L2 - General 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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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 course introduces the basic principles of object-oriented modeling and programming. The supporting languages are UML and Java, with possible elements of Python at the end of the semester.

From a modeling point of view, this course focuses on static view modeling, using class and instance diagrams. These diagrams cover the notions of classes, instances, attributes, operations, associations, interfaces and specialization. Their parallel implementation in Java will give them a concrete application, and show in particular the translation of associations in a programming language that doesn't have them. In Java, particular emphasis will be placed on the notions of class, instance, inheritance, instance variable, class variable and method, visibility and package organization, and static and dynamic binding. Data collections widely used in Java will be presented to translate some of the associations (associative lists and dictionaries). These collections will introduce students to the use of generic classes. Implementation of object-oriented programming concepts with Python may be tackled at the end of the semester, depending on progress.

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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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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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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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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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