Elective HAS103H Calculus for PCSI

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This module focuses on experimental techniques in chemistry. The first part will be devoted to an overview of health and safety rules in the chemistry laboratory. Each lab session will be preceded by a preparatory tutorial session. At the end of each lab session, students will be required to complete a lab notebook or report (including analysis and interpretation of results, etc.).

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- Definition of an acid-base reaction.

- Acidity constant.

- Predominance chart.

- Common examples of acids and bases: name, formula, and type—weak or strong—of sulfuric, nitric, hydrochloric, phosphoric, and acetic acids; sodium hydroxide; potassium hydroxide; the hydrogen carbonate ion; and ammonia.

- Buffer solutions.

- Temporal evolution of a chemical system and reaction mechanisms in a closed reactor of uniform composition. Rates of reactant consumption and product formation. Reaction rate 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-life. The half-life of a radioactive nuclide. Document-based approach: Using documents related to radionuclides, explore, for example, issues related to their use, storage, or reprocessing.

- Arrhenius's empirical law; activation energy.

- Reaction mechanisms. Elementary reactions, molecularity, reaction intermediates, transition state. Kinetically determining step, quasi-steady-state approximation (AEQS).

Numerical approach: Use the results of a numerical method to identify approximations of the kinetically decisive step or the quasi-steady state.

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The main objective of this course is to teach you how to formulate and solve simple physics problems. The areas of application are the mechanics of a point particle and geometric optics.

Mechanics of the Material Point:

• Statics: Analysis of Mechanical Systems in Equilibrium.
• Kinematics: the study of the motion of bodies, independent of the causes that produce it.
• Dynamics: the relationships between the causes of motion and motion itself.
• Work and Energy: Work Done by Forces (Conservative and Non-Conservative), the Kinetic Energy Theorem, the Mechanical Energy Theorem, and Their Applications.

Geometric Optics:

• Light Propagation (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 first-year students (L1) who have chosen the PCSI track. It introduces the basic rules of calculation that will enable you to better follow more formal lectures, complete the tutorials, read and understand the books in the university library, and so on. It complements the “Mathematical Tools 1” and “Mathematical Tools 2” courses. This course is primarily based on practice in calculation through exercises. Course reviews are generally brief, and the emphasis is primarily on developing certain automatic skills designed to master, speed up, and streamline the mathematical operations most commonly used in the sciences (at the L1 level). The topics covered include: elementary calculations and operations, trigonometry (particularly geometric trigonometry), complex numbers, vectors and coordinate systems, elementary geometry, basics of polynomials, and basics of statistics and probability.

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This course unit is an introduction to analysis (functions of a real variable) for first-year students in the PCSI program.

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