9 credits
45.0 h + 45.0 h
Q2
Teacher(s)
Glineur François; Keunings Roland;
Language
French
Prerequisites
LFSAB1101
Main themes
Linear operators, euclidean spaces and quadratic forms, linear differential equations, continuity and differentiability for functions of several real variables, optimization problems, vector analysis and integral theorems
Aims
At the end of this learning unit, the student is able to : | |
| 1 | Contribution of the course to the program objectives:
Specific learning outcomes of the course:
|
The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
This activity is aimed to introduce algebraic concepts and techniques of calculus, optimization, and vector analysis which play an important role in several courses of the bachelor and master's degree in engineering sciences.
The following content are covered during the course:
The following content are covered during the course:
- Euclidean spaces, orthogonal projection and approximation problems.
- Linear operators, eigenvectors and diagonalization.
- Adjoint operator, spectral theorem, quadratic forms, law of inertia.
- Cauchy problem for linear differential equations with constant coefficients.
- Closed, open, compact sets and boundary in Rn.
- Limits, continuity and continuous extension for functions of several variables.
- Directional Derivative, differentiation, tangent plane and Jacobian matrix.
- Partial derivatives of higher order and Taylor polynomial.
- Free extrema and extrema under constraints, Lagrange multipliers;.
- Multiple integrals and changes of variables.
- Line and surface integrals, circulation and flow of a vector field.
- Bord and theorems of Stokes type.
Teaching methods
The course is organized following an alternation between lectures and tutorial sessions. The tutorial sessions help to appropriate content presented during lectures and acquire calculation techniques. Four problem sessions are integrated in the course, in order to help students to think about issues that will be addressed in the course and to make them more receptive during lecture sessions and tutorial sessions. On the occasion of the tutorial and problem sessions an active learning for students is encouraged.
Evaluation methods
Students are assessed individually in order to test the competences announced above.
A mid-semester written test is organized for this course. Standard EPL rules apply regarding how grades from the test and the final exam are combined.
The final written exam involves solving exercises similar to those proposed during tutorials and the understanding and application of the theory (e.g. asking short proofs -- memorizing complex proofs is not required). Each exam consists features one question extracted from the compilation of former exams available on Moodle.
A mid-semester written test is organized for this course. Standard EPL rules apply regarding how grades from the test and the final exam are combined.
The final written exam involves solving exercises similar to those proposed during tutorials and the understanding and application of the theory (e.g. asking short proofs -- memorizing complex proofs is not required). Each exam consists features one question extracted from the compilation of former exams available on Moodle.
Online resources
Bibliography
Pour l'algèbre linéaire et les équations différentielles : syllabus ( iCampus).
Pour le calcul différentielle et l'optimisation : livre R. Adams and C. Essex : Calculus, a complete course (Pearson, eighth ed.) et transparents présentés aux cours (iCampus).
Pour le calcul intégral et l'analyse vectorielle : livre R. Adams and C. Essex : Calculus, a complete course (Pearson, eighth ed.) et transparents rédigés aux cours.
Pour les séances APP et APE : exercices corrigés et questions d'examen corrigées (iCampus).
Pour le calcul différentielle et l'optimisation : livre R. Adams and C. Essex : Calculus, a complete course (Pearson, eighth ed.) et transparents présentés aux cours (iCampus).
Pour le calcul intégral et l'analyse vectorielle : livre R. Adams and C. Essex : Calculus, a complete course (Pearson, eighth ed.) et transparents rédigés aux cours.
Pour les séances APP et APE : exercices corrigés et questions d'examen corrigées (iCampus).
Faculty or entity
BTCI
