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This course is intended for L1 students who have chosen the PCSI path. It introduces you to the basic rules of calculus, which should enable you to follow the more formal courses more easily, to do the tutorials, to read and understand the books in the BU, and so on. It complements UE Outils Mathématiques 1 and 2. This course is essentially based on calculus training through exercises. Course reminders are generally succinct, and the emphasis is on the acquisition of certain automatisms designed to master, accelerate and fluidify the mathematical manipulations most commonly used in science (at L1 level). Chapters covered include: elementary calculations and manipulations, trigonometry (especially geometry), complex numbers, vectors and coordinate systems, elementary geometry, polynomial rudiments, rudiments of statistics and probability.

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The main aim of this course is to teach you how to pose and solve simple physics problems. The fields of application are material point mechanics and geometrical optics.

Mechanics of the material point :

• Force statics: studies of mechanical systems in equilibrium.
• Kinematics: the 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.

Geometrical optics :

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

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This course is an introduction to analysis (functions of one real variable) for first-year PCSI students.

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This course is an introduction to the differential calculus of functions in several variables. It is intended for first-year PCSI students and provides an introduction to the mathematical tools used - among other things - 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.

- Time 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. Reaction rates 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, tackle issues such as their use, storage and reprocessing.

- Empirical Arrhenius law; activation energy.

- Reaction mechanisms. Elementary acts, molecularity, reaction intermediates, transition states. Kinetically decisive step, quasi-steady-state approximation (QSSA).

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

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This course is intended for L1 students who have chosen the PCSI path. It introduces you to the basic rules of calculus, which should enable you to follow the more formal courses more easily, to do the tutorials, to read and understand the books in the BU, and so on. It complements UE Outils Mathématiques 1 and 2. This course is essentially based on calculus training through exercises. Course reminders are generally succinct, and the emphasis is on the acquisition of certain automatisms designed to master, accelerate and fluidify the mathematical manipulations most commonly used in science (at L1 level). Chapters covered include: elementary calculations and manipulations, trigonometry (especially geometry), complex numbers, vectors and coordinate systems, elementary geometry, polynomial rudiments, 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 will be given of the different types of resource (energy, mineral, water) and the major economic and environmental issues involved.

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

- The notion of mineral resources will be explored in greater 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 introduce basic notions of solid state chemistry and mineralogy, illustrated by mineralogy tutorials and practical exercises.

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

- Finally, the major challenges facing water resources worldwide will be explored in greater depth. The global water cycle on Earth will be presented, and the essential concepts needed to understand today's 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 course is an introduction to the differential calculus of functions in several variables. It is intended for first-year PCSI students and provides an introduction to the mathematical tools used - among other things - in thermodynamics.

See full page

The main aim of this course is to teach you how to pose and solve simple physics problems. The fields of application are material point mechanics and geometrical optics.

Mechanics of the material point :

• Force statics: studies of mechanical systems in equilibrium.
• Kinematics: the 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.

Geometrical optics :

• Propagation of light (Fermat's principle, Snell-Descartes laws, refractive index),
• 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 experimental techniques in chemistry. The first part will be devoted to the presentation of hygiene and safety rules in the chemistry laboratory. Each lab session will be preceded by a preparatory lab session. At the end of each lab session, students will be asked to write up a laboratory notebook/report (analysis, use of results, etc.).

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This course is an introduction to analysis (functions of one real variable) for first-year PCSI students.

See full page

See full page

See full page

This course is intended for L1 students who have chosen the PCSI path. It introduces you to the basic rules of calculus, which should enable you to follow the more formal courses more easily, to do the tutorials, to read and understand the books in the BU, and so on. It complements UE Outils Mathématiques 1 and 2. This course is essentially based on calculus training through exercises. Course reminders are generally succinct, and the emphasis is on the acquisition of certain automatisms designed to master, accelerate and fluidify the mathematical manipulations most commonly used in science (at L1 level). Chapters covered include: elementary calculations and manipulations, trigonometry (especially geometry), complex numbers, vectors and coordinate systems, elementary geometry, polynomial rudiments, rudiments of statistics and probability.

See full page

The main aim of this course is to teach you how to pose and solve simple physics problems. The fields of application are material point mechanics and geometrical optics.

Mechanics of the material point :

• Force statics: studies of mechanical systems in equilibrium.
• Kinematics: the 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.

Geometrical optics :

• Propagation of light (Fermat's principle, Snell-Descartes laws, refractive index),
• 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 course is an introduction to analysis (functions of one real variable) for first-year PCSI students.

See full page

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

See full page