L1 - CUPGE Math

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

Mechanics of the material point :

• Static of forces: studies of mechanical systems in equilibrium.
• Kinematics: 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.

Geometric optics:

• Propagation of light (Fermat's principle, Snell-Descartes laws, index of refraction),
• 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 from plane and space geometry. It includes an introduction to matrix calculus.

The EU also introduces the basic language of polynomials.

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

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4 knowledge control sessions during the semester in Mathematics and Physics.

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This UE aims at working on the geometry of the plane, its objects but also the demonstrations. The UE also aims at introducing complex numbers. The parts geometry and complex numbers represent each half of the UE.

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

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

- work on mathematical demonstration

- introduction of complex numbers, geometric interpretation, calculation with complex numbers

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

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This UE aims to introduce the elementary concepts of arithmetic and enumeration useful for the beginning of the degree in mathematics.

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After some reminders of classical mechanics we will approach the fundamental quantities of thermodynamics: elementary work, macroscopic...
The distinction heat/temperature will be exposed at length.
The notion of pressure will be exposed macroscopically while giving however the microscopic interpretation.
Then with a historical approach we will show how the principles 1 and 2 could have been stated

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

Thanks to the introduction of changes of state, examples (critical point) will be exposed.
We will finish with thermics: essentially diffusion. Depending on the remaining time notions about radiation will be exposed.

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This module is an introduction to the use of Python for students in the sciences. It will cover notions of algorithmics and the Python language, but the approach is primarily oriented towards a usefulness in Science. The examples will be based on problems related to the other first year subjects.

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This course is a continuation of the S1 course (Algebra I) where linear algebra in R², R³ and ^Rn, matrix calculus and polynomials with real coefficients were introduced.

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

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This course in Solid Mechanics studies articulated systems made up of rigid solids through their movements and equilibrium positions. The concepts covered are velocity fields in solids, the classification of links and forces. Methods of kinematics and statics are also used.

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This course follows the S1 course (Analysis I) where continuity and derivability of real functions, usual 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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