L2 - CUPGE Maths

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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 course introduces probability spaces, the concepts of probability and independence, and defines discrete and density random variables, with an emphasis on modeling.

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

See the syllabus in the "+ info" tab.

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In this course, we introduce an overview of algebraic structures (ring, ideal, body) before tackling K[X] algebra and defining arithmetic on polynomials, drawing parallels with integer arithmetic seen in L1. Calculations on polynomial functions and rational fractions will be covered (explicit factorizations/decompositions).

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This module completes and formalizes the notions of thermodynamics introduced in EU Thermodynamics 1, by exploring several aspects in greater depth: thermodynamic potentials defined on the basis of Legendre transformations, thermodynamics of open systems, pure-body phase transitions and irreversible processes, with incursions at the microscopic level to provide an insight into the physical foundations of the theory.

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

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This course introduces the main statistical concepts (graphical representation of data, indicators of central tendency and dispersion, relationships between two variables, confidence intervals).

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This course deals with numerical methods applied to linear algebra, and more specifically to matrices. The notions of conditioning, matrix decompositions and iterative methods, and the calculation of eigenvalues will be introduced.

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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 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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