Applied mathematics for engineer
Written exam
Chimie Paris mathematics course provides students with the essential notions of mathematics allowing them to understand first-year courses and practical work (Physics I: Quantum Mechanics, Physics II: radiation-matter interactions, TP IRM and Materials …). It is thus a teaching with applied purpose for which practicing of concepts is essential.
The course is divided into three parts:
1) Mathematics applied to quantum mechanics where are introduced the notion of Hilbert space, the Dirac notation, the computation of quantities in a complex vector space, and their application in the framework of the theory of measurement in quantum mechanics.
2) Mathematics applied to signal processing where are discussed the use of Fourier series and Fourier transforms as tools for processing and analysis.
3) Mathematics applied to data analysis where are presented the notions of probabilities, statistics and distributions. Essential concepts such as mean, standard deviation, and linear
regression will be reported and applied to error calculations and data analysis.
At the end of the course students will be able:
– to use Dirac’s formalism and computation in a Hilbert space in the context of a quantum physics or quantum chemistry problem,
– to analyze a signal and to understand a process for processing or producing a signal by using the properties of Fourier transformation and Dirac distribution,
– to assess uncertainties about a measured quantity in a relevant way and to understand the principles underlying data analysis methods.
Teaching language: FR
Documents:
handouts, slide presentation, online quiz
Link: https://coursenligne.chimie-paristech.fr/course/view.php?id=29