L1 - CUPGE Mechanics

The aim of this course is to clarify the notions of limits of sequences and functions, to deepen the study of sequences and functions, and to study the notions of continuity and derivability of functions, as well as to introduce the main "usual" functions.

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This UE is an introduction to linear algebra (formalized in S2), based on intuition from plane and space geometry. It includes an introduction to matrix calculus.

The UE also introduces the basic language of polynomials.

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This UE aims to work on plane geometry and its objects, as well as demonstrations. It also introduces complex numbers. The geometry and complex numbers sections each account for half of the UE.

- plane geometry objects: points, lines, vectors, angles, circles, triangles, etc.

- geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating with complex numbers

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The aim of this UE is to rework certain analysis concepts from high school, deepening them and developing the practice and interpretation of calculations.

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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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4 tests during the semester in Mathematics and Physics.

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This course follows on from S1 (Analysis I), which introduced continuity and derivability of real functions, usual functions and the study of real sequences.

The aim is to continue and deepen work on sequences and functions, and to introduce the study of numerical series.

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This follows on from S1 (Algebra I), which introduced linear algebra in R², R³ and ^Rn, matrix calculus and polynomials with real coefficients.

The aim is to introduce a few elementary concepts of algebraic structure, and deepen work on vector spaces and linear applications, as well as polynomials.

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After a reminder of classical mechanics, we'll look at the fundamental quantities of thermodynamics: elementary and macroscopic work...
The heat/temperature distinction will be explained at length.
The notion of pressure will be explained macroscopically, but with a microscopic interpretation.
Then, with a historical approach, we'll show how Principles 1 and 2 came to be formulated.

From there, applications will be seen: cycles, perfect/real gas....

Thanks to the introduction of changes of state, examples (critical point) will be shown.
We will finish with thermics: essentially diffusion. Depending on the time available, we'll also cover radiation.

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This course introduces the basic concepts of Newtonian dynamics, complementing the notions of material point dynamics covered in the General Physics course and extending them to non-inertial reference frames, collision theory and variable-mass systems. Basic notions of hydrostatics and perfect fluid dynamics will also be covered.

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This Solid Mechanics course studies articulated systems made up of rigid solids through their movements and equilibrium positions. Concepts covered include velocity fields in solids, link classification and forces. Graphical kinematics and statics are also used.

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This module is an introduction to the use of Python for science students. It covers the basics of algorithms and the Python language, but the approach is primarily geared towards use in the sciences. Examples are given of problems related to other first-year subjects.

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This is a practical course for CUPGE Physics and Mathematics and CUPGE Mechanics students, in common with part of the practical course of the PCSI portal. This practical work will enable students to acquire fundamental concepts from the 3 disciplines (physics, mechanics, EEA), which are essential for further study in the chosen speciality, or for bridging between the other disciplines.

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4 assessment sessions during the semester in Mathematics and Physics/Mechanics.

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