Bachelor's Degree in Modeling and Digital Sciences in Materials Science

Atomistics: Periodic table, Lewis and VSEPR models
# Electronic configuration
# Periodic table
# Description of molecular chemical entities: Lewis and VSEPR

Introduction to organic chemistry and basic reaction mechanisms
# Nomenclature
# Stereochemistry
# Basics of reactivity in organic chemistry
# Aliphatic nucleophilic substitutions
# β-eliminations
# Electrophilic addition to alkenes
# Nucleophilic addition using organomagnesium compounds as an example

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First-year mathematics program at Lycée Joffre

# Reasoning and set-theoretic vocabulary

# Supplementary courses in algebraic calculus, elementary analysis, and geometry

# Enumeration

# Real analysis: numerical sequences, limits and continuity, differentiability, calculation of primitives and integrals.

# Complex numbers

# Differential equations

# Linear algebra: vectors, linear applications and matrices, bases and dimension,

# Asymptotic analysis

# Basics of statistics

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The program below covers the two physics courses in the first year of CPES at Lycée Joffre.

Geometric optics

# Laws of geometric optics
- Light: source models and spectra.
- Descartes' laws, plane diopter

# Lenses
- Spherical diopter, spherical mirror - Spherical lenses, thin
- Conjugation relations

# Optical instruments
- Eye and corrective eyewear
- Astronomical telescope or Galileo telescope
- Microscope

Point mechanics, vibrations

# Point kinematics
- Coordinate systems
- Position, velocity, acceleration
- Classical motions (constant acceleration, circular)
- Chronophotography

# Laws of dynamics

# Energy approach

# Oscillators

Electrostatics, Magnetostatics

# Electric charge, electric field

# Electrostatic potential, potential energy

# Gauss's theorem: statement and examples

# Current element, magnetostatic field

# Circulation and flow of the magnetic field

# Electrostatic dipoles

# Motion of a charged particle in an electrostatic or magnetostatic field

Electrokinetics

# Current and voltage, charge and current densities, conservation law. Mesh and node laws

# Simple dipoles and models.

# RC, RL, RLC circuits, filtering.

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This modern language course focuses on written and oral English, with particular emphasis on scientific and socio-economic contexts.

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The first-year program is as follows:

# Introduction to Contemporary Issues

# introduction to economics introduction to geopolitics

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The program below covers the two first-year computer science courses at Lycée Joffre:

Algorithms and programming 1: basic concepts in algorithms and programming:
• Notion of problem, problem instance, complexity, termination, proof of validity
• Algorithms and iterative processing
• Proof: validity, termination, complexity
• Linear structures: arrays, linked lists, stacks, queues
• Sorting: insertion, selection, merge sort, other sorting examples
• Introduction to recursive processing (dichotomous search, etc.)
• Programming in Python

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Use of computer systems: introduction to the main concepts of computer systems:
• Practical mastery of a Linux environment
• Knowledge of the main Linux commands
• Understanding of documentation pages (man)
• Sessions, files, directories, access rights
• Programs, processes, commands, and command languages
• Console (terminal) vs. graphical execution mode
• Familiarization with shells, writing a few scripts

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Introduction to numerical analysis 

# Basic concepts, challenges and limitations, machine representation of numbers

# Additional analysis tools for numerical analysis

# Numerical solution of nonlinear equations

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Teaching takes the form of projects, undertaken by pairs of students, supplemented on an ongoing basis by digital sessions allowing students to practice physics and chemistry concepts on a computer.

Depending on requirements, a few more traditional classes are planned to supplement the students' training.

Indicative program:

1. Preliminaries: visualization of scalar and vector fields: gradient, divergence, rotational, Laplacian, contour lines, surface and volume integrals, numerical solutions to point mechanics problems

2. Supervised projects offered to students: these involve the acquisition, processing, and interpretation of data. The general theme we have chosen is to train students to understand the ideas of "statistical field theory," i.e., the concept of probability applied to functions. This theme is omnipresent in modern science: image processing and analysis, AI, statistical physics, dynamic systems and stochastic processes, sequencing, epidemiology, economics, observational cosmology, etc. and the combination of numerical methods, mathematical ideas, and modeling seems to emerge naturally (examples of projects, purely indicative list: sand grain statistics, Poisson and Gaussian distributions, link with Beer-Lambert's law via the concept of effective cross section; observational data in cosmology: matter/radiation distribution on the scale of the universe; statistics and epidemiological dynamics; microscopy and analysis of Brownian motion; etc.).

3. Chemistry supplements: Slater's effective theory for atoms (effective screen potential), molecular orbitals, fragment approach

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General knowledge (epistemology and philosophy):

# history of ideas

# epistemology of science and digital technology

#argumentation and communication

See the full page

The program below covers the two physics courses in the first year of CPES at Lycée Joffre.

Geometric optics

# Laws of geometric optics
- Light: source models and spectra.
- Descartes' laws, plane diopter

# Lenses
- Spherical diopter, spherical mirror - Spherical lenses, thin
- Conjugation relations

# Optical instruments
- Eye and corrective eyewear
- Astronomical telescope or Galileo telescope
- Microscope

Point mechanics, vibrations

# Point kinematics
- Coordinate systems
- Position, velocity, acceleration
- Classical motions (constant acceleration, circular)
- Chronophotography

# Laws of dynamics

# Energy approach

# Oscillators

Electrostatics, Magnetostatics

# Electric charge, electric field

# Electrostatic potential, potential energy

# Gauss's theorem: statement and examples

# Current element, magnetostatic field

# Circulation and flow of the magnetic field

# Electrostatic dipoles

# Motion of a charged particle in an electrostatic or magnetostatic field

Electrokinetics

# Current and voltage, charge and current densities, conservation law. Mesh and node laws

# Simple dipoles and models.

# RC, RL, RLC circuits, filtering.

See the full page

Summary program:

– Probabilistic vocabulary

– Random variables and probability distributions

– Expectation and variance

– Applications

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Thermodynamics
# Basics: state functions, thermodynamic equilibrium, changes of state
# Kinetic theory of gases
# First law
# Thermochemistry
# Second law
# Thermal machines (simple).

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The first-year program is as follows:

# Introduction to Contemporary Issues

# introduction to economics

# introduction to geopolitics

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This course is an introduction to the research process: it includes immersion in a research laboratory (meeting researchers, discovering research projects) and a bibliographic study aimed at helping students understand the research process, the objectives, and the expected and hoped-for results of a project.

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First-year mathematics program at Lycée Joffre

# Reasoning and set-theoretic vocabulary

# Supplementary courses in algebraic calculus, elementary analysis, and geometry

# Enumeration

# Real analysis: numerical sequences, limits and continuity, differentiability, calculation of primitives and integrals.

# Complex numbers

# Differential equations

# Linear algebra: vectors, linear applications and matrices, bases and dimension,

# Asymptotic analysis

# Basics of statistics

See the full page

Teaching takes the form of projects, undertaken by pairs of students, supplemented on an ongoing basis by digital sessions allowing students to practice physics and chemistry concepts on a computer.

Depending on requirements, a few more traditional classes are planned to supplement the students' training.

Indicative program:

1. Preliminaries: visualization of scalar and vector fields: gradient, divergence, rotational, Laplacian, contour lines, surface and volume integrals, numerical solutions to point mechanics problems

2. Supervised projects offered to students: these involve the acquisition, processing, and interpretation of data. The general theme we have chosen is to train students to understand the ideas of "statistical field theory," i.e., the concept of probability applied to functions. This theme is omnipresent in modern science: image processing and analysis, AI, statistical physics, dynamic systems and stochastic processes, sequencing, epidemiology, economics, observational cosmology, etc. and the combination of numerical methods, mathematical ideas, and modeling seems to emerge naturally (examples of projects, purely indicative list: sand grain statistics, Poisson and Gaussian distributions, link with Beer-Lambert's law via the concept of effective cross section; observational data in cosmology: matter/radiation distribution on the scale of the universe; statistics and epidemiological dynamics; microscopy and analysis of Brownian motion; etc.).

3. Chemistry supplements: Slater's effective theory for atoms (effective screen potential), molecular orbitals, fragment approach

See the full page

The program below covers the two first-year computer science courses at Lycée Joffre:

Algorithms and programming 1: basic concepts in algorithms and programming:
• Notion of problem, problem instance, complexity, termination, proof of validity
• Algorithms and iterative processing
• Proof: validity, termination, complexity
• Linear structures: arrays, linked lists, stacks, queues
• Sorting: insertion, selection, merge sort, other sorting examples
• Introduction to recursive processing (dichotomous search, etc.)
• Programming in Python

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VBA programming in Excel Development of VBA macros in Excel:

# Using macros in Excel

# Applying the basics of VBA language in Excel

# Debugging VBA macros in Excel

# Writing custom functions

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General knowledge (epistemology and philosophy):

# history of ideas

# epistemology of science and digital technology

#argumentation and communication

See the full page

This modern language course focuses on written and oral English, with particular emphasis on scientific and socio-economic contexts.

See the full page

Second-year mathematics program, taught at Lycée Joffre:

# Linear algebra refresher and Euclidean geometry supplements

# Advanced Probabilities

# Additional analysis of functions of a variable

# Functions of several variables

See the full page

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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Complements to linear algebra, reduction theory, and applications 

# Linear algebra supplements, concept of direct sum

# Determinants

# Reduction: diagonalization and applications to the study of discrete and continuous dynamic systems in physics, chemistry, biology, or economics.

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This course continues the training of students in applied mathematics with a focus on numerical methods.

Program (subject to change depending on the year and time available):

# numerical matrix analysis

#digital integration

# numerical solution of differential equations

# Introduction to the qualitative study of nonlinear differential equations

.

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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 is only taken by students in the Materials Science track of the CPES program. It includes a mathematics section and a chemistry section, focusing on the concept of symmetry groups (of chemical molecules) and their application to determining molecular orbitals through linear combinations of atomic orbitals.

Indicative program:

# introduction to group theory, finite groups, symmetry groups of molecules

# Linear representations of groups, character theory, and applications to molecular orbitals or vibrational modes of a molecule

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The 10th grade computer science course taught at the high school focuses on advanced concepts in algorithms and programming:

# Tree data structures: binary trees, heaps, ABRs, priority queues

# Sort by pile, lower bound on sort

# Graph structure: representations (adjacency matrices, edge lists, neighbor lists)

# Basic algorithms (connectivity, depth-first and breadth-first search, topological sorting)

# Distance calculation (Dijkstra, implementation with heap)

# Introduction to object-oriented programming (encapsulation, late binding, classes, methods, etc.)

# Programming in Python

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Program taught at Lycée Joffre during the second year

# Solid mechanics (statics, dynamics, not torsors)

# Electromagnetism in a vacuum

# Diffraction optics, Fourier optics

# Waves and radiation, wave propagation.

# Kinetics and thermochemistry, introduction to electrochemistry

# Organic chemistry: some reaction mechanisms well suited to quantum modeling with frontier orbitals

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This course complements computer science training by introducing students to the study of information systems and databases (designing processes in an information system and managing relational databases):

# Information systems: introduction to the entity/association model, relational model, process modeling (conceptual process model, organizational process model)

# Databases: creation, manipulation, and querying of relational databases.

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As in the first year, this course consists of supervised projects involving data acquisition, processing, and interpretation: the approach combines numerical methods, mathematical concepts, and modeling.

The topics of study may change from year to year in order to renew students' interest.

See the full page

This modern language course focuses on written and oral English, with particular emphasis on oral expression.

See the full page

General knowledge (epistemology and philosophy):

# history of ideas

# epistemology of science and digital technology

#argumentation and communication

See the full page

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General knowledge (epistemology and philosophy):

# history of ideas

# epistemology of science and digital technology

#argumentation and communication

See the full page

Introduction to the use of data mining methods:

# Motivations, areas of application

# Data mining tasks (classification, estimation, prediction, etc.)

# Data processing (pre/post-processing)

# Supervised learning (Bayesian method, k-nearest neighbors, neural networks, etc.)

# Unsupervised learning (k-means)

# Evaluation of methods

# Data mining software (R, Scikit, Weka, etc.)

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Second-year mathematics program, taught at Lycée Joffre:

# Linear algebra refresher and Euclidean geometry supplements

# Advanced Probabilities

# Additional analysis of functions of a variable

# Functions of several variables

See the full page

Program taught at Lycée Joffre during the second year

# Solid mechanics (statics, dynamics, not torsors)

# Electromagnetism in a vacuum

# Diffraction optics, Fourier optics

# Waves and radiation, wave propagation.

# Kinetics and thermochemistry, introduction to electrochemistry

# Organic chemistry: some reaction mechanisms well suited to quantum modeling with frontier orbitals

See the full page

The first part of this course presents the basics of quantum chemistry for chemists and physical chemists. It begins by reviewing the principles of quantum mechanics and its master equation, the Schrödinger equation. The solution of the Schrödinger equation in simple cases and the concepts of wave functions and quantization are presented and illustrated in simple cases. The hydrogen atom is then studied.

The course also examines approximation methods that can be used to determine the properties of complex systems where Schrödinger's equation cannot be solved directly. The effect of spin on the electronic properties of atoms and molecules will also be discussed.

The second part of this course focuses on the quantum description of molecular properties and reactivity. The qualitative construction of molecular orbitals using symmetry properties will be introduced, and the link between molecular orbital diagrams and chemical bonding will be explained. The link between molecular geometry and electronic structure will be discussed. This course will then focus on Hückel's method, which is used to obtain molecular orbital diagrams of π systems. The classic concepts of conjugation, delocalization, donor or acceptor character, and aromaticity will be studied in this approach. Frontier orbital theory is used to rationalize molecular reactivity (cycloadditions, electrocyclization) and molecular geometries.

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This course continues the training of students in applied mathematics, particularly the use of statistical tools:

# Concepts of populations and random samples.

# Estimators.

Mean square error and bias-variance decomposition.

# Hypothesis testing: null hypothesis, alternative hypothesis. Type I and Type II errors. Power of a test. Test statistic, rejection region. Examples of classical tests.

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This course, similar in spirit to the first-year project, is an introduction to the research process, more advanced than in the first year: it includes immersion in a research laboratory, a bibliographic study, and the completion of a project involving the study of a physical or chemical context, the acquisition of experimental or observational data, and the implementation of a modeling and/or numerical simulation approach.

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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 covers the theoretical tools used to describe distributed and conserved quantities, such as density, energy, or charge density.

The first introductory chapter presents the general conservation equation and the vector analysis tools needed to understand it, as well as the various fields in which this equation is used (practically all of physics, but also chemistry, economics, etc.).

The following chapters are mainly devoted to the case of one spatial dimension and one time dimension (1+1 D). Chapter 2 discusses convective transport and presents the characteristic method for solving the corresponding first-order quasi-linear partial differential equation. Diffusive transport is then studied in Chapter 3, with the heat equation and the Fourier solution method. Finally, Chapter 4, devoted to reaction-diffusion equations, considers the case of convective and diffusive transport with the Smoluchowski equation, and the derivation of the famous Einstein equation for diffusion.

The course is accompanied by theoretical and numerical tutorials, covering topics such as road traffic and queue modeling.

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The 10th grade computer science course taught at the high school focuses on advanced concepts in algorithms and programming:

# Tree data structures: binary trees, heaps, ABRs, priority queues

# Sort by pile, lower bound on sort

# Graph structure: representations (adjacency matrices, edge lists, neighbor lists)

# Basic algorithms (connectivity, depth-first and breadth-first search, topological sorting)

# Distance calculation (Dijkstra, implementation with heap)

# Introduction to object-oriented programming (encapsulation, late binding, classes, methods, etc.)

# Programming in Python

See the full page

As in the first year, this course consists of supervised projects involving data acquisition, processing, and interpretation: the approach combines numerical methods, mathematical concepts, and modeling.

The topics of study may change from year to year in order to renew students' interest.

See the full page

This modern language course focuses on written and oral English, with particular emphasis on oral expression.

See the full page

Thermodynamics: micro and macroscopic aspects

Thermodynamics is the tool of choice for studying matter on a macroscopic scale. In particular, in the case of chemical reactions, it allows us to predict the direction of their evolution and their state of equilibrium. In the first years of the bachelor's degree, we focus on describing the principles of thermodynamics and their direct application to chemistry in the case of simple single-phase equilibrium reactions or reactions between homogeneous phases. This teaching unit will deepen this knowledge in two directions.

First, we will generalize this macroscopic thermodynamic description framework to more complex systems, such as interfacial systems where surface tension plays a role, or non-uniform phases where the composition is not the same everywhere due to an external field. We will also study ruptures and equilibrium displacements.

Next, we will look at the link with the microscopic world, where matter is described at the atomic scale. We will show that the evolution predicted by thermodynamics is statistical in nature, with the state of equilibrium corresponding to the most probable macroscopic state given the constraints applied to the system. This will allow us to deduce the macroscopic thermodynamic properties of a physicochemical system from its microscopic description.

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The first part of the module will consist of presenting metals and alloys through crystallography (from the "ideal" crystalline solid to defects and solid solutions), followed by a second part devoted to their characterization by X-ray diffraction, and a final part addressing their synthesis through their solid/liquid binary diagram (description and construction) and the various transformations in the solid state.

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This course builds on the mathematics taught in the first year and^first semester of the second year. It will introduce the mathematical tools needed by physicists in integration theory, functional transformations, complex variables, and distributions.

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This module is an introduction to the concepts and methods of statistical physics of systems in equilibrium, using a bottom-up approach: starting with examples and then presenting the general principles. It draws heavily on the course taught by Harvey Gould and Jan Tobochnik. A historical introduction to the development of Brownian motion theory forms the final chapter of the course.

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This course aims to introduce the basics of physical hydrodynamics. Kinematic aspects are covered first: Euler and Lagrange formalism, analysis of the motion of a fluid volume element, introduction of velocity current and potential functions, and applications to different types of flows. In the next part of fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of ideal fluids, then Navier-Stokes' equation describing the flow of viscous Newtonian fluids. This section will lead us to define the stress tensor and the Reynolds number, which can be used to determine whether a flow is laminar or turbulent. The course ends with an introduction to the mechanics of deformable solids: displacement field, dilation tensor, and deformation tensor.

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

See the full page

See the full page

Thermodynamics: micro and macroscopic aspects

Thermodynamics is the tool of choice for studying matter on a macroscopic scale. In particular, in the case of chemical reactions, it allows us to predict the direction of their evolution and their state of equilibrium. In the first years of the bachelor's degree, we focus on describing the principles of thermodynamics and their direct application to chemistry in the case of simple single-phase equilibrium reactions or reactions between homogeneous phases. This teaching unit will deepen this knowledge in two directions.

First, we will generalize this macroscopic thermodynamic description framework to more complex systems, such as interfacial systems where surface tension plays a role, or non-uniform phases where the composition is not the same everywhere due to an external field. We will also study ruptures and equilibrium displacements.

Next, we will look at the link with the microscopic world, where matter is described at the atomic scale. We will show that the evolution predicted by thermodynamics is statistical in nature, with the state of equilibrium corresponding to the most probable macroscopic state given the constraints applied to the system. This will allow us to deduce the macroscopic thermodynamic properties of a physicochemical system from its microscopic description.

See the full page

The first part of the module will consist of presenting metals and alloys through crystallography (from the "ideal" crystalline solid to defects and solid solutions), followed by a second part devoted to their characterization by X-ray diffraction, and a final part addressing their synthesis through their solid/liquid binary diagram (description and construction) and the various transformations in the solid state.

See the full page

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This course builds on the mathematics taught in the first year and^first semester of the second year. It will introduce the mathematical tools needed by physicists in integration theory, functional transformations, complex variables, and distributions.

See the full page

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This module is an introduction to the concepts and methods of statistical physics of systems in equilibrium, using a bottom-up approach: starting with examples and then presenting the general principles. It draws heavily on the course taught by Harvey Gould and Jan Tobochnik. A historical introduction to the development of Brownian motion theory forms the final chapter of the course.

See the full page

See the full page

This course aims to introduce the basics of physical hydrodynamics. Kinematic aspects are covered first: Euler and Lagrange formalism, analysis of the motion of a fluid volume element, introduction of velocity current and potential functions, and applications to different types of flows. In the next part of fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of ideal fluids, then Navier-Stokes' equation describing the flow of viscous Newtonian fluids. This section will lead us to define the stress tensor and the Reynolds number, which can be used to determine whether a flow is laminar or turbulent. The course ends with an introduction to the mechanics of deformable solids: displacement field, dilation tensor, and deformation tensor.

See the full page

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See the full page

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

See the full page

See the full page

Thermodynamics: micro and macroscopic aspects

Thermodynamics is the tool of choice for studying matter on a macroscopic scale. In particular, in the case of chemical reactions, it allows us to predict the direction of their evolution and their state of equilibrium. In the first years of the bachelor's degree, we focus on describing the principles of thermodynamics and their direct application to chemistry in the case of simple single-phase equilibrium reactions or reactions between homogeneous phases. This teaching unit will deepen this knowledge in two directions.

First, we will generalize this macroscopic thermodynamic description framework to more complex systems, such as interfacial systems where surface tension plays a role, or non-uniform phases where the composition is not the same everywhere due to an external field. We will also study ruptures and equilibrium displacements.

Next, we will look at the link with the microscopic world, where matter is described at the atomic scale. We will show that the evolution predicted by thermodynamics is statistical in nature, with the state of equilibrium corresponding to the most probable macroscopic state given the constraints applied to the system. This will allow us to deduce the macroscopic thermodynamic properties of a physicochemical system from its microscopic description.

See the full page

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This course builds on the mathematics taught in the first year and^first semester of the second year. It will introduce the mathematical tools needed by physicists in integration theory, functional transformations, complex variables, and distributions.

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This course unit is a natural continuation of the course units on classical Newtonian mechanics.

In the first part of the course, we cover classical mechanics, starting with the principle of least action and arriving at two new formulations: Lagrangian formalism and 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 foreshadows those of quantum mechanics.

In the second part of the EU, starting from an examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: quantum mechanics. This theory is conceptually completely different from previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. This is a radical paradigm shift that revolutionized physics in the last century and led to a deeper understanding of physical nature, with fundamental and practical implications that have radically changed the lives of humanity (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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This module is an introduction to the concepts and methods of statistical physics of systems in equilibrium, using a bottom-up approach: starting with examples and then presenting the general principles. It draws heavily on the course taught by Harvey Gould and Jan Tobochnik. A historical introduction to the development of Brownian motion theory forms the final chapter of the course.

See the full page

See the full page

This course aims to introduce the basics of physical hydrodynamics. Kinematic aspects are covered first: Euler and Lagrange formalism, analysis of the motion of a fluid volume element, introduction of velocity current and potential functions, and applications to different types of flows. In the next part of fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of ideal fluids, then Navier-Stokes' equation describing the flow of viscous Newtonian fluids. This section will lead us to define the stress tensor and the Reynolds number, which can be used to determine whether a flow is laminar or turbulent. The course ends with an introduction to the mechanics of deformable solids: displacement field, dilation tensor, and deformation tensor.

See the full page

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

See the full page

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