Duration
26h Th, 26h Pr
Number of credits
| Bachelor of Science (BSc) in Engineering | 6 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
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;
- Vector calculus : regular curve and surface, gradient's theorem, Green's, Stokes' and divergence theorems, scalar potential.
Learning outcomes of the learning unit
At the end of the course, the student will master the concepts of (numerical and function) sequences and series, the basis of Lebesgue integration theory as well as the main results of vector calculus. 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.
This course contributes to the learning outcomes I.1, II.1, III.1, III.2 of the BSc in engineering.
Prerequisite knowledge and skills
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.
Planned learning activities and teaching methods
The course includes both ex-cathedra lectures (26 h) and exercise sessions (26 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.
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.
- A forum is open on e-Campus to ease the interaction between the students and the instructors. Questions can be asked at any time about both the theoretical aspects and the applications.
- 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.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Additional information:
Lectures notes and exercices sessions are face to face but podcasts are available at http://www.mmm.uliege.be.
Recommended or required readings
Analyse Mathématique - tomes 3 & 4, E.J.M. DELHEZ (In french).
Lecture notes distributed by the CdC (Centrale des Cours FSA) with full coverage of the theory and exercices.
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions )
Additional information:
The final assessment takes place in May/June as a single written exam. The test is about all the theory, exercices and applications addressed during the lectures and training sessions.
All the theoretical concepts must 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. At the exam, candidates are never asked to reproduce long demonstrations. However, the theoretical results and hypothesis of the main theorems must be known and students must be able to elaborate abstract reasonings similar to those developed during the lectures.
Retake.
Students who have not been awarded the credits for the course can retake the exam in August/September (retakes).
This exam has the same format as the May/June test.
Work placement(s)
Organisational remarks and main changes to the course
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.uliege.be
Contacts
Prof. Eric J.M. DELHEZ
Institut de Mathématique, B37
Tél. 04/366.94.19
E.Delhez@uliege.be
List of assistants and their contact details available at http://www.mmm.uliege.be.
Association of one or more MOOCs
Items online
Lecture notes
Theory and applications