CPES BACHELOR'S DEGREE IN NUMERICAL MODELING AND MATERIALS SCIENCE

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

Introduction to Organic Chemistry and Basic Reaction Mechanisms
# BOM
# Stereochemistry
# Basics of Reactivity in Organic Chemistry
# Aliphatic nucleophilic substitutions
# β-eliminations
# Electrophilic addition on alkenes
# Nucleophilic addition on the example of organomagnesium

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Program of the first year of mathematics at the Lycée Joffre

# Reasoning and set vocabulary

# Complements of algebraic calculus, elementary analysis and geometry

# Enumeration

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

# Complex numbers

# Differential equations

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

# Asymptotic analysis

# Basics of statistics

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The program below covers the two physics courses of the first year of CPES at the 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 glasses
- Astronomical or Galileo telescope
-Microscope

Mechanics of the point, vibrations

# Point kinematics
- Coordinate systems
- Position, speed, acceleration
- Classical movements (constant acceleration, circular)
- Chronophotography

# Laws of Dynamics

# Energy approach

# Oscillators

Electrostatic, Magnetostatic

# Electric Charge, Electric Field

# Electrostatic potential, potential energy

# Gauss's theorem: statement and examples

# Current Element, Magnetostatic Field

# Circulation and flux of the magnetic field

# Electrostatic Dipoles

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

Electrokinetics

# Current and voltage, load and current densities, conservation law. Laws of meshes and knots

# Simple dipoles and models.

# RC, RL, RLC circuits, filtering.

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This modern language teaching is based on the written and oral practice of English, with particular emphasis on the scientific or socio-economic context.

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The first-year program is as follows:

# Introduction to the problems of the contemporary world

# Introduction to economics Introduction to geopolitics

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

Algorithmics and Programming 1: Basic Concepts in Algorithmics 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: inserting, selecting, merging sorting, other sorting examples
• Introduction to recursive processing (dichotomous search, etc.)
• Python programming

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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 digital analysis 

# Basics, issues and limitations, representation of numbers in a machine

# Analytical add-ons for numerical analysis

# Numerical solution of nonlinear equations

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Teaching takes place in the form of projects, carried out by pairs of students, supplemented as they go along by digital sessions allowing students to practice the ideas of physics and chemistry on a computer.

Depending on the needs, a few more traditional course sessions are planned to complete the students' training

Indicative programme:

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

2. Tutored projects offered to students: these provide for the acquisition, processing and interpretation of data.  The general theme we have chosen is to train students capable of understanding 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, dynamical systems and stochastic processes, sequencing, epidemiology, economics, observational cosmology, etc., and the conjunction of an approach combining numerical methods, mathematical ideas and modeling seems to emerge naturally (examples of projects, a purely indicative list: sand grain statistics, Poisson and Gauss's law, link with Beer Lambert's law via the concept of stopping cross-section; observation data in cosmology: matter/radiation distribution at 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 shield potential), molecular orbitals, fragment approach

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General culture (epistemology and philosophy):

# history of ideas

# Epistemology of science and digital technology

#argumentatition and communication

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The program below covers the two physics courses of the first year of CPES at the 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 glasses
- Astronomical or Galileo telescope
-Microscope

Mechanics of the point, vibrations

# Point kinematics
- Coordinate systems
- Position, speed, acceleration
- Classical movements (constant acceleration, circular)
- Chronophotography

# Laws of Dynamics

# Energy approach

# Oscillators

Electrostatic, Magnetostatic

# Electric Charge, Electric Field

# Electrostatic potential, potential energy

# Gauss's theorem: statement and examples

# Current Element, Magnetostatic Field

# Circulation and flux of the magnetic field

# Electrostatic Dipoles

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

Electrokinetics

# Current and voltage, load and current densities, conservation law. Laws of meshes and knots

# Simple dipoles and models.

# RC, RL, RLC circuits, filtering.

See full page

Synthetic program:

– Probabilistic vocabulary

– Random variables and probability distributions

– Expectation and variance

–Applications

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

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The first-year program is as follows:

# Introduction to the problems of the contemporary world

# Introduction to Economics

# Introduction to geopolitics

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This teaching is an introduction to the research process: it includes an immersion in a research laboratory (meeting with researchers, discovery of research projects) and a bibliographic study with the aim of providing students with their understanding of the research approach, the objectives and the expected and hoped results of a project.

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Program of the first year of mathematics at the Lycée Joffre

# Reasoning and set vocabulary

# Complements of algebraic calculus, elementary analysis and geometry

# Enumeration

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

# Complex numbers

# Differential equations

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

# Asymptotic analysis

# Basics of statistics

See full page

Teaching takes place in the form of projects, carried out by pairs of students, supplemented as they go along by digital sessions allowing students to practice the ideas of physics and chemistry on a computer.

Depending on the needs, a few more traditional course sessions are planned to complete the students' training

Indicative programme:

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

2. Tutored projects offered to students: these provide for the acquisition, processing and interpretation of data.  The general theme we have chosen is to train students capable of understanding 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, dynamical systems and stochastic processes, sequencing, epidemiology, economics, observational cosmology, etc., and the conjunction of an approach combining numerical methods, mathematical ideas and modeling seems to emerge naturally (examples of projects, a purely indicative list: sand grain statistics, Poisson and Gauss's law, link with Beer Lambert's law via the concept of stopping cross-section; observation data in cosmology: matter/radiation distribution at 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 shield potential), molecular orbitals, fragment approach

See full page

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

Algorithmics and Programming 1: Basic Concepts in Algorithmics 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: inserting, selecting, merging sorting, other sorting examples
• Introduction to recursive processing (dichotomous search, etc.)
• Python programming

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VBA Programming in Excel Development of VBA Macros in Excel:

# Practice macros in Excel

# Application of the basics of the VBA language in Excel

# Debugging VBA macros in Excel

# Writing custom functions

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General culture (epistemology and philosophy):

# history of ideas

# Epistemology of science and digital technology

#argumentatition and communication

See full page

This modern language teaching is focused on the written and oral practice of English, with a particular emphasis on a scientific or socio-economic context.

See full page

Second year mathematics program, part taught at Lycée Joffre :

# Reminders of linear algebra and complements of Euclidean geometry

# Advanced probability

# Analysis of functions of one variable

# Functions of several variables

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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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Linear Algebra Complements, Reduction Theory, and Applications 

# Complements of linear algebra, the notion of direct sum

# Determinants

# Reduction: diagonalization and applications to the study of discrete and continuous dynamical 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 (may be modified depending on the year and the time available):

# Matrix Numerical Analysis

# Digital Integration

# numerical solution of diffential equations

# Introduction to the qualitative study of nonlinear differential equations

.

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

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This course is followed only by students of the Material Sciences track of the CPES. It includes a mathematical part and a chemical part, around the notion of symmetry group (of a chemical molecule) and its application to the determination of molecular orbitals by linear combination of atomic orbitals.

Indicative programme:

# Introduction to group theory, finite groups, moldecule symmetry groups

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

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The 2nd year computer science course taught at the Lycée is focused on advanced concepts in algorithmics and programming:

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

# Sort by heap, lower bound on sorting

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

# Basic algorithms (connectedness, depth and width paths, topological sorting)

# Distance calculation (Dijkstra, heap implementation)

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

# Programming in Python

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Program taught at the Lycée Joffre during the 2nd year

# Solid mechanics (static, dynamic, not torsors)

# Electromagnetism in a vacuum

# Diffraction optics, Fourier optics

# Waves and radiation, diffusion of waves.

# Kinetics and thermochemistry, intro to electrochemistry

# Organic chemistry: some reaction mechanisms that lend themselves well to quantum modeling with boundary orbitals

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This course completes the training in computer science by opening up to the study of information systems and databases (design of processing in an information system and the management of relational databases):

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

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

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As in the first year,; This teaching consists of tutored projects with data acquisition, processing and interpretation: the approach combines numerical methods, mathematical ideas and modelling.

The themes of study may evolve from year to year, in order to renew the interests of the students.

See full page

This modern language teaching is focused on the written and oral practice of English, with a particular emphasis on oral expression.

See full page

General culture (epistemology and philosophy):

# history of ideas

# Epistemology of science and digital technology

#argumentatition and communication

See full page

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General culture (epistemology and philosophy):

# history of ideas

# Epistemology of science and digital technology

#argumentatition and communication

See full page

Introduction to the use of data mining methods:

# Motivations, areas of application

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

# Processing on the data (pre/post-processing)

# Supervised learning (Bayes 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, part taught at Lycée Joffre :

# Reminders of linear algebra and complements of Euclidean geometry

# Advanced probability

# Analysis of functions of one variable

# Functions of several variables

See full page

Program taught at the Lycée Joffre during the 2nd year

# Solid mechanics (static, dynamic, not torsors)

# Electromagnetism in a vacuum

# Diffraction optics, Fourier optics

# Waves and radiation, diffusion of waves.

# Kinetics and thermochemistry, intro to electrochemistry

# Organic chemistry: some reaction mechanisms that lend themselves well to quantum modeling with boundary orbitals

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The first part of this course presents the basics of quantum chemistry for chemists and physical chemists. He began by taking up the principles of quantum mechanics and his master equation, the Schrödinger equation. The solution of the Schrödinger equation in simple cases and the notions of wave functions and quantization are presented and illustrated in simple cases. The hydrogen atom is then studied.

The teaching also focuses on approximation methods that make it possible to determine the properties of complex systems where the Schrödinger 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 diagram and chemical bonding is made. The link between molecular geometry and electronic structure will be discussed. This course will then focus on the Huckel method which allows to obtain diagrams of molecular orbitals of π systems. The classical notions of conjugation, delocalization, donor or acceptor character and aromaticity will be studied in this approach. The theory of boundary orbitals is used to rationalize molecular reactivity (cycloaddition, electrocyclization) and molecular geometries.

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

# Notions of populations and random samples.

# Estimators.

#Erreur mean square and bias-variance decomposition.

# Empirical estimators of mean and variance. Construction of estimators by the method of moments. Maximum plausibility.
Interval estimation.

# Hypothesis tests: null hypothesis, alternative hypothesis. Errors of the first and second kinds. Power of a test. Test Statistic, Rejection Region. Examples of classic 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 an immersion in a research laboratory, a bibliographic study, and the realization 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 is an introduction to the use of computer tools in physics: it involves analyzing a phenomenon, idealizing/modeling it, then studying it on a computer. Critical interpretation of results is also included. Examples are chosen in relation to other current subjects in the course.

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This course discusses the theoretical tools for describing distributed and conserved quantities, such as a density, an energy or a charge density.

The first introductory chapter presents the general conservation equation, and the vector analysis tools necessary to understand it, as well as the different fields where this equation comes into play (practically all physics but also chemistry, economics, etc.).

The following chapters are mainly devoted to the case of a dimension of space and a dimension of time (1+1 D). In Chapter 2, we discuss convective transport, and we present the method of characteristics to solve the corresponding first-order quasilinear 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 Smoluchowsky equation, and the derivation of the famous Einstein equation for diffusion.

The course is accompanied by theoretical and numerical tutorials, for example on road traffic and queue modelling.

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The 2nd year computer science course taught at the Lycée is focused on advanced concepts in algorithmics and programming:

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

# Sort by heap, lower bound on sorting

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

# Basic algorithms (connectedness, depth and width paths, topological sorting)

# Distance calculation (Dijkstra, heap implementation)

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

# Programming in Python

See full page

As in the first year,; This teaching consists of tutored projects with data acquisition, processing and interpretation: the approach combines numerical methods, mathematical ideas and modelling.

The themes of study may evolve from year to year, in order to renew the interests of the students.

See full page

This modern language teaching is focused on the written and oral practice of English, with a particular emphasis on oral expression.

See 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 enables 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 extend this knowledge in two directions.

First, we'll generalize this macroscopic thermodynamic 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. Equilibrium breaks and displacements will also be studied.

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

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

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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 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 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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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.

See full page

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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 enables 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 extend this knowledge in two directions.

First, we'll generalize this macroscopic thermodynamic 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. Equilibrium breaks and displacements will also be studied.

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

See full page

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

See full page

See full page

See full page

See full page

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.

See full page

See full page

See full page

See full page

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

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

See full page

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.

See full page

See 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 enables 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 extend this knowledge in two directions.

First, we'll generalize this macroscopic thermodynamic 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. Equilibrium breaks and displacements will also be studied.

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

See full page

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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 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

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

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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.

See full page

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