 |  |  |  |  |
| | |
||||
| MATH0231-1 | Applied Mathematics | |||||
| ||||||
| Duration : | 30h Th, 20h Pr | |||||
| ||||||
| Credits/ECTS : |
| |||||
| ||||||
| Holder(s) : | André Burnel | |||||
| ||||||
| ||||||
| Course contents : | The part "Signal Analysis" is divided into 6 chapters: 1) Needed functions are either recalled or introduced. 2) The Fourier transform is defined and its properties are given together with some examples. 3) Linear systems and the mathematical notion of the convolution of functions are introduced and related to the Fourier transform. 4) Elementary notions of numerical analysis such that the replacement of a function by a polynomial, the solution of a given algebraic equation, the numerical calculation of integrals... are briefly discussed 5) Fourier series and their properties are discussed. 6) The last chapter is devoted to the numerical Fourier transform and its problems The "Statistics" part of the course introduces and uses the fundamental notions of statistics : probabilities, linear regression, errors and tests. Informatics allows now to make numerous mathematical calculations with the help of a PC or even a hand calculator. The use of these helps is encouraged but not imposed. | |||||
| ||||||
| Course objective : | The course is divided into 2 parts, signal analysis and elements of statistics. The aim of the first part consists to give to the students the mathematical elements which are necessary in the use of experimental technics in the frequency analysis such that infrared spectroscopy and medical imaginery. These mathematical elements are the Fourier transform and the convolution. The aim of the second part consists of the introduction of elements of statistics which are useful for a chemist. | |||||
| ||||||
| Prerequisites : | A good knowledge of basic mathematics as derivation and integration is necessary. It is assumed to exist by th efact that the student is in the second year of its curriculum. | |||||
| ||||||
| Organization : | The course is given during the first part of the academical year. It is given ex cathedra with the use of transparenties for the representatin of the various functions. The students may, at any time, ask the questions they will ask. A brief interruption is made in the middle of the the lecture. Exercices are done by the students themselves alone or by small groups. The teacher answers their questions and suggest methods for resolving the problem. At the end, a synthesis of the solution is given. During these sessions of exercices, the students are urged to complete their knowlegde of fundamental notions. | |||||
| ||||||
| Written notes : | Notes for the lecturres and the exercices are published by "Editions de l'Université de Liège" (in French). They can be obtained either at the office of the Faculty of Sciences for the signal analysis part or at the "Point de vue" for the statistics part. Thes notes are complete and selfsufficient. No work adapted to the level of the students exists in the literature. | |||||
| ||||||
| Assessment : | Evaluation of the students is made through a written examination during the official sessions. Four questions will be asked, 2 on signal analysis, 1 on numerical analysis and the last one on statistics. The students can use a hand calculator and its help as well as a set of formulas given by the teacher. The general rules for examinations strictly apply. | |||||
| ||||||
| Contacts : | A. Burnel Département de Physique - Institut de Physique (Bât. B5) - 4000 Liège 1 (Sart Tilman) Tél. : 04/366.36.36 - E-mail : a.burnel@ulg.ac.be | |||||
| ||||||
ULg : Students and Studies Administration - Academic Affairs
Contact : Monique Marcourt, direction A.E.E.
Date of data : 8/04/2005
Developed by SEGI