L2 - CUPGE - Physics and Mathematics

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

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The two main objectives of physics are, on the one hand, to better understand—or learn more about—the world we live in and, on the other hand, to contribute to the advancement of techniques and technologies. Its purpose is to develop theories and test them against experience.

In this module, you will conduct experiments that illustrate concepts in mechanics, electricity, and thermodynamics that were presented in the^first-year bachelor's degree modules.

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This module complements and formalizes the concepts of thermodynamics introduced in the Thermodynamics 1 course, exploring several aspects in greater depth: thermodynamic potentials defined using Legendre transformations, thermodynamics of open systems, phase transitions of pure substances and irreversible processes, with forays into the microscopic level to provide an overview of the physical foundations of the theory.

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This course will cover the concepts of symmetric groups and determinants, and will address the reduction of endomorphisms in finite dimensions (up to Jordan form) and its applications. It is a first step toward spectral analysis.

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This course will build on the S2 analysis course by covering the concepts of series with terms of any sign. Riemann integrals will be defined and applied to solve differential equations, particularly linear ones. The integration section will be expanded to include generalized integrals.

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This course unit concerns the study of rigid body mechanics. It is the natural continuation of the course unit devoted to the kinematics and statics of rigid bodies in L1. In this course unit, we will place ourselves in a dynamic framework and apply the Fundamental Principle of Dynamics. Writing this principle requires knowledge of the tensor of external actions, studied in L1, as well as knowledge of the dynamic tensor. The latter can be calculated using the kinetic tensor, which involves the concept of moment of inertia for a rigid solid. The main applications studied in this course 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 we will discuss the kinetic energy theorem.

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The oscillator is an essential concept in physics: matter is often modeled as a collection of oscillators (harmonic or otherwise) 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 allows us to lay the theoretical foundations for problems of radiation-matter interaction and thus to construct one of the fundamental tools for the study of matter (in the broad sense): spectroscopy.

Spectroscopy is the basic tool for studying the physical properties of the objects around 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 that make up the medium being studied.

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

The principle adopted here is a step-by-step progression from harmonic oscillators, then coupled oscillators, to waves processed within discrete systems: infinite then finite coupled oscillators with different boundary conditions.

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The first step is to review various concepts in wave physics (D'Alembert's equation, progressive waves, standing waves, reflection, transmission) through the study of different physical systems: mechanical (springs, strings, acoustics, etc.), electrical (telegraph lines, coaxial cables, etc.) or electromagnetic systems, and to arrive at a general formalism for the study of linear wave phenomena.

Then, after studying standing waves, we will move on to studying interference (wave tanks and other devices) and the related physical concepts: phase shift, path difference, conditions for constructive interference, destructive interference.

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The first semester course reviews the grammar concepts 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, airplane engines, bike parts, electronic devices) through lessons and videos on topics related to mechanical engineering.

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

S4

Grammar 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 combustion engines and on emerging technologies (drones, driverless vehicles, 3D printing).

Students must also produce a CV in English and practice writing emails in a formal style, so that they are prepared for situations when looking for internships or jobs where English proficiency will either be necessary or an additional skill.

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

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The two main objectives of physics are, on the one hand, to better understand—or learn more about—the world we live in and, on the other hand, to contribute to the advancement of techniques and technologies. Its purpose is to develop theories and test them against experience.

In this module, you will conduct experiments that illustrate concepts in geometric optics, electromagnetism, and waves that were presented in the^first- and^second-year modules of the bachelor's degree program.

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This course will cover the concepts of sequences and series of functions and various types of convergence. Entire series and Fourier series will also be discussed.

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The first part of this course aims to consolidate the concepts of magnetostatics and establish the relationships between 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 volume or wire circuits. The second part is devoted to the properties of fields and potentials in variable regimes. After introducing Faraday's law describing induction phenomena, we establish Maxwell's time-dependent equations. An energy treatment allows us to define electrical and magnetic energies, as well as the Poynting vector. We apply these concepts to various examples, such as electromechanical conversion and induction heating via eddy currents. The final chapter is devoted to the propagation equations of fields and potentials, and their application in systems assimilated to a vacuum, as well as in perfect conductors and insulators. The concept of skin depth is also introduced.

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This module provides an introduction to the use of computer tools in physics: analyzing a phenomenon, idealizing/modeling it, and then studying it on a computer. Critical interpretation of the results is also part of the module. The examples discussed are chosen in relation to other current topics in the course.

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

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