Incoming Exchange Student Courses
| General Data | ||||
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| Academic program | Incoming Exchange Student Courses | :
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| Type d'EC | Classes (LIIEXP05EMathEng5) | |||
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Status :
Obligatoire |
Period :
Semester 5 |
Education language :
English |
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| Learning Outcomes |
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| This module is dedicated to the study of mathematical tools that are commonly used in applications (Fourier Series and Transform, Laplace Transform, classic examples of Partial Differential Equations, Distribution and/or optimization.) General objectives (learning outcomes : LO) : * LO1 to develop abstract reasonning skills (e.g. being able to comprehend the extension of analysis and algebra studied during the first two years to Hilbert spaces / Lebesgue integration / Generalized functions ) * LO2 to understand the foundations of common tools like Fourier Series, Fourier Transform, Laplace Transform * LO3 to be able to analyze a problem (for instance a PDE problem, optimization problem) and find the appropriate method to solve it (Fourier, Laplace,...) * LO3 to develop rigorous problem solving approaches |
| Content |
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| * Lebesgue integration and Hilbert Spaces - Parameter dependant integrals. * Fourier Series * Fourier Transform * Laplace Transform * Some Classical examples in Partial Differential Equations * optimization: non linear optimization (unconstrained and constrained optimisation for functions of several variables) linear optimisation (simplex method) |
| Pre-requisites / co-requisites |
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| Calculus and algebra Year 1 and Year 2, Improper Integrals, Infinite Series, Vector Spaces, |
| Bibliography |
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| Essential Textbooks: James, G. & Dyke, P. (2018) Advanced Modern Engineering Mathematics, 5th Edn., Pearson Recommended textbooks: Croft, A. et al. (2017) Engineering Mathematics, 5th Edn., Pearson Education Stroud, K.A. (2020) Advanced Engineering Mathematics, 6th Edn., Red Globe Press Kreyszig, E. (2011) Advanced Engineering Mathematics, 10th Edn., John Wiley & Sons |