L2 - CUPGE Mechanics

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This course is the first step in teaching electromagnetism at university. It covers electrostatics, stationary currents and magnetostatics.

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This course will cover the notions of symmetric group, determinants and will deal with the reduction of endomorphisms in finite dimension (up to Jordan form) and its applications. This is a first step towards spectral analysis.

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In this course, we'll look at the particularities of floating-point calculus and then go into detail on the most common elementary numerical methods for solving non-linear equations, interpolating a function and approximating an integral. Students will learn how to implement an algorithm to solve a numerical analysis problem.

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This is a basic module on the physical properties of materials and on techniques for dimensioning mechanically simple components or systems.

Material properties are covered using tensile testing, binary diagrams and microstructure.

Component dimensioning involves selecting the most suitable material and defining the geometry to ensure static and fatigue strength. Dimensional analysis can also be used to determine the characteristics of a more complex system, based on experiments carried out on a scale model.

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Following on from the analysis course in S2, this course deals with the notion of series with terms of any sign. The Riemann integral will be defined and applied to linear and other differential equations. The integration section will be extended to generalized integrals.

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This unit deals with the study of the mechanics of rigid solids. It is the natural continuation of the unit devoted to the kinematics and statics of rigid solids in L1. In this unit, we'll take a dynamic approach and apply the Fundamental Principle of Dynamics. Writing this principle requires knowledge of the external action torsor, studied in L1, as well as knowledge of the dynamic torsor. The latter can be calculated using the kinetic torsor, which for a rigid solid involves the notion of moment of inertia. The main applications studied in this unit concern rigid solids or simple cases of articulated systems of rigid solids. In addition, we will study the special case of contact and friction actions (Coulomb friction) and the Kinetic Energy Theorem.

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This is a basic module on the physical properties of materials and on techniques for dimensioning mechanically simple components or systems.

Material properties are covered using tensile testing, binary diagrams and microstructure.

Component dimensioning involves selecting the most suitable material and defining the geometry to ensure static and fatigue strength. Dimensional analysis can also be used to determine the characteristics of a more complex system, based on experiments carried out on a scale model.

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This course includes presentations on career opportunities, themed lectures and round-table discussions on the various mathematical professions.

For students with a pre-professionalization AED contract, the UE accompanies their activity in the establishment, providing a few elements to enrich their observation and give them perspective. It also prepares them for the written work they will be required to submit.

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This UE covers the study of mechanical systems as chains of rigid solids linked together by mechanical connections.

Mechanical systems will be studied from a kinematic, sthenic and energetic point of view.

The concepts of torsors, links, the Fundamental Principle of Statics, mass geometry, the Fundamental Principle of Dynamics and energy will be used in the study of mechanical systems to determine link forces and the equations of motion.

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The first-semester course reviews the grammar essential for oral and written communication(tenses and aspect, asking questions, comparisons and superlatives, passive voice) as well as essential general vocabulary(numbers, measurements, shapes); it also includes an introduction to technical vocabulary(basic building materials, plane engine, bike parts, electronic device) through themed lessons and videos in the field of mechanical engineering.

Finally, numerous activities are offered to promote oral expression skills (presentation vocabulary, simulations, role-playing and board games), so that students are able to describe the specific features, functions and uses of a piece of technical equipment of their choice in an oral presentation by groups of two.

S4

Grammatical aspects are limited to a review of modal auxiliaries.

The vocabulary is much more focused on the various elements involved in the design and operation of different types of heat engines, and on emerging technologies(drones, driverless vehicles, 3D-printing).

Students are also expected to produce a CV in English and practice writing emails in a formal style, so as to be prepared for internship or job-seeking situations where fluency in English will either be necessary or an additional skill.

The practice of expression is always the main objective, with an individual oral presentation at the end of the semester of their second-year project in mechanics.

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This course covers an introduction to the topology of R^n, the basics of differential calculus for R^n functions in R and optimization. Parametric curves will also be covered.

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This course covers the notions of function sequences and series, and the various convergences. Integer and Fourier series will also be developed.

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This course provides skills in computer-aided design and mechanism simulation.

In CAD, aspects such as part mode (3D design of a mechanical part), assembly mode (design of a mechanism), drawing of parts or overall drawings will be covered.

The kinematic and dynamic behavior of rigid solid mechanisms will be simulated using CAD/CAM software.

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The first part of this course is designed to consolidate the concepts of magnetostatics and establish the relations between the electromagnetic field at the interface of a plane of charges or currents. We also introduce the expression of Laplace forces (force and moment) acting on volumetric or filiform circuits. The second part is devoted to the properties of fields and potentials in the variable regime. After introducing Faraday's law describing induction phenomena, we establish Maxwell's time-dependent equations. An energetic treatment allows us to define the electric and magnetic energies, as well as the Poynting vector. We apply these concepts to various examples, such as electromechanical conversion or induction heating via eddy currents. A final chapter is devoted to the equations of field and potential propagation, and their application in vacuum-like systems, as well as in perfect conductors and insulators. The notion of skin depth is also introduced.

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This course is an introduction to bilinear algebra, covering Euclidean and Hermitian spaces. It covers isometries, duality, quadratic forms and endomorphisms.

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