Profile Physics EEA Mechanics Health

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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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