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| MATH0502-1 | Mathematical Analysis 2
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| Duration : | 20h Th, 22h Pr |
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| Number of credits : |
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| Lecturer : | Eric Delhez |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| The course provides an introduction to the advanced tools of calculus for the engineering science.
The following topics are addressed :
- Sequences and series : numerical sequences and series, sequences and series of functions, power series.
- Lebesgue Integration theory : multivariate integration, integration criteria, line, surface and volume integrals, parametric integrals.
Each of these topics is introduced through applications showing how the corresponding tools can be used to tackle practical problems, while keeping a rigorous theoretical presentation of the concepts. |
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Learning outcomes of the course :
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| At the end of the course, the student will master the concepts of (numerical and function) sequences and series as well as the basis of Lebesgue integration theory. He/she will be able to use the corresponding tools of calculus in both abstract mathematical contexts and in simple applications from the engineering world.
The student will also be capable of following and understanding abstract reasonings (demonstrations), reproducing them in a structured way, giving proper rigorous justifications of the different logical steps and producing short original abstract reasonings. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| The course relies on the knowledge of the theory of univariate and multivariate functions and of ordinary differential equations as well as the mastering of the corresponding tools as introduced in the course MATH0002 Mathematical Analysis 1.
The course MATH0003 Geometry, or any other introduction to the parameterisation of curves, surfaces and volumes, is a corequisite. |
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Planned learning activities and teaching methods :
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| The course includes both ex-cathedra lectures (20 h) and exercise sessions (22 h).
- The new concepts are introduced during the lectures with references to practical or theoretical issues. The main theoretical results are then derived and are used to introduce and justify the tools of calculus.
- During the exercise sessions, the focus is on the development of the technical skills of the students, first in a pure mathematical context, then in simple academic problems. In the same time, the theoretical concepts are illustrated and clarified.
These two activities are complementary and form a coherent approach of the subject. Mastering the techniques used to solve the exercise requires a good knowledge of the underlying theory. Conversely, the illustrations developed during the exercise sessions help to understand the abstract concepts.
In order to benefit from the various learning activities, the students will work regularly in order to keep abreast. The introduction of concepts and derivation of new theoretical results occurs through a gradual approach in which the different elements are presented sequentially and rely on each other. Attending a session requires the understanding of the concepts introduced at the previous sessions.
Volontary learning activites are organized during the semester.
- Question and answer sessions are planned at various key moments of the academic year. These provide good opportunities to meet the professor and assistants and ask them all possible questions about both theoretical and practical aspects.
- Formative assessments are proposed at the end of each of the main chapters. The questions are similar to those of real exams. Through these assessments, the students can better understand the level of understanding that they are expected to reach. Participation is voluntary. The marks are never taken into account in the final evaluation.
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face learning. |
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Recommended or required readings :
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| Analyse Mathématique - tome II, E.J.M. DELHEZ (In french).
Lecture notes distributed by the AEES with full coverage of the theory and exercices. |
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Assessment methods and criteria :
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| A written test and an oral test are organized in May/June.
- The written test is about solving mathematical problems and applications using the tools introduced in the course. The proper use of this tools and the justification of the reasonings requires a good knowledge of the concept and main theoretical results.
- The oral test explicitly aims at the assesment of the mastering of the concepts and theoretical results developped in the course. Students taking this test have to answer one main question about a theoretical topics. He/she can then use the official notes to prepare his/her answer at the blackboard which he/she will then explain and develop orally. The test is more about the understanding of the concepts and the reasoning than on the memorization. Mastering the theoretical concepts and knowledge of the main theorems (and hypotheses) is required to develop a rigorous and precise reasoning.
The final mark is a weighted average of the marks obtained at the written test (60 %) and the oral test (40 %).
Retake.
Students who have not been awarded the credits for the course can retake the exam in August/September (retakes).
This examen is organized as a single written test about the theory, exercices and applications. At written tests, students are never asked to reproduce complete demonstrations. At the exam, candidates are never asked to reproduce full demonstrations. The theoretical results and hypothesis of the main theorems must however be known. All the theoretical concepts must also be fully understood and mastered. Candidates must be able to solve problems using the exposed mathematical concepts and techniques, to provide theoretical justifications for the calculus methods that they use, to provide clear and comprensive definitions of the concepts and to elaborate abstract reasonings similar to those developed during the lectures. |
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Work placement(s) :
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Organizational remarks :
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| The course takes place during the second quadrimesters at the rate of one half day per week.
Ex-cathedra lectures are given in front of the full group of students. In order to promote a better interaction, the group is then split into smaller groups for the exercise sessions.
The schedule and organization details are available at http://www.mmm.ulg.ac.be. |
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Contacts :
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| Prof. Eric J.M. DELHEZ
Institut de Mathématique, B37
Tél. 04/366.94.19
E.Delhez@ulg.ac.be
List of assistants and their contact details available at http://www.mmm.ulg.ac.be. |
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| Items online : |
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| Lecture notes. |
| Official syllabus (in French). |
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