L2 - CUPGE - Physics and Mathematics

This course is the first step in the teaching of electromagnetism at the university. Electrostatics, stationary currents and magnetostatics are covered.

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The two main objectives of Physics are, on the one hand, to better understand -or to better know- the world in which we live, and on the other hand to contribute to the development of techniques and technologies. Its vocation is to elaborate theories and to confront them with experience.

In this module you will perform experiments that will illustrate concepts of mechanics, electricity and thermodynamics that were presented in the^1st year undergraduate modules.

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This module completes and formalizes the notions of thermodynamics introduced by the EU Thermodynamics 1, by deepening several aspects: thermodynamic potentials defined from Legendre transformations, thermodynamics of open systems, phase transitions of the pure body and irreversible processes, with incursions at the microscopic level in order to give an overview of the physical foundations of the theory.

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This course will cover the notions of symmetric group, determinants and will deal with the reduction of endomorphisms in finite dimension (up to Jordan form) and its applications. It is a first step towards spectral analysis.

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This course will approach, in the continuity of the analysis course of S2, the notion of series with terms of any sign. The Riemann integral will be defined and applied to treat differential equations, especially linear ones. The integration part will be extended to generalized integrals.

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This unit concerns the study of the mechanics of rigid solids. It is the natural continuation of the unit devoted to the kinematics and statics of rigid solids in L1. In this unit we will place ourselves in a dynamic framework and apply the Fundamental Principle of Dynamics. The writing of this principle requires the knowledge of the torsor of the external actions, studied in L1, but also the knowledge of the dynamic torsor. The latter can be calculated with the help of the kinetic torsor which, for a rigid solid, uses the notion of moment of inertia. The main applications studied in this unit concern the rigid solid or simple cases of articulated systems of rigid solids. In addition, we will study the particular case of contact and friction actions (Coulomb friction) and we will approach the Kinetic Energy Theorem.

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The oscillator is an essential concept in physics: matter is often modeled by a collection of oscillators (harmonic or not) interacting with each other and with the external environment. The latter acts on the matter through a wave, such as an acoustic or electromagnetic wave. This makes it possible to lay the theoretical foundations of the problems of radiation-matter interaction and thus to build one of the fundamental tools for the study of matter (in the broad sense): spectroscopy.

Spectroscopy is indeed the basic tool for the study of the physical properties of objects that surround us, such as a molecule, a crystal, a star, a galaxy. These properties are deduced either from their spontaneous emission or from their response to an external excitation. For example we measure the properties of absorption, reflection, transmission of an applied electromagnetic radiation (visible, infra-red, X, neutrons, ...). The response to this radiation is then a way to discover which are the various types of oscillators constituting the studied medium.

 In short, the study of the physical media that surround us requires the use of two fundamental theoretical tools: oscillators and waves, which are the subject of this course.  

The principle adopted here is a step-by-step progression from the harmonic oscillator, then from coupled oscillators, to waves treated in the framework of discrete systems: infinite and then finite coupled oscillators with different edge conditions.

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The aim of this course is to review various notions of wave physics (D'alembert's equation, progressive waves, standing waves, reflection, transmission) through the study of different physical systems: mechanical (spring, string, acoustic...), electrical (telegraph line, co-axial...) or electromagnetic, and to arrive at a general formalism for the study of linear wave phenomena

Then, in a second time, after having studied the stationary waves it will be a question of studying the interferences (wave tank and other devices) and the physical concepts which are related to them: phase shift, difference of march, condition of constructive interference, destructive interference

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The first-semester course reviews the grammar essential for oral and written communication(tenses and aspect, asking questions, comparisons and superlatives, passive voice) as well as essential general vocabulary(numbers, measurements, shapes); it also includes an introduction to technical vocabulary(basic building materials, plane engine, bike parts, electronic device) through themed lessons and videos in the field of mechanical engineering.

Finally, numerous activities are offered to promote oral expression skills (presentation vocabulary, simulations, role-playing and board games), so that students are able to describe the specific features, functions and uses of a piece of technical equipment of their choice in an oral presentation by groups of two.

S4

Grammatical aspects are limited to a review of modal auxiliaries.

The vocabulary is much more focused on the various elements involved in the design and operation of different types of heat engines, and on emerging technologies(drones, driverless vehicles, 3D-printing).

Students are also expected to produce a CV in English and practice writing emails in a formal style, so as to be prepared for internship or job-seeking situations where fluency in English will either be necessary or an additional skill.

The practice of expression is always the main objective, with an individual oral presentation at the end of the semester of their second-year project in mechanics.

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The two main objectives of Physics are, on the one hand, to better understand -or to better know- the world in which we live, and on the other hand to contribute to the development of techniques and technologies. Its vocation is to elaborate theories and to confront them with experience.

In this module you will perform experiments that will illustrate the concepts of geometric optics, electromagnetism and waves that were presented in the^1st and^2nd year modules.

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This course will cover the concepts of sequences and series of functions and the various convergences. The integer and Fourier series will also be developed.

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The first part of this course aims to consolidate the notions of magnetostatics and to establish the relations of the electromagnetic field at the interface of a plane of charges or current. We also introduce the expression of Laplace forces (force and moment) acting on volumetric or filiform circuits. The second part is devoted to the properties of fields and potentials in variable regime. After introducing Faraday's law describing induction phenomena, we establish Maxwell's time-dependent equations. An energetic treatment allows us to define the electric and magnetic energies, as well as the Poynting vector. We apply these concepts to different examples such as electromechanical conversion or induction heating via eddy currents. A last chapter is devoted to the equations of propagation of fields and potentials, and to their application in vacuum-like systems, as well as in perfect conductors and insulators. The notion of skin depth is also introduced.

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This module constitutes an introduction to the approach of using computer tools in Physics: it is a question of analyzing a phenomenon, of idealizing/modeling it, then of studying it on computer. The critical interpretation of the results is also part of it. The examples are chosen in relation with the other current subjects in the training.

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This course is an introduction to bilinear algebra and will cover Euclidean and Hermitian spaces. It will deal with isometries, duality, quadratic forms and endomorphisms.

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