L2 - CUPGE - Physics and Mathematics

This course is the first step in university-level electromagnetism instruction. It covers electrostatics, steady-state currents, and magnetostatics.

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The two main objectives of physics are, on the one hand, to better understand—or gain a deeper knowledge of—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 experimental evidence.

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

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This module supplements and formalizes the thermodynamic concepts introduced in the Thermodynamics 1 course unit, exploring several aspects in greater depth: thermodynamic potentials defined using Legendre transformations, the thermodynamics of open systems, phase transitions in 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 to finite dimensions (up to Jordan form) and its applications. It serves as an introduction to spectral analysis.

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Building on the analysis course from the second semester, this course will cover the concepts of series with terms of arbitrary sign. The Riemann integral will be defined and applied to solve differential equations, particularly linear ones. The section on integration will be expanded to include generalized integrals.

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This unit focuses on the mechanics of rigid bodies. It is the natural continuation of the unit on the kinematics and statics of rigid bodies covered in the first year of undergraduate studies. In this unit, we will adopt a dynamic framework and apply the Fundamental Principle of Dynamics. Deriving this principle requires knowledge of the torque of external forces, which was studied in the first year, as well as knowledge of the dynamic torque. The latter can be calculated using the kinetic torque, which, for a rigid body, involves the concept of moment of inertia. The main applications studied in this unit concern rigid bodies or simple cases of articulated systems of rigid bodies. In addition, we will study the special case of contact and friction forces (Coulomb friction) and discuss the Kinetic Energy Theorem.

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The oscillator is a fundamental concept in physics: matter is often modeled as a collection of oscillators (harmonic or otherwise) that interact with one another and with the external environment. The environment acts on the matter through a wave, such as an acoustic or electromagnetic wave. This allows us to lay the theoretical foundations for problems involving radiation-matter interaction and thus to develop one of the fundamental tools for the study of matter (in the broadest sense): spectroscopy.

Spectroscopy is, in fact, the fundamental 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 then provides a way to identify the various types of oscillators that make up the medium under study.

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

The approach taken here is a step-by-step progression, starting with the harmonic oscillator, then moving on to coupled oscillators, and finally to waves analyzed within the framework of discrete systems: infinite and 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, traveling waves, standing waves, reflection, transmission) through the study of various physical systems—mechanical (springs, strings, acoustics...), electrical (telegraph lines, coaxial cables, etc.), or electromagnetic systems, and to arrive at a general framework for the study of linear wave phenomena.

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

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The first-semester course covers the grammatical 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, bicycle parts, electronic devices) through themed lessons and videos in the field of mechanical engineering.

Finally, a wide range of activities are offered to develop oral communication skills (presentation vocabulary, simulations, role-playing, and board games) so that students will be able to describe—during an oral presentation in pairs—the specific features, functions, and uses of a piece of technical equipment of their choice.

S4

The grammatical aspects are limited to a review of modal auxiliaries.

The vocabulary focuses much more on the various components involved in the design and operation of different types of internal combustion engines and on emerging technologies (drones, driverless vehicles, 3D printing).

Students must also submit a resume in English and practice writing formal emails, so that they are prepared for situations involving internship or job searches where proficiency in English will be either required or considered an added asset.

The focus is always on practical application, culminating in 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 gain a deeper knowledge of—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 experimental evidence.

In this module, you will conduct experiments that illustrate concepts in geometric optics, electromagnetism, and waves that were introduced in the^first- and^second-year undergraduate modules.

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This course will cover the concepts of sequences and series of functions, as well as various types of convergence. Integral series and Fourier series will also be discussed.

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The first part of this course aims to reinforce the concepts of magnetostatics and to establish the relationships governing the behavior of the electromagnetic field at the interface of a plane of charges or currents. We also introduce the expression for Laplace’s forces (force and torque) acting on volumetric or filiform circuits. The second part is devoted to the properties of fields and potentials in a time-varying regime. After introducing Faraday’s law, which describes induction phenomena, we derive the time-dependent Maxwell’s equations. An energy-based approach 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 propagation of fields and potentials, and their application in systems approximated as 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 process of using computer tools in physics: it involves analyzing a phenomenon, idealizing or modeling it, and then studying it on a computer. The critical interpretation of the results is also part of this process. The examples covered are chosen to relate 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 address topics such as isometries, duality, quadratic forms, and endomorphisms.

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