# Fiches de cours

Picasso Marco

English

#### Summary

The student will learn state-of-the-art algorithms for solving ordinary differential equations, nonlinear systems, and optimization problems. The analysis and implementation of these algorithms will be discussed in some detail.

#### Content

Numerical Solution of Ordinary Differential Equations

Explicit Runge-Kutta methods. Order 4 conditions. Step size control. Convergence.

Numerical Optimization

Newton, BFGS and conjugate gradient methods. Constrained optimization problems. Optimality (KKT) conditions. Quadratic programming. Optimal control.

#### Keywords

Explicit Runge-Kutta methods, Newton, BFGS and conjugate gradient methods, Constrained optimization problems, Optimality (KKT) conditions, Quadratic programming, Optimal control.

#### Learning Prerequisites

##### Recommended courses

Some background in numerical analysis and proficiency in programming - Matlab/Octave recommended

##### Important concepts to start the course

Numerical methods for approximation, differentiation and integration of functions. Basic knowledge of ordinary differential equations and their solutions. Basic knowledge of numerical techniques for solving systems of linear equations.

#### Learning Outcomes

By the end of the course, the student must be able to:
• Analyze methods
• Choose an appropriate method
• Prove basis properties of methods
• Derive new methods
• Conduct computational experiments
• Implement computational methods

#### Teaching methods

Lecture style with computational experiments in class to illustrate analysis.

#### Expected student activities

Students are expected to attend lectures and participate actively in class and exercises. Exercises will include both theoretical work and implementation and test of a variety of methods.

#### Assessment methods

Written examination.

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

#### Resources

##### Bibliography

Lecture notes will be provided by the instructor. Complimentary reading:

Hairer, E.; Norsett, S. P.; Wanner, G. Solving ordinary differential equations. I. Springer, 1987.

Nocedal, J.; Wright, S. J. Numerical optimization. Second edition. Springer, 2006

### Dans les plans d'études

• Mathématiques, 2019-2020, Bachelor semestre 5
• Semestre
Automne
• Forme de l'examen
Ecrit
• Crédits
5
• Matière examinée
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Ingénierie financière, 2019-2020, Master semestre 1
• Semestre
Automne
• Forme de l'examen
Ecrit
• Crédits
5
• Matière examinée
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Ingénierie financière, 2019-2020, Master semestre 3
• Semestre
Automne
• Forme de l'examen
Ecrit
• Crédits
5
• Matière examinée
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Science et ingénierie computationnelles, 2019-2020, Master semestre 1
• Semestre
Automne
• Forme de l'examen
Ecrit
• Crédits
5
• Matière examinée
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Science et ingénierie computationnelles, 2019-2020, Master semestre 3
• Semestre
Automne
• Forme de l'examen
Ecrit
• Crédits
5
• Matière examinée
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines

### Semaine de référence

LuMaMeJeVe
8-9
9-10
10-11MAA330 MAA330
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand