L2 - CUPGE - Physics and Mathematics

This course is the first step in teaching electromagnetism at university. It covers electrostatics, stationary currents and magnetostatics.

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The two main aims of physics are to better understand the world we live in, and to contribute to the development of techniques and technologies. Its vocation is to develop theories and confront them with experience.

In this module, you'll carry out experiments to illustrate the concepts of mechanics, electricity and thermodynamics that were introduced in the^1st year undergraduate modules.

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This module completes and formalizes the notions of thermodynamics introduced in EU Thermodynamics 1, by exploring several aspects in greater depth: thermodynamic potentials defined on the basis of Legendre transformations, thermodynamics of open systems, pure-body phase transitions and irreversible processes, with incursions at the microscopic level to provide an insight into 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. This is a first step towards spectral analysis.

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Following on from the analysis course in S2, this course deals with the notion of series with terms of any sign. The Riemann integral will be defined and applied to linear and other differential equations. The integration section will be extended to generalized integrals.

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This unit deals with 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'll take a dynamic approach and apply the Fundamental Principle of Dynamics. Writing this principle requires knowledge of the external action torsor, studied in L1, as well as knowledge of the dynamic torsor. The latter can be calculated using the kinetic torsor, which for a rigid solid involves the notion of moment of inertia. The main applications studied in this unit concern rigid solids or simple cases of articulated systems of rigid solids. In addition, we will study the special case of contact and friction actions (Coulomb friction) and 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 matter via a wave, such as an acoustic or electromagnetic wave. This lays the theoretical foundations for the problems of radiation-matter inter-action, and thus for the construction of one of the fundamental tools for the study of matter (in the broadest sense): spectroscopy.

Spectroscopy is the basic tool for studying the physical properties of the objects that surround us, such as molecules, crystals, stars and galaxies. These properties are deduced either from their spontaneous emission, or from their response to external excitation. For example, we measure the absorption, reflection and transmission properties of applied electromagnetic radiation (visible, infrared, X-rays, neutrons, etc.). The response to this radiation is then a means of discovering the various types of oscillators making up the medium under study.

 In short, the study of the physical environments 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 coupled oscillators, to waves treated as discrete systems: infinite then finite coupled oscillators with different edge conditions.

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The aim is to review various notions of wave physics (D'alembert's equation, travelling 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, after studying standing waves, we'll move on to studying interference (wave tank and other devices) and the related physical concepts: phase shift, step difference, constructive interference condition, 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 aims of physics are to better understand the world we live in, and to contribute to the development of techniques and technologies. Its vocation is to develop theories and confront them with experience.

In this module you'll carry out experiments to illustrate the concepts of geometrical optics, electromagnetism and waves that were introduced in the^1st and^2nd year modules.

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This course covers the notions of function sequences and series, and the various convergences. Integer and Fourier series will also be developed.

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The first part of this course is designed to consolidate the concepts of magnetostatics and establish the relations between the electromagnetic field at the interface of a plane of charges or currents. 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 the 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 various examples, such as electromechanical conversion or induction heating via eddy currents. A final chapter is devoted to the equations of field and potential propagation, and 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 is an introduction to the use of computer tools in physics: it involves analyzing a phenomenon, idealizing/modeling it, then studying it on a computer. Critical interpretation of results is also included. Examples are chosen in relation to other current subjects in the course.

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This course is an introduction to bilinear algebra, covering Euclidean and Hermitian spaces. It covers isometries, duality, quadratic forms and endomorphisms.

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