Choice of Profiles

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This course is intended for L1 students who have chosen the PCSI path. It presents the rules of basic calculus which should allow you to better follow the most formal courses, to be able to do the TD, to be able to read and understand the books of the BU, etc. It complements the UE Mathematical Tools 1 and 2. This teaching is essentially based on the training of calculation through exercises. The reminders of the course are generally succinct and the emphasis is mainly put on the acquisition of certain automatisms intended to master, accelerate and fluidify the mathematical manipulations most commonly used in sciences (at the L1 level). The chapters covered are: elementary calculations and manipulations, trigonometry (in particular geometry), complex numbers, vectors and coordinate systems, elementary geometry, rudiments of polynomials, rudiments of statistics and probability.

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The main objective of this course is to teach you to pose and solve simple physics problems. The areas of application are material point mechanics and geometric optics.

Mechanics of the material point :

• Static of forces: studies of mechanical systems in equilibrium.
• Kinematics: study of the movement of bodies independently of the causes that generate them.
• Dynamics: links between the causes of movement and the movement itself.
• Work and energy: work of forces (conservative and non-conservative), kinetic energy theorem, mechanical energy theorem and their applications.

Geometric optics:

• Propagation of light (Fermat's principle, Snell-Descartes laws, index of refraction),
• Image formation and optical systems (stigmatism, Gaussian approximation, mirrors, thin lenses, dispersive systems, centered systems, optical instruments)

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This UE is an introduction to analysis (functions of one real variable) for the first year students of the PCSI portal.

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This UE is an introduction to the differential calculus of functions in several variables. It is intended for first year PCSI students and is an introduction to the mathematical tools used - among others - in thermodynamics.

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- Definition of an acid-base reaction.

- Acidity constant.

- Predominance diagram.

- Common examples of acids and bases: name, formula and nature - weak or strong - of sulfuric, nitric, hydrochloric, phosphoric, acetic acids, soda, potash, hydrogen carbonate ion, ammonia.

- Buffer solutions.

- Temporal evolution of a chemical system and reaction mechanisms in a closed reactor of uniform composition. Rates of disappearance of a reactant and formation of a product. Rate of reaction for a transformation modeled by a single chemical reaction.

- Speed laws: reactions without order, reactions with simple order (0, 1, 2), global order, order

apparent.

- Half-reaction time. Half-life of a radioactive nuclide. Documentary approach: using documents on radionuclides, address, for example, the problems related to their use, storage or reprocessing.

- Empirical Arrhenius law; activation energy.

- Reaction mechanisms. Elementary acts, molecularity, reaction intermediate, transition state. Kinetically determining step, quasi-steady state approximation (QSSA).

Numerical approach: use the results of a numerical method to highlight the approximations of the kinetically determining step or the quasi-stationary state.

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This course is intended for L1 students who have chosen the PCSI path. It presents the rules of basic calculus which should allow you to better follow the most formal courses, to be able to do the TD, to be able to read and understand the books of the BU, etc. It complements the UE Mathematical Tools 1 and 2. This teaching is essentially based on the training of calculation through exercises. The reminders of the course are generally succinct and the emphasis is mainly put on the acquisition of certain automatisms intended to master, accelerate and fluidify the mathematical manipulations most commonly used in sciences (at the L1 level). The chapters covered are: elementary calculations and manipulations, trigonometry (in particular geometry), complex numbers, vectors and coordinate systems, elementary geometry, rudiments of polynomials, rudiments of statistics and probability.

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This course is designed to make first-year students aware of the issues surrounding the use, exploitation and management of the Earth's natural resources.

By way of introduction, an overview identifying the different types of these resources (energy, mineral, water) and the major associated issues (economic and environmental) will be presented.

Different types of resources will then be presented in three stages:

- The notion of mineral resources will be explored in depth by presenting the itinerary of chemical elements, from their creation in the Universe to their storage in the minerals that make up rocks and their use in the technologies employed in everyday life. This aspect will allow the introduction of basic notions in solid state chemistry and mineralogy, illustrated by mineralogy tutorials and practical exercises.

- The problem and the functioning of geological reservoirs trapping natural resources will be addressed by focusing on conventional energy resources (hydrocarbons) and future resources (underground storage of resources, geothermal energy).

- Finally, the major issues related to water resources in the world will be studied in depth. The global cycle of water on Earth will be presented and the essential notions allowing to understand the current major issues will be identified (definitions of an aquifer and a hydrosystem and the main types encountered, chemical interactions between water and rocks and illustration of processes centered on the chemistry of mineral and thermal waters).

Hourly volumes:

CM :18

TD :12

TP :6

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This UE is an introduction to the differential calculus of functions in several variables. It is intended for first year PCSI students and is an introduction to the mathematical tools used - among others - in thermodynamics.

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The aim of the "From molecules to cells" course is to provide L1 students with the basic notions of biology that will be necessary to follow the biochemistry, cell biology, molecular biology, virology and microbiology courses of the following semesters. The structure of biomolecules (nucleic acids, proteins, lipids and sugars) and the structural organization of the cell will be detailed with a view to understanding the origin of life and the organization of viruses, prokaryotic and eukaryotic cells.

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The main objective of this course is to teach you to pose and solve simple physics problems. The areas of application are material point mechanics and geometric optics.

Mechanics of the material point :

• Static of forces: studies of mechanical systems in equilibrium.
• Kinematics: study of the movement of bodies independently of the causes that generate them.
• Dynamics: links between the causes of movement and the movement itself.
• Work and energy: work of forces (conservative and non-conservative), kinetic energy theorem, mechanical energy theorem and their applications.

Geometric optics:

• Propagation of light (Fermat's principle, Snell-Descartes laws, index of refraction),
• Image formation and optical systems (stigmatism, Gaussian approximation, mirrors, thin lenses, dispersive systems, centered systems, optical instruments)

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This module focuses on an approach to experimental techniques in chemistry. A first part will be devoted to the presentation of the rules of hygiene and safety in the chemistry laboratory. Each lab session will be preceded by a preparatory lab session. At the end of each lab session, the student will have to write a laboratory notebook/report (analysis, exploitation of results...).

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This UE is an introduction to analysis (functions of one real variable) for the first year students of the PCSI portal.

See full page

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This course is intended for L1 students who have chosen the PCSI path. It presents the rules of basic calculus which should allow you to better follow the most formal courses, to be able to do the TD, to be able to read and understand the books of the BU, etc. It complements the UE Mathematical Tools 1 and 2. This teaching is essentially based on the training of calculation through exercises. The reminders of the course are generally succinct and the emphasis is mainly put on the acquisition of certain automatisms intended to master, accelerate and fluidify the mathematical manipulations most commonly used in sciences (at the L1 level). The chapters covered are: elementary calculations and manipulations, trigonometry (in particular geometry), complex numbers, vectors and coordinate systems, elementary geometry, rudiments of polynomials, rudiments of statistics and probability.

See full page

The main objective of this course is to teach you to pose and solve simple physics problems. The areas of application are material point mechanics and geometric optics.

Mechanics of the material point :

• Static of forces: studies of mechanical systems in equilibrium.
• Kinematics: study of the movement of bodies independently of the causes that generate them.
• Dynamics: links between the causes of movement and the movement itself.
• Work and energy: work of forces (conservative and non-conservative), kinetic energy theorem, mechanical energy theorem and their applications.

Geometric optics:

• Propagation of light (Fermat's principle, Snell-Descartes laws, index of refraction),
• Image formation and optical systems (stigmatism, Gaussian approximation, mirrors, thin lenses, dispersive systems, centered systems, optical instruments)

See full page

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This UE is an introduction to analysis (functions of one real variable) for the first year students of the PCSI portal.

See full page

This UE is an introduction to the differential calculus of functions in several variables. It is intended for first year PCSI students and is an introduction to the mathematical tools used - among others - in thermodynamics.

See full page