L1 - CUPGE Mathematics

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

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This course aims to introduce the basic concepts of arithmetic and counting that are useful for beginning a bachelor's degree in mathematics.

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After reviewing classical mechanics, we will discuss the fundamental quantities of thermodynamics: elementary work, macroscopic work, etc.
The distinction between heat and temperature will be explained in detail.
The concept of pressure will be explained macroscopically, while also providing a microscopic interpretation.
Next, using a historical approach, we will show how principles 1 and 2 were formulated.

From there, applications will be examined: cycles, ideal/real gas, etc.

Thanks to the introduction of state changes, examples (critical point) will be presented.
We will conclude with thermodynamics: mainly diffusion. Depending on the time remaining, concepts related to radiation will be presented.

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This module is an introduction to using Python for students pursuing a degree in science. It covers concepts in algorithmics and the Python language, but the approach is primarily geared toward practical applications in science. The examples will therefore focus on issues related to other first-year subjects.

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

The objective is to introduce some basic concepts of algebraic structure and to deepen the study of vector spaces and linear applications, as well as polynomials.

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This Solid Mechanics course focuses on the study of articulated systems consisting of rigid solids through their movements and equilibrium positions. The concepts covered include velocity fields in solids, the classification of connections, and forces. Graphical kinematic and static methods are also used.

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This follows on from S1 (Analysis I), where continuity and differentiability of real functions, common functions, and the study of real sequences were introduced.

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

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

The EU is also introducing the basic language of polynomials.

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The aim of this EU is to revisit certain concepts from high school analysis, exploring them in greater depth and developing calculation skills and the interpretation of calculations.

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Four knowledge assessment sessions during the semester in Mathematics and Physics.

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This unit aims to cover plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The geometry and complex numbers sections each represent half of the unit.

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

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

- work on mathematical proof

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

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The aim of this course is to clarify the concepts of limits of sequences and functions, to deepen the study of sequences and functions, to study the concepts of continuity and differentiability of functions, and to introduce the main "usual" functions.

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