L2-L3 LICENCE PHYSIQUE

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

See the syllabus in the "+ info" tab.

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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 UE extends the concepts covered in Newtonian Dynamics 1 to gravitational interaction and, more generally, to the motion of a material point subjected to a central force. The statics and dynamics of rigid bodies are also covered.

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This course is a continuation of the mathematics taught in L1. The mathematical tools necessary for the physicist in analysis will be studied, in particular functions of several variables, differential operators, generalized and multiple integrals and sequences and series, including integer and Fourier series.

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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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This course is a continuation of the mathematics taught in L1 and the^1st semester of L2. The mathematical tools required by physicists in linear and bilinear algebra will be studied. Next, differential equations and Fourier analysis will be covered. Finally, all the mathematical knowledge acquired in L2 will be applied to the solution of physics problems, either analytically or with the aid of computer tools.

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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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ManipLab is a hands-on physics laboratory discovery module.

These are real experiments, supervised by a researcher and carried out in research laboratories. During these experiments, students carry out their own manipulations, measurements and observations, whether in an experimental, theoretical or simulation context. The aim is for students to come away enriched by the discovery of a laboratory and new physics concepts, which they will find more concrete and put into the context of research.

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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.

See full page

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

See the syllabus in the "+ info" tab.

See full page

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.

See full page

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.

See full page

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.

See full page

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

See full page

See full page

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.

See full page

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.

See full page

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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Introduction to the synthesis of chemical elements in the Universe (Big Bang, stars)

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This optional course introduces the physical concepts used in Nanoscience and Nanotechnology. It will enable students to better understand the specific phenomena associated with the nanometric scale. It also includes an introduction to the 4 microscopes used to observe and measure at this scale: AFM, STM, MEB, MET...

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This optional course focuses on solving physics problems on the computer. It includes the use of the Python language for scientific programming, with particular emphasis on visualization and animation. It provides an introduction to the possibilities offered by numerical physics through various simulations (FDTD simulation of the propagation of a 1D electromagnetic wave, etc.).

See full page

The course aims to provide an initial general introduction to physics as it relates to the biological sciences, and to put into context the use of modern physics concepts, methods and approaches to describe biological systems and their complexity, from the molecular to the cellular scale. This means understanding the central role that physics has played over the past century in learning about the organization and dynamics of complex living matter (from cells to populations of individuals). At the same time, we need to understand that biological systems represent a new opportunity for physicists to learn more about the complexity of living matter and its capacity for self-organization, regulation and control, with an eye also to new biomimetic applications.

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This UE is a continuation of the mathematics courses of L1 and the 1st^{semester of} L2. The mathematical tools necessary for the physicist in integration theory, functional transformations, complex variables and distributions will be presented.

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This UE represents the natural continuation of the UEs in classical Newtonian mechanics.

In the first part of the course, we take Classical Mechanics from the principle of least action to two new formulations: the Lagrangian formalism and the Hamiltonian formalism. We study the link between physical symmetries and conservation laws (E. Noether's theorem) and introduce Poisson brackets, which allow us to write the classical laws of temporal evolution of physical quantities in a form that already prefigures those of quantum mechanics.

In the second part of the course, starting from an examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: Quantum Mechanics. This is a theory that is conceptually completely different from previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. It's a radical paradigm shift that has turned physics on its head over the last century, enabling a deeper understanding of physical nature, with fundamental and practical spin-offs that have radically changed the lives of mankind (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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This UE is a continuation of the electromagnetism and waves courses taken in L2.

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Practical work in various areas of physics.

Topics covered include the study of mechanical and electrical oscillating systems (simple and torsion pendulums, coupled pendulums, RLC circuits, inductively coupled circuits), acoustic waves, a few notions of wave optics (diffraction and interference), the use of electronic circuits to study components or electrical systems (diodes, LEDs and photodiodes, transmission lines) and the study of a few properties of matter (magnetism, photoelectric effect, Faraday effect).

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This module is an introduction to the concepts and methods of the statistical physics of equilibrium systems, with a bottom-up approach: start with examples and then give the general principles. It draws heavily on Harvey Gould and Jan Tobochnik's course. A historical introduction to the construction of Brownian motion theory forms the final chapter of the course.

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The course builds on the knowledge acquired in L1 and L2 to acquire the basics of special relativity (1/3 of the EU) and offer students a brief introduction to subatomic particle physics (2/3 of the EU). It will also provide an introduction to the description of the intimate structure of matter. After developing the tools of special relativity necessary for the rest of the course, we'll go into detail on both the study of atomic nuclei (nuclear physics) and that of "elementary" particles (subatomic physics proper). A first description of the standard model of particle physics and the basic concepts of nuclear physics will be given.

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Practical work in wave optics studies interference phenomena using Michelson and Fabry-Pérot interferometers as an application for high-resolution spectroscopy. (Michelson interferometer and Fabry-Pérot interferometer hands-on)

Interference phenomena are also recorded on holographic plates for the restitution and study of holograms (TP holography).

The polarization of light is studied and used to study birefringent materials (calcite, for example), liquid crystals, isotropic materials placed under stress (induced birefringence)... (TP birefringence)

The emission of electromagnetic waves by heated bodies is studied in blackbody practical exercises. The temperature of various hot bodies is determined using a pyrometer, spectroscopy and an infrared camera (for the human body, for example).

Lasers are also studied, their emission, longitudinal and transverse modes either on a "fixed" cavity, or on an open, adjustable cavity. (TP HeNe laser I and II)

The propagation speed of an intensity-modulated electromagnetic wave is measured by the phase shift of its modulation induced by its propagation. (TP speed of light)

Objects are analyzed using Fourier optics, which, after filtering, brings out or removes certain details. The study is also compared with digital Fourier filtering (TP strioscopie).

Finally, the property of certain substances subjected to a magnetic field to deviate the plane of polarization of the light passing through them is being studied in the Faraday effect TP.

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The aim of this course is to introduce the basics of physical hydrodynamics. The kinematic aspects are dealt with first: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of current and potential velocity functions, and applications to different types of flow. In the following section on fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, followed by the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This will lead to the definition of the stress tensor and the Reynolds number, enabling us to deduce whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensors.

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The tutored project is an experimental or digital simulation project carried out in groups of 3 students. It takes place in the practical workroom, on one of the many physics and chemistry topics on offer. It confronts students with the project approach, and mobilizes their creativity, initiative, autonomy and experimental rigor. The project culminates in a report and oral presentation, subject to peer and jury assessment.

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This module covers selected methods of numerical physics with applications relevant to the Fundamental Physics pathway. After a review of programming with Python 3, numerical algorithms for solving nonlinear equations, ordinary differential equations and systems of linear equations will be studied. A major part of the module will concern numerical linear algebra and its applications in physics and numerical analysis. Finally, there will be an introduction to formal calculus systems.

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This course builds on the basic concepts acquired in Quantum Mechanics in Semester 5. The course is structured around the following main themes: extension of the wave mechanics formalism, angular momentum theory, hydrogen atom, perturbations, introduction to relativistic quantum mechanics.

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Practical work in various areas of physics.

Topics covered include the study of mechanical oscillating systems (simple pendulum, torsion pendulum, coupled pendulums), acoustic waves, a few notions of wave optics (diffraction and interference), the use of electronic circuits to study electrical components or systems (diodes, LEDs and photodiodes, transmission line) and the study of a few properties of matter (magnetism, photoelectric effect, Faraday effect).

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Introduction to the synthesis of chemical elements in the Universe (Big Bang, stars)

See full page

This optional course introduces the physical concepts used in Nanoscience and Nanotechnology. It will enable students to better understand the specific phenomena associated with the nanometric scale. It also includes an introduction to the 4 microscopes used to observe and measure at this scale: AFM, STM, MEB, MET...

See full page

This optional course focuses on solving physics problems on the computer. It includes the use of the Python language for scientific programming, with particular emphasis on visualization and animation. It provides an introduction to the possibilities offered by numerical physics through various simulations (FDTD simulation of the propagation of a 1D electromagnetic wave, etc.).

See full page

The course aims to provide an initial general introduction to physics as it relates to the biological sciences, and to put into context the use of modern physics concepts, methods and approaches to describe biological systems and their complexity, from the molecular to the cellular scale. This means understanding the central role that physics has played over the past century in learning about the organization and dynamics of complex living matter (from cells to populations of individuals). At the same time, we need to understand that biological systems represent a new opportunity for physicists to learn more about the complexity of living matter and its capacity for self-organization, regulation and control, with an eye also to new biomimetic applications.

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Learn about analog and digital electronics.

Analog teaching is based on the study and application of the main electronic components: diodes, transistors and operational amplifiers.

For the numerical part, the basics of sequential logic will be covered.

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At the start of this course, we will review the concepts of light rays and the approximation conditions of geometrical optics, as well as the important concepts of wave physics for physical optics.

Then, starting from the scalar approximation of light waves, a special case of electromagnetic waves, we describe light sources, 2-wave and N-wave interference phenomena and diffraction in the Fraunhofer approximation.

We'll go on to study a number of widely-used physical systems, focusing on their resolving power and applications: microscope, telescope, Michelson interferometer, grating spectrometer, Fabry-Pérot interferometer.

Finally, we'll look at the concepts of spatial coherence and temporal coherence of light bursts, and how they are used (stellar interferometry, speckle, etc.).

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This course is a simplified introduction to quantum physics.
It begins with an historical overview of the beginnings of quantum mechanics: atomic emission line spectra, black-body radiation (the logic of this name will be explained), the photoelectric effect, etc.
A simplified presentation of Fourier transforms will enable us to understand the link between spectral line width and time evolution,
and, further on, to understand Heisenberg's inequalities.
An important part of the course will be devoted to matter waves, through the Schrödinger equation, in very simple special cases.
Finally, we'll conclude with a few aspects of magnetism (necessarily quantum).

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Statistical physics is one of the fundamental branches of modern physics, whose probabilistic approach establishes relationships between the microscopic and the macroscopic. It deals with the evolution of systems with very large numbers of particles (atoms, molecules, photons, etc.) and links macroscopic quantities such as pressure, temperature, etc. characterizing their state at thermodynamic equilibrium to quantities defining the microscopic state of their constituents. This introductory course in statistical physics will cover the microcanonical and canonical sets, and relate the partition function to thermodynamic quantities such as mean energy, pressure, temperature and entropy. These results will be illustrated on perfect gases and on a few simple quantum systems.     

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This UE is made up of two blocks of 18 hours each (9h CM+ 9h TD).

For the first "acoustics" block, after establishing the equation for the propagation of mechanical vibrations in an infinite medium, plane-wave solutions will be presented. Emphasis will then be placed on the notion of scalar potential. Spherical wave solutions will be presented. A large part will be devoted to the notion of acoustic impedance. Energy aspects will also be discussed. Various applications (particularly ultrasonic) will be covered.

The second "thermal" block of the course studies heat transport properties in solids and fluids under stationary (time-independent) conditions. We first define diffusive and convective heat transfer regimes, and introduce the Fourier equation linking heat flow to temperature variation via thermal conductivity or the conducto-convective coefficient. We then establish the heat propagation equation, which we apply to the simple cases of walls and pipes. We then review the main laws describing heat transfer by radiation (Planck's law, Stefan-Boltzmann's law) and study the case of radiative flux between two bodies under total influence. All this knowledge will be used to carry out heat balances for homogeneous or composite walls, building models, bars and fins. We'll also look at heat exchangers.

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This UE includes a refresher and a deepening of programming techniques as well as an introduction to numerical physics. It begins with a review of procedural programming using the Python 3 language. We will then introduce the use of numerical methods relevant to the simulation and solution of physical problems.

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This UE is a continuation of the point dynamics and rigid solid mechanics taught in L1 and L2. The aim here is to provide elements of the mechanics of deformable continuous media, essentially in the limit of small deformations, linear elasticity, viscoelasticity and viscosity. Emphasis is placed on simple cases and common applications.

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The tutored project is an experimental or digital simulation project carried out in groups of 3 students. It takes place in the practical workroom, on one of the many physics and chemistry topics on offer. It confronts students with the project approach, and mobilizes their creativity, initiative, autonomy and experimental rigor. The project culminates in a report and oral presentation, subject to peer and jury assessment.

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This course is divided into two parts. The first part focuses on the Dirac formalism in quantum mechanics, with illustrations in the case of the 1D harmonic oscillator and angular momentum, in particular for spin. The second part is an introduction to the use of quantum mechanics in solid state physics, through its application to semiconductors.

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Classification of solids. Crystalline structures. Energy bands. Metals. Semiconductors. Insulators. Electrical, dielectric and magnetic properties.

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Study of the basic principles of nucleus physics with a view to concrete everyday applications. The aim of this course is to provide a basic understanding of the physics of the nucleus, followed by a presentation of the applications of radioactivity and nuclear energy in industry (physics of nuclear reactors, fuels), medicine (nuclear imaging) and radiation protection (measuring instruments, units, etc.).

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Practical work and application of analog and digital electronics in connection with UE HLPH507.

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Introduction to the synthesis of chemical elements in the Universe (Big Bang, stars)

See full page

This optional course introduces the physical concepts used in Nanoscience and Nanotechnology. It will enable students to better understand the specific phenomena associated with the nanometric scale. It also includes an introduction to the 4 microscopes used to observe and measure at this scale: AFM, STM, MEB, MET...

See full page

This optional course focuses on solving physics problems on the computer. It includes the use of the Python language for scientific programming, with particular emphasis on visualization and animation. It provides an introduction to the possibilities offered by numerical physics through various simulations (FDTD simulation of the propagation of a 1D electromagnetic wave, etc.).

See full page

The course aims to provide an initial general introduction to physics as it relates to the biological sciences, and to put into context the use of modern physics concepts, methods and approaches to describe biological systems and their complexity, from the molecular to the cellular scale. This means understanding the central role that physics has played over the past century in learning about the organization and dynamics of complex living matter (from cells to populations of individuals). At the same time, we need to understand that biological systems represent a new opportunity for physicists to learn more about the complexity of living matter and its capacity for self-organization, regulation and control, with an eye also to new biomimetic applications.

See full page

See full page

This UE represents the natural continuation of the UEs in classical Newtonian mechanics.

In the first part of the course, we take Classical Mechanics from the principle of least action to two new formulations: the Lagrangian formalism and the Hamiltonian formalism. We study the link between physical symmetries and conservation laws (E. Noether's theorem) and introduce Poisson brackets, which allow us to write the classical laws of temporal evolution of physical quantities in a form that already prefigures those of quantum mechanics.

In the second part of the course, starting from an examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: Quantum Mechanics. This is a theory that is conceptually completely different from previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. It's a radical paradigm shift that has turned physics on its head over the last century, enabling a deeper understanding of physical nature, with fundamental and practical spin-offs that have radically changed the lives of mankind (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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In the first part: deepen the basic notions of differential calculus seen in L2.

In the second part: introduce the qualitative study of differential equations.

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This UE is a continuation of the electromagnetism and waves courses taken in L2.

See full page

Practical work in various areas of physics.

Topics covered include the study of mechanical and electrical oscillating systems (simple and torsion pendulums, coupled pendulums, RLC circuits, inductively coupled circuits), acoustic waves, a few notions of wave optics (diffraction and interference), the use of electronic circuits to study components or electrical systems (diodes, LEDs and photodiodes, transmission lines) and the study of a few properties of matter (magnetism, photoelectric effect, Faraday effect).

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The aim of this first Fluid Mechanics module is to provide a basic understanding of the behavior of industrial fluids (air, water, hydraulic fluids), with a view to dimensioning simple systems involving static or dynamic fluids (flow rates, pressure, velocity, pressure drops, etc.). Emphasis is placed on the study and design of hydraulic installations.

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This module is an introduction to the concepts and methods of the statistical physics of equilibrium systems, with a bottom-up approach: start with examples and then give the general principles. It draws heavily on Harvey Gould and Jan Tobochnik's course. A historical introduction to the construction of Brownian motion theory forms the final chapter of the course.

See full page

The course builds on the knowledge acquired in L1 and L2 to acquire the basics of special relativity (1/3 of the EU) and offer students a brief introduction to subatomic particle physics (2/3 of the EU). It will also provide an introduction to the description of the intimate structure of matter. After developing the tools of special relativity necessary for the rest of the course, we'll go into detail on both the study of atomic nuclei (nuclear physics) and that of "elementary" particles (subatomic physics proper). A first description of the standard model of particle physics and the basic concepts of nuclear physics will be given.

See full page

Practical work in wave optics studies interference phenomena using Michelson and Fabry-Pérot interferometers as an application for high-resolution spectroscopy. (Michelson interferometer and Fabry-Pérot interferometer hands-on)

Interference phenomena are also recorded on holographic plates for the restitution and study of holograms (TP holography).

The polarization of light is studied and used to study birefringent materials (calcite, for example), liquid crystals, isotropic materials placed under stress (induced birefringence)... (TP birefringence)

The emission of electromagnetic waves by heated bodies is studied in blackbody practical exercises. The temperature of various hot bodies is determined using a pyrometer, spectroscopy and an infrared camera (for the human body, for example).

Lasers are also studied, their emission, longitudinal and transverse modes either on a "fixed" cavity, or on an open, adjustable cavity. (TP HeNe laser I and II)

The propagation speed of an intensity-modulated electromagnetic wave is measured by the phase shift of its modulation induced by its propagation. (TP speed of light)

Objects are analyzed using Fourier optics, which, after filtering, brings out or removes certain details. The study is also compared with digital Fourier filtering (TP strioscopie).

Finally, the property of certain substances subjected to a magnetic field to deviate the plane of polarization of the light passing through them is being studied in the Faraday effect TP.

See full page

The aim of this course is to introduce the basics of physical hydrodynamics. The kinematic aspects are dealt with first: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of current and potential velocity functions, and applications to different types of flow. In the following section on fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, followed by the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This will lead to the definition of the stress tensor and the Reynolds number, enabling us to deduce whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensors.

See full page

The tutored project is an experimental or digital simulation project carried out in groups of 3 students. It takes place in the practical workroom, on one of the many physics and chemistry topics on offer. It confronts students with the project approach, and mobilizes their creativity, initiative, autonomy and experimental rigor. The project culminates in a report and oral presentation, subject to peer and jury assessment.

See full page

This module covers selected methods of numerical physics with applications relevant to the Fundamental Physics pathway. After a review of programming with Python 3, numerical algorithms for solving nonlinear equations, ordinary differential equations and systems of linear equations will be studied. A major part of the module will concern numerical linear algebra and its applications in physics and numerical analysis. Finally, there will be an introduction to formal calculus systems.

See full page

This course builds on the basic concepts acquired in Quantum Mechanics in Semester 5. The course is structured around the following main themes: extension of the wave mechanics formalism, angular momentum theory, hydrogen atom, perturbations, introduction to relativistic quantum mechanics.

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Introduce the basic tools of complex analysis.

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