Choice HAS103H Calculus for PCSI

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

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