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| MATH0202-1 | analysis I - partim a) Introduction to the s - partim b) mathematical analysi  | |||||
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| Duration : | partim a) Introduction to the s : 10h Th partim b) mathematical analysi : 90h Th, 60h Pr | |||||
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| Holder(s) : | partim a) Introduction to the s : Jean Schmets
partim b) mathematical analysi : Jean Schmets | |||||
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| Course contents : | The first part of the course is dedicated to the theory of functions. It begins with the introduction of the finite dimensional euclidean spaces. Then comes the general theory of functions (limits, continuity, differentiability) and the study of the elementary functions. This part ends with the study of the linear differential equations with constant coefficients (one variable) as well as some ordinary differential equations. The second part is an introduction to integration. Ten results being accepted without proof (proofs are developed in later years), the Lebesgue integral is presented; the aim of this presentation is pedagogy and efficacy. | |||||
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| Course objective : | Mathematical analysis consists in the study of functions. In high schools almost only real valued functions of one real variable are considered. Applications of mathematics require complex valued functions of several real variables. | |||||
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| Prerequisites : | The matter of the course of analysis presented in high school is studied rigorously and in details, in the more general framework of the euclidean spaces of finite dimension and for complex valued functions. A good knowledge of the high school programme is a big help; a good knowledge of logic is one too. | |||||
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| Workshops : | The assistants organize these works. They consist in explanations on the theory developed in the course and in exercises solved by the assistants or by the students. Written interrogations are organized; their results are incorporated in the final mark only if they are favourable to the student. | |||||
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| Organization : | The official timetable for the course and the works is handed to the students at the beginning of the academic year. | |||||
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| Written notes : | Courses : 1) J. Schmets, Analyse mathématique, 2) J. Schmets, Analyse mathématique, introduction au calcul intégral. Exercises : 1) A. Garcet, Exercices d'analyse mathématique, 2) A. Garcet, Exercices de calcul intégral. These books are for sale at the Editions Derouaux, 77 Boulevard d'Avroy à 4000 Liège. Other references are indicated to the students; they are at their disposal at the library of the Institute of Mathematics. | |||||
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| Assessment : | Five written interrogations take place during the academic year. Their results are put on the official board. These results are taken into account for the final mark only if they are favourable to the student. A written examination will take place in January 2005 on: - theory: matter developed during the course until the notion of an asymptote to the graph of a function; - exercises: depending on the matter. There are two questions about the theory and two exercises. During the June examinations, there are: 1) a written examination about exercises: 2 exercises about continuity and differentiability, 2 exercises about integration; 2) an oral examination: 1 question about theory and 1 exercise about continuity and differentiability; 1 question about theiry and 1 exercise about integration. Moreover the student answers 10 (short) questions about elementary functions and states 5 main definitions or theorems dealing with the matter of the examination of January. | |||||
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| Contacts : | Professor Dr. J. SCHMETS Functional analysis Institut de Mathématique (Bureau 1/59) - Grande Traverse, 12 - Sart Tilman -Bât. B 37 - 4000 LIEGE 1 Tél.: ++ 32 (04) /366.93.91; Fax: ++ 32 (04) /366.95.47; e-mail: j.schmets@ulg.ac.be | |||||
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ULg : Students and Studies Administration - Academic Affairs
Contact : Monique Marcourt, direction A.E.E.
Date of data : 8/04/2005
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