Physical and Chemical Profile

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

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

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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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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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