HAS103H Calculus for PCSI

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This module focuses on experimental techniques in chemistry. The first part will be devoted to presenting health and safety rules in chemistry laboratories. Each practical session will be preceded by a preparatory tutorial session. At the end of each practical session, students will be required to write a laboratory notebook/report (analysis, interpretation 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, and 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. 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. Half-life of a radioactive nuclide. Documentary approach: using documents on radionuclides, address issues related to their use, storage, or reprocessing, for example.

- Arrhenius empirical law; activation energy.

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

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

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

Mechanics of the material point:

• Statics: study of mechanical systems in equilibrium.
• Kinematics: the study of the motion of bodies independently of the causes that produce it.
• Dynamics: links between the causes of motion and motion itself.
• Work and energy: work done by 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, 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 who have chosen the PCSI track. It presents the basic rules of calculation that will enable you to better follow the more formal courses, complete the tutorials, read and understand the books in the university library, etc. It complements the Mathematical Tools 1 and 2 courses. This course is mainly based on calculation practice through exercises. Course reviews are generally brief, and the emphasis is on acquiring certain automatic skills designed to master, accelerate, and streamline the most commonly used mathematical operations in science (at the first-year level). The chapters covered are: elementary calculations and operations, trigonometry (particularly geometric), complex numbers, vectors and coordinate systems, elementary geometry, basics of polynomials, and basics of statistics and probability.

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

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