectures: 18 hours; Required Sections: 18 hours)
Probability Theory. Probabilistic models. Random variables. Mean, variance, conditional expected value, correlation. Distribution functions (normal, exponential, Poisson, binomial, geometric, hyper-geometric). Joint distribution functions of multiple random variables. The multinomial distribution. Multivariate normal distribution.
Statistics. Random sample.
Chi-deux, Fisher-Snedecor and Student distributions.
Estimation: Point Estimation (Unbiased estimator. Best linear unbiased estimator. Unbiased estimator of lower variance. Maximum likelihood estimator).
Confidence Intervals. (Confidence limits, most selective limits, shortest confidence intervals)
Tests: Hypothesis testing. Adjustment and comparative tests. Various comparatives of two or more samples. Analysis of variance. Tests of independence.
Numerical Analysis I
Prof. Daniel Verwaerde (Year 2 ñ Lectures: 12 hours; Required Sections: 12 hours)
Linear Systems. Direct and iterative methods.
Matrix Computation. Norm and convergence.
Minimization of a Quadratic Form. Conjugate gradient method.
The Eigenvalue Problem. Power method and subspace iterations.
Ordinary Differential Equations. Runge Kutta and Adams methods. Convergence and error propagation.
Numerical Analysis II
Prof. Pascal Laurent (Year 2 ñ Lectures: 12 hours; Required Sections: 12 hours)
Boundary Value Problems in Mathematical Physics,
Variational Formulation of Elliptic Problems.
Finite Element Method. Theory and software design. Examples of non-linear problems.
Transient Problems. Finite elements and finite differences. Convergence and stability. Examples of modelisation of engineering problems
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