# AAT B2

## Description

Identify appropriate mathematical, physical or computing models and adapt them to similar situations, whether or not they relate to the same discipline.

## Progression

M1 ():

M2 ():

M3 ():

## AAv List (195)

01_XBMAT-AAv1 (25H): At the end of this course, students will be able to use the relevant trigonometric tools to model an engineering situation (e.g. building height, navigation, astronomy, tidal studies, waves, sounds, etc.), and then solve the problem.

01_XBMAT-AAv2 (30H): At the end of this course, each student knows how to write a complex number in algebraic and exponential forms and solve certain equations with complex solutions (second degree equations with complex coefficients or reverting to it, equation reverting to the search for an nth root).

01_XBMAT-AAv3 (35H): At the end of this course, each student knows how to implement fundamental analysis techniques concerning the study of numerical functions of the real variable (limits , derivation, basic integration) to solve optimization problems with a real variable in particular. He knows how to apply these techniques to solve simple concrete problems.

01_XBMAT-AAv5 (12H): At the end of this course, each student knows how to study a parameterized curve and draw it. He also knows how to configure an elementary curve (segment, circle, etc.). Precisely :

01_XBMAT-AAv6 (19H): At the end of this course, students will be able to factor certain polynomials and decompose a rational fraction into simple elements in $\mathbb{R}(X)$ or $\mathbb{C}(X)$.

01_XBMAT-AAv7 (17H): At the end of this course, students will be able to model and solve an elementary problem involving discrete probabilities.

01_XBALR-AAv1 (8H): At the end of the 1st semester, students are able to execute step by step algorithms comprising variables, conditional, iterative structures and function calls and in determine their results without error

01_XBALR-AAv2 (40H): At the end of the 1st semester, students must be able to construct algorithms comprising variables, conditional, iterative structures and function calls responding to a need expressed by a simple statement

01_XBALR-AAv4 (15H): At the end of the 1st semester, students must be able to propose reusable functions explicitly in different contexts of use

01_XBALR-AAv6 (8H): At the end of the 1st semester, students must be able to measure and compare the complexity in terms of calculation time of the algorithms provided

01_XCELE-AAv3 (72H): At the end of semester 1, students will be able to solve a given problem on a diagram they have never seen before, using the method of their choice if it is not imposed. The student will be able to determine the literal expression of any electrical quantity in a circuit as a function of its components. The student will be able to determine the operating point of a combination of dipoles operating in continuous operation, both graphically and analytically. To adapt to complex dipole structures not previously seen, they will use Thevenin/Norton modeling to represent the active dipole(s) of the combination before putting it into an equation. They will be able to evaluate power exchanges between receivers and generators, explaining their reasoning and justifying their results.

02_XSZG2-AAv 1 (24H): At the end of General Zone 2, students are able, on a given example, to reveal the constants (of time, of natural pulsation, of factor damping, gain), to calculate them analytically or numerically, to relate them to the physical properties of the systems and their temporal evolution.

02_XSZG2-AAv2 (14H): At the end of ZG2, the group of students is able to correctly measure and identify the influence of physical parameters (Electronics: R , L, C - Mechanics: k, m, lambda) on the response of the system (damping, pseudo-period and natural frequency) of the 2nd order in two different ways: using simulation software OR physically with experimental models to be built . All the measurements and simulation results will be summarized in a document to be completed.

02_XBALG-AAv1 (18H): At the end of this course, the student knows how to implement the notions relating to vector spaces (vector subspaces, free family, generator, base) and is able to identify a vector space.

02_XBALG-AAv2 (15H): At the end of this teaching, the student knows how to recognize or show that an application is linear, determine its kernel and its image. In finite dimension the student is able to explain the matrix of a linear application in a base.

02_XBALG-AAv3 (14H): At the end of this course, the student masters matrix calculation (sum, product, inverse, determinant) and is able to recognize an algebra problem linear in a concrete situation.

02_XBALG-AAv4 (15H): At the end of this course, the student knows how to diagonalize a square matrix and geometrically interpret the characteristic elements (eigenvalues, eigenvectors, eigensubspaces) . He can apply this to situations relating to the resolution of a system of recurring sequences, the calculation of the power of a matrix, the resolution of a linear differential system with constant coefficients.

02_XBANA-AAv1 (18H): At the end of this course, each student knows how to implement integral calculation techniques in different situations (calculation of areas, volumes, arc lengths curve) and different fields or disciplines related to engineering (in mechanics, electronics, physics, probability).

02_XBANA-AAv2 (18H): At the end of this course, each student knows how to solve a physical problem modeled by first and second order differential equations.

02_XBANA-AAv3 (8H): At the end of this course, each student is able to model and solve an elementary continuous probability problem.

02_XCOPT-AAv1 (4H): At the end of the course, students must state the conditions of validity of geometric optics and calculate the characteristic parameters of a light wave (wavelength, frequency , speed, energy), as well as explain the distribution of electromagnetic waves in the spectral domain.

02_XCOPT-AAv2 (9.5H): At the end of the course, students are able to characterize the angular conditions of reflection on and refraction (Snell-Descartes law) through a diopter and to distinguish the regimes guiding and non-guiding in optical fibers (total reflection condition).

02_XCOPT-AAv3 (3H): At the end of the course, students are able to determine the refractive index of a material by measuring the refraction of a light ray in this material.

02_XCOPT-AAv4 (14H): At the end of the course, students are able to construct images produced by simple optical instruments (plane and spherical diopters, plane and spherical mirrors, lenses thin) and to determine the nature (real or virtual) of the foci of such optical instruments, as well as the nature of the object and the image.

02_XCOPT-AAv5 (9.5H): At the end of the course, students will be able to characterize by calculation (positions of an object and its image, magnification or magnification, resolution precision, etc.) the formation of images by complex optical instruments (eye, telescope, microscope, camera, etc.)

02_XCCIN-AAv1 (12H): At the end of this course, the student will be able to write logical equations and construct the diagram of a combinatorial circuit with elementary logic gates, from of its description (textual formulation, operating table, chronogram, etc.).

02_XCCIN-AAv2 (8H): At the end of this course, the student will be able to use a technical sheet of a combinational circuit and to correctly exploit electrical information (voltages, currents ) and temporal order (propagation time) in order to allow its integration into a digital system.

02_XCELE-AAv2 (30H): At the end of the 2nd semester, the student will be able to qualitatively and analytically determine the temporal expression of the response of a circuit of the 1st order for a given excitation. He will be able to exploit the properties of the passive components used to determine the reactions of the circuit to input discontinuities and in continuous steady state. He will be able to differentiate what constitutes transient phenomena, evaluate their duration and determine the expression of the output signal of the circuit in steady state. The result can always be sketched in time agreement with the input signal.

02_XCELE-AAv3 (30H): At the end of the 2nd semester, the student will be able to describe the properties of a system according to the frequency of the input signals. To do this, he will have determined the complex transfer function of each circuit and identified in it the parameters allowing the drawing of the Bode diagram of the system. He will verify his result using the properties of passive dipoles as a function of frequency making it possible to simplify the diagram and obtain the equations of the asymptotes of the Bode diagram.

02_XDIPI-AAv3 (10H): An S2 student, at the end of IPI, is capable of mastering time within a program.

03_XBANA-AAv1 (15H): At the end of this course, each student is able to determine the parametric and Cartesian equations of a family of curves using the correspondence between geometric properties and their analytical counterparts. Conversely, it is capable of recognizing and representing a simple surface described by equations.

03_XBANA-AAv2 (15H): At the end of this course, each student is able to prove the continuity or non-continuity of a function of 2 or 3 variables, calculate first and second partial derivatives in particularly in situations of function composition and variable change.

03_XBANA-AAv3 (15H): At the end of this course, each student is able to carry out, independently, the research and classification of critical points (and possible extrema) according to the sign of the determinant of Hessiana. It will be able to suggest avenues in the case not determined by the classification.

03_XBANA-AAv4 (15H): At the end of this teaching, in relation to physics situations such as the study of vibrating strings or the evolution of the temperature of a bar, each student is able to solve elementary differential equations (1st and 2nd order linear), to apply or propose a change of variable to reduce to the simple case, to particularize the solutions verifying boundary conditions.

03_XBANA-AAv5 (15H): At the end of this course, each student knows how to determine, through calculation, the law of a function of a VA or a pair of VAs as well as the marginal laws which result from it and apply it to probability calculations.

03_XBELE-Aav1 (30H): At the end of the semester, an S3 student will be able to explain the operation of a given circuit containing diodes, bipolar or field-effect transistors, optocouplers, operational amplifiers, make hypotheses about the operation of non-linear elements, and verify them by calculating circuit currents and voltages and/or LTSpice simulation, determine input-output relations analytically and verify them by LTSpice simulation.

03_XBELE-Aav2 (15H): At the end of the semester, an S3 student will be able to identify the essential characteristics of an ADC and a DAC (quantum, full scale, conversion time).

03_XEMG1-AAv1 (14.5H): Based on a given kinematic diagram, the student will be able to analyze it (explaining the various possible movements between parts). They will then be able to correctly* associate a reference frame with each kinematic sub-assembly, indicate the parameterization in the plane figures and then correctly* determine the rotation speed vectors.

03_XEEUC-AAv1 (25H): At the end of the teaching, each student knows how to implement the relevant mathematical tools to define and calculate an orthogonal projection on a finite orthonormal family, in order to solve problems of approximation, in any type of vector space provided with a scalar product.

03_XEEUC-AAv2 (25H): At the end of the teaching, each student knows how to implement the relevant mathematical tools to construct an orthonormal basis from a finite family of vectors, in a vector space provided of a scalar product.

04_XBANA-AAv1 (25H): At the end of this course, each student knows how to calculate double and triple integrals, and use these notions to determine volumes, surface areas, coordinates of a center of inertia or the inertia matrix of a solid.

04_XBANA-AAv2 (10H): At the end of this course, each student knows how to determine the nature (convergent or divergent) of a generalized integral and calculate the value of a convergent integral in different fields (probability, electromagnetism, signal theory, etc.).

04_XBANA-AAv3 (15H): At the end of this course, each student knows how to determine the circulation of a vector field (resp. the curvilinear integral of a differential form) and apply this notion in different situations (electric field, magnetic field, speed of a fluid at a point, etc.).

04_XBEUC-AAv1 (25H): At the end of the teaching, each student knows how to implement the relevant mathematical tools to define and calculate an orthogonal projection on a finite orthonormal family, in order to solve problems of approximation, in any type of vector space provided with a scalar product.

04_XBEUC-AAv2 (25H): At the end of the teaching, each student knows how to implement the relevant mathematical tools to construct an orthonormal basis from a finite family of vectors, in a vector space provided of a scalar product.

04_XCELE-AAv1 (15H): At the end of the 4th semester of electronics, the student will be able to determine in analytical or numerical form the characteristic parameters of a circuit of the 2nd order according to the value of its components by first determining its transfer function.

04_XCELM-AAv1 (20H): At the end of the semester, students will be able to precisely describe the physical properties (Coulomb forces, electric field, electric potential) induced in a vacuum by simple charge distributions point, linear, surface and volume statics.

04_XCELM-AAv2 (19H): At the end of the semester, students will be able to carefully explain, through simple and documented calculations and/or diagrams and/or precise descriptions, physical phenomena (electric field , electric potential, flow of the electric field) generated by distributions of point, linear, surface or volume electric charges both in a vacuum, on the passage of charged surfaces, as well as on the surfaces and inside conductors in equilibrium electrostatics and dielectrics.

04_XCELM-AAv4 (10H): At the end of the semester, the student must be able to determine the direction, the direction and the module of the magnetic induction vector generated by a system formed of rectilinear wires, turns and solenoids each carrying a current.

04_XSZG4-AAv2 (60H): On the basis of working hypotheses, the student can solve the problem posed and validate each step;

04_XBANA-AAv1 (20H): At the end of this course, each student will be able to calculate double and triple integrals, and use these concepts to determine volumes, surface areas, the coordinates of a center of inertia or the inertia matrix of a solid.

04_XBANA-AAv2 (8H): At the end of this course, students will be able to determine the nature (convergent or divergent) of a generalized integral and calculate the value of a convergent integral in various fields (probability, electromagnetism, signal theory, etc.).

04_XBANA-AAv3 (8H): At the end of this course, students will be able to calculate probabilities for pairs of continuous (joint law, marginal laws) or discrete random variables.

04_XBANA-AAv4 (9H): At the end of this course, each student knows how to determine the circulation of a vector field (resp. the curvilinear integral of a differential form) and apply this notion in different situations (electric field, magnetic field, speed of a fluid at a point, etc.).

04_XBPST-AAv1 (25H): At the end of the Probability and Statistics course, students will be able to use classical probability laws (discrete and continuous) and approximation results (law of large numbers, central limit theorem) to model a situation with one or more precisely defined random variables and determine their law.

04_XBPST-AAv2 (20H): At the end of the Probability and Statistics course, students will be able to answer computational questions about random variables, including calculating their distribution.

04_XBPRG-AAV1 (24H): At the end of this course, a student is able to follow programming rules and practices imposed on them.

04_XDELE-AAv1 (15H): At the end of the 4th semester of electronics, the student will be able to determine in analytical or numerical form the characteristic parameters of a circuit of the 2nd order according to the value of its components by first determining its transfer function.

04_XDELM-AAv1 (20H): At the end of the semester, students will be able to precisely describe the physical properties (Coulomb forces, electric field, electric potential) induced in a vacuum by simple charge distributions point, linear, surface and volume statics.

04_XDELM-AAv2 (19H): At the end of the semester, students will be able to carefully explain, through simple and documented calculations and/or diagrams and/or precise descriptions, physical phenomena (electric field , electric potential, flow of the electric field) generated by distributions of point, linear, surface or volume electric charges both in a vacuum, on the passage of charged surfaces, as well as on the surfaces and inside conductors in equilibrium electrostatics and dielectrics.

04_XDELM-AAv4 (10H): At the end of the semester, the student must be able to determine the direction, the direction and the module of the magnetic induction vector generated by a system formed of rectilinear wires, turns and solenoids each carrying a current.

04_XDTHE-AAv2 (13H): At the end of the semester, the S3 student will be able to calculate in detail the distribution of the 1D temperature in steady and transient regimes, in a solid subjected to conduction and/or external heat sources or exchanges.

05_XBOPT-AAv1 (9H): At the end of the course, students of semester 5 are able to calculate the characteristic parameters of a monochromatic plane electromagnetic wave (wavelength, frequency, phase speed and speed of group, intensity, electric and magnetic fields) in a linear, homogeneous, isotropic and transparent dielectric medium where it propagates and to characterize its structure.

05_XBOPT-AAv2 (8H): At the end of the course, students are able to determine the polarization state of a plane electromagnetic wave from the parametric expression of the electric field of the wave and vice versa

05_XBOPT-AAv3 (13H): At the end of the course, students are able to describe and analyze the change in polarization state of an electromagnetic wave using polarimetry instruments (birefringent plates, rectilinear polarizer ideal, and their combination).

05_XBOPT-AAv4 (7.5H): At the end of the course, students are able to calculate and characterize the Fresnel coefficients in amplitude and intensity relating to the reflection and transmission of a plane wave on a diopter plane and determine the polarization state of the reflected wave and the transmitted wave.

05_XBOPT-AAv5 (9H): At the end of the course, students are able to calculate the interference of electromagnetic waves of the same frequency, polarized or non-polarized.

05_XBOPT-AAv6 (16H): At the end of the course, students are able to characterize and analyze interferometric setups (photodetection of an optical beat, Young interferometer, Mach-Zehnder and Fabry interferometers -Perot, anti-reflective layer, etc.) and to explain and interpret phenomena linked to interference (Newton rings, iridescence, etc.).

05_XBOPT-AAv7 (7.5H): At the end of the course, students are able to state the principles of diffraction, analyze the distribution of light intensity due to diffraction through various apertures (slit rectangular, circular slit, diffraction gratings), as well as describing the phenomena linked to diffraction (Airy spot, resolving power limited by diffraction, etc.).

05_XDASA-AAv2 (15H): At the end of the semester, students will be able to use mathematical tools such as the Laplace transform to characterize temporal behavior (static deviation, overshoot, response time) d a closed-loop SLIT system.

05_XDSIG-AAv1 (4H): At the end of the semester, the student must be able to recognize usual continuous signals (gate, triangle, step, ramp, harmonic, exponential, impulse) and model them using an analytical expression.

05_XDSIG-AAv2 (4H): At the end of the semester, the student must be able to apply and identify transformations on the temporal representation of analog continuous signals (superposition, shift, scale transformation and amplitude).

05_XDSIG-AAv3 (50H): At the end of the semester, the student must be able to analyze the frequency content of continuous signals, composed of usual signals, using the Fourier transformation. This spectral analysis consists in particular of: (1) Manipulating the complex formalism of the Fourier transformation (positive and negative frequencies) and finding the real, physically interpretable form of the decomposition (amplitude, phase, energy spectra and power); (2) Identify whether the signal is more or less rich in low and high frequencies and make the connection with its temporal form; (3) Determine the decay rate of the spectrum; (4) Identify particular frequencies according to the nature of the spectrum (discrete/continuous); (5) Determine spectrally (and temporally) the mean value, rms value, energy and power of the signal; (6) Determine the percentage of signal energy or power located in a given frequency band; (7) Synthesize a real signal by imposing a percentage of its total average power. The student will have consulted and assimilated the scientific resources necessary to complete the work to be carried out.

05_XDSIG-AAv4 (8H): At the end of the semester, the student must be able to analyze using a spectrum analyzer the frequency content of usual signals and real signals in sensor output. The student will have consulted and assimilated the scientific resources necessary to complete the work to be carried out.

05_XDSIG-AAv5 (12H): At the end of the semester, the student must be able to predict the response of a SLIT system (continuous, linear and time invariant system) to a model input ( combination of usual signals) using temporal convolution, or frequency filtering.

05_XDSIG-AAv6 (12H): At the end of the semester, the student must be able to carry out the temporal and frequency analysis of signals at the input and output of a continuous system of convolution-filtering (SLIT) and make the link with the frequency response and the amplitude and phase distortions of such a system. Analyzing here means in particular: (1) Making the link between the impulse response of a SLIT and its bandwidth; (2) Determine the amplitude and phase distortion, phase delay and group delay of classical transfer functions of order 1 and 2.

06_XBROP-AAv1 (15H): By the end of the course, all students will be able to apply the relevant mathematical tools correctly to solve problems involving the calculation of optimal paths (depth, width, shortest path via Ford or Dijkstra) in directed or undirected, valuated or valueless graphs. Correctly means here:

06_XBROP-AAv2 (15H): At the end of the course, each student will be able to correctly apply the relevant mathematical tools to solve flow maximisation problems in a transport network, taking possible costs into account. Correctly means here:

06_XBSTA-AAv1 (25H): At the end of this course, each student will be able to carry out a parametric point and confidence interval estimation problem in the context of sampling.

06_XBSTA-AAv2 (26H): At the end of this course, each student will be able to carry out a hypothesis test (test of independence, suitability for a law, proportion, mean and variance).

06_XDASN-AAv3 (10H): Students will be able to digitise a common analogue corrector (P, PI, PID) using a discretisation strategy and express its digitised version as a Z transfer function or recurrence equation.

06_XDSIG-AAv1 (3H): At the end of the semester, the student should be able to establish the analytical expression of discrete-time signals and systems (this course is limited to the case of regular sampling).

06_XDSIG-AAv2 (9H): At the end of the semester, the student should be able to perform the spectral analysis of sampled signals and systems (discrete-time and continuous-frequency analysis) based on the concept of the Fourier transform in the sense of distributions.

06_XDSIG-AAv3 (13H): At the end of the semester, the student must be able to analyse and design a digitisation-reconstruction chain for an analogue DC signal. The digital signal processing concepts to be put into practice are in particular : (1) Shannon's theorem on the choice of sampling frequency (oversampling and undersampling) and the spectral properties derived from it; (2) Issues on the choice of anti-aliasing filter parameters to be able to minimise overlap noise; (3) The issues involved in choosing the quantisation method and the number of digitiser bits to maximise the signal-to-noise ratio; (4) The issues involved in choosing the parameters of the low-pass reconstruction filter (interpolator filter) to correctly reproduce the analogue DC signal.

06_XDSIG-AAv5 (12H): At the end of the semester, the student must be able to carry out a complete analysis (time response, frequency response, stability study, number of coefficients in the recurrence equation, number of delay elements, fluence graph, digital sensitivity and calculation noise) of a digital filter of the RIF or RII type using discrete convolution and the Z transfer function.

06_XEMOD-AAv1 (10H): Correctly produce a mechanical model of a multi-ddl system from a meaningful example.

06_XEMOD-AAv3 (15H): Correctly produce a numerical model of the system (on a machine).

06_XSZG6-AAv1 (25H): design the prototype of a non-mobile mechatronic system with two self-controlled axes

06_XBROP-AAv1 (15H): By the end of the course, all students will be able to apply the relevant mathematical tools correctly to solve problems involving the calculation of optimal paths (depth, width, shortest path via Ford or Dijkstra) in directed or undirected, valuated or valueless graphs. Correctly means here:

06_XBROP-AAv2 (15H): At the end of the course, each student will be able to correctly apply the relevant mathematical tools to solve flow maximisation problems in a transport network, taking possible costs into account. Correctly means here:

06_XBSTA-AAv1 (25H): At the end of this course, each student will be able to carry out a parametric point and confidence interval estimation problem in the context of sampling.

06_XBSTA-AAv2 (26H): At the end of this course, each student will be able to carry out a hypothesis test (test of independence, suitability for a law, proportion, mean and variance).

06_XDASN-AAv3 (10H): Students will be able to digitise a common analogue corrector (P, PI, PID) using a discretisation strategy and express its digitised version as a Z transfer function or recurrence equation.

06_XDSIG-AAv1 (3H): At the end of the semester, the student should be able to establish the analytical expression of discrete-time signals and systems (this course is limited to the case of regular sampling).

06_XDSIG-AAv2 (9H): At the end of the semester, the student should be able to perform the spectral analysis of sampled signals and systems (discrete-time and continuous-frequency analysis) based on the concept of the Fourier transform in the sense of distributions.

06_XDSIG-AAv3 (13H): At the end of the semester, the student must be able to analyse and design a digitisation-reconstruction chain for an analogue DC signal. The digital signal processing concepts to be put into practice are in particular : (1) Shannon's theorem on the choice of sampling frequency (oversampling and undersampling) and the spectral properties derived from it; (2) Issues on the choice of anti-aliasing filter parameters to be able to minimise overlap noise; (3) The issues involved in choosing the quantisation method and the number of digitiser bits to maximise the signal-to-noise ratio; (4) The issues involved in choosing the parameters of the low-pass reconstruction filter (interpolator filter) to correctly reproduce the analogue DC signal.

06_XDSIG-AAv5 (12H): At the end of the semester, the student must be able to carry out a complete analysis (time response, frequency response, stability study, number of coefficients in the recurrence equation, number of delay elements, fluence graph, digital sensitivity and calculation noise) of a digital filter of the RIF or RII type using discrete convolution and the Z transfer function.

06_XEMOD-AAv1 (10H): Correctly produce a mechanical model of a multi-ddl system from a meaningful example.

06_XEMOD-AAv3 (15H): Correctly produce a numerical model of the system (on a machine).

05AOBMAT-AAv1 (27H): The student masters the basics of integral calculus: (primitive search, simple definite integrals and multiple integrals).

05AOBMAT-AAv3 (27H): At the end of this course, students will be able to apply the concepts relating to vector spaces (vector subspaces, free family, generatrix, base) and will be able to identify a vector space.

05AOBMAT-AAv4 (21H): At the end of this course, students will be able to recognise or show that an application is linear and to determine its kernel and image. In finite dimension, students will be able to explain the matrix of a linear application in a basis.

05AOBMAT-AAv5 (21H): At the end of this course, students will have mastered matrix calculus (sum, product, inverse, determinant) and will be able to recognise a linear algebra problem in a concrete situation.

05AOCCIN-AAv1 (12H): At the end of the first three days of the course, students will be able to describe the positions, velocities and accelerations of a moving point in space, using the appropriate mathematical entities:

05AOCCIN-AAv2 (9H): At the end of the 4th and 5th days of the course, students will be able to determine the nature of point movements and apply the laws of composition of speeds and accelerations:

05AOCCIN-AAv3 (9H): At the end of the last two days of the course, students will be able to determine the speeds and accelerations in a solid, whatever the point chosen, from the laws of the solid and the expression of the kinematic torso:

05AODPRC-AAv1 (6H): At the end of the programming course, a fifth semester student will be able to execute step by step algorithms comprising variables, conditional, iterative structures and function calls and determine their results without error

05AODPRC-AAv2 (30H): At the end of the programming course, a fifth semester student will be able to construct algorithms comprising variables, conditional, iterative and call structures. functions responding to a need expressed by a simple statement

05AODPRC-AAv4 (8H): At the end of the programming course, a fifth semester student will be able to propose reusable functions explicitly in different contexts of use

05AOGASA-AAv2 (15H): At the end of the semester, students will be able to use mathematical tools such as the Laplace transform to characterize temporal behavior (static deviation, overshoot, response time) of a closed-loop SLIT system.

05AOGELM-AAv1 (14H): At the end of the semester, students will be able to precisely describe the physical properties (Coulomb forces, electric field, electric potential) induced in a vacuum by simple distributions of static point, line, surface and volume loads.

05AOGELM-AAv2 (13H): At the end of the semester, students will be able to carefully explain, through simple and documented calculations and/or diagrams and/or precise descriptions, physical phenomena (field electric, electric potential, flow of the electric field) generated by distributions of point, linear, surface or volume electric charges both in a vacuum, on the passage of charged surfaces, as well as on the surfaces and inside conductors in electrostatic and dielectric balance.

05AOGELM-AAv4 (6H): At the end of the semester, the student must be able to determine the direction, the direction and the module of the magnetic induction vector generated by a system formed of rectilinear wires, turns and of solenoids each carrying a current.

05AOGSIA-AAv1 (4H): At the end of the semester, the student must be able to recognize usual continuous signals (gate, triangle, step, ramp, harmonic, exponential, impulse) and model them by an analytical expression.

05AOGSIA-AAv2 (4H): At the end of the semester, the student must be able to apply and identify transformations on the temporal representation of analog continuous signals (superposition, shift, scale transformation and amplitude).

05AOGSIA-AAv3 (50H): At the end of the semester, the student must be able to analyze the frequency content of continuous signals, composed of usual signals, using the Fourier transformation. This spectral analysis consists in particular of: (1) Manipulating the complex formalism of the Fourier transformation (positive and negative frequencies) and finding the real, physically interpretable form of the decomposition (amplitude, phase, energy spectra and power); (2) Identify whether the signal is more or less rich in low and high frequencies and make the connection with its temporal form; (3) Determine the decay rate of the spectrum; (4) Identify particular frequencies according to the nature of the spectrum (discrete/continuous); (5) Determine spectrally (and temporally) the mean value, rms value, energy and power of the signal; (6) Determine the percentage of signal energy or power located in a given frequency band; (7) Synthesize a real signal by imposing a percentage of its total average power. The student will have consulted and assimilated the scientific resources necessary to complete the work to be carried out.

05AOGSIA-AAv4 (8H): At the end of the semester, the student must be able to analyze the frequency content of usual signals and real signals using a spectrum analyzer at the sensor output. The student will have consulted and assimilated the scientific resources necessary to complete the work to be carried out.

05AOGSIA-AAv5 (12H): At the end of the semester, the student must be able to predict the response of a SLIT system (continuous, linear and time invariant system) to a model input (combination of usual signals) using temporal convolution, or frequency filtering.

05AOGSIA-AAv6 (12H): At the end of the semester, the student must be able to carry out the temporal and frequency analysis of signals at the input and output of a continuous system of convolution-filtering (SLIT) and make the link with the frequency response and the amplitude and phase distortions of such a system. Analyzing here means in particular: (1) Making the link between the impulse response of a SLIT and its bandwidth; (2) Determine the amplitude and phase distortion, phase delay and group delay of classical transfer functions of order 1 and 2.

06POBMAT-AAv1 (18H): At the end of this course, students will be able to diagonalize a square matrix and geometrically interpret the characteristic elements (eigenvalues, eigenvectors, eigensubspaces). They will be able to apply this to situations such as solving a system of recurrent sequences, calculating the power of a matrix or solving a linear differential system with constant coefficients.

06POBMAT-AAv2 (15H): At the end of this course, each student will be able to prove the continuity or non-continuity of a function of 2 or 3 variables, calculate partial first and second derivatives, particularly in situations involving the composition of functions and changes of variables.

06POBMAT-AAv3 (18H): At the end of this course, each student will be able to search for and classify critical points (and possible extrema) independently according to the sign of the Hessian determinant. He/she will be able to suggest avenues in the case not determined by the classification.

06POBMAT-AAv4 (15H): At the end of this course, in relation to physics situations such as the study of vibrating strings or the evolution of the temperature of a bar, each student will be able to solve elementary differential equations (linear 1st and 2nd order), to apply or propose a change of variable in order to return to the simple case, and to specify solutions verifying boundary conditions.

06POCOPT-AAv1 (6.5H): By the end of the course, students in semester 5 will be able to calculate the characteristic parameters of a monochromatic electromagnetic plane wave (wavelength, frequency, phase velocity and group velocity, intensity, electric and magnetic fields) in a linear, homogeneous, isotropic and transparent dielectric medium in which it propagates and to characterize its structure.

06POCOPT-AAv2 (6H): At the end of the course, students will be able to determine the polarization state of a plane electromagnetic wave from the parametric expression of the wave's electric field and vice versa.

06POCOPT-AAv3 (9H): At the end of the course, students will be able to describe and analyse the change in polarisation state of an electromagnetic wave using polarimetric instruments (birefringent plates, ideal rectilinear polariser, and their combination).

06POCOPT-AAv4 (5.25H): By the end of this course, students will be able to calculate and characterize the Fresnel coefficients in amplitude and intensity for the reflection and transmission of a plane wave on a plane diopter and determine the polarization state of the reflected and transmitted waves.

06POCOPT-AAv5 (7H): At the end of the course, students will be able to calculate the interference of electromagnetic waves of the same frequency, polarized or unpolarized.

06POCOPT-AAv6 (12H): At the end of the course, students will be able to characterise and analyse interferometric set-ups (photodetection of an optical beat, Young's interferometer, Mach-Zehnder and Fabry-Perot interferometers, anti-reflection layer, etc.) and explain and interpret phenomena related to interference (Newton rings, iridescence, etc.).

06POCOPT-AAv7 (4.25H): At the end of the course, students will be able to state the principles of diffraction, analyse the distribution of light intensity due to diffraction through various apertures (rectangular slit, circular slit, diffraction gratings) and describe phenomena related to diffraction (Airy spot, resolving power limited by diffraction, etc.).

06POEASN-AAv3 (10H): Students will be able to digitise a conventional analogue corrector (P, PI, PID) using a discretisation strategy and express its digitised version in the form of a Z transfer function or a recurrence equation.

06POESIN-AAv1 (3H): At the end of the semester, the student should be able to establish the analytical expression of discrete-time signals and systems (this course is limited to the case of regular sampling).

06POESIN-AAv2 (9H): At the end of the semester, the student should be able to perform the spectral analysis of sampled signals and systems (discrete-time and continuous-frequency analysis) based on the concept of the Fourier transform in the sense of distributions.

06POESIN-AAv3 (9H): At the end of the semester, students should be able to analyse and design a digitisation-reconstruction chain for continuous analogue signals. The digital signal processing concepts to be put into practice are in particular: (1) Shannon's theorem on the choice of sampling frequency (oversampling and undersampling) and the spectral properties derived from it; (2) The issues involved in choosing the parameters of the anti-aliasing filter to be able to minimise the overlapping noise; (3) The issues involved in choosing the parameters of the low-pass reconstruction filter (interpolator filter) to correctly reconstruct the analogue DC signal.

06POESIN-AAv5 (12H): At the end of the semester, the student must be able to carry out a complete analysis (time response, frequency response, stability study, number of coefficients in the recurrence equation, number of delay elements, fluence graph, digital sensitivity and calculation noise) of a digital filter of the RIF or RII type using discrete convolution and the Z transfer function. This analysis should lead to an appropriate and argued choice with regard to the signal to be filtered.

06POGROP-AAv1 (15H): At the end of the course, each student will be able to correctly apply the relevant mathematical tools to solve problems involving the calculation of optimal paths (depth, width, shortest via Ford or Dijkstra) in directed or undirected, valuated or valueless graphs.

06POGROP-AAv2 (15H): At the end of the course, each student will be able to correctly apply the relevant mathematical tools to solve flow maximisation problems in a transport network, taking possible costs into account.

07_X-IPS-AAv4 (26H): General knowledge of instrumentation. At the end of this course, the seventh semester student will have a general knowledge of instrumentation.

07_X-IPS-AAv5 (12H): Comparison of experimental results with theoretical calculations or simulations. At the end of this course, the seventh semester student will be able, in a group of 4 to 5 students, to make the link between experimental data that they have produced and theoretical results obtained by calculation and/or numerical simulation.

07_X-SEN-AAv3 (30H): At the end of semester 7, the student will be able to design an application on an STM32 microcontroller in which the The entire work to be carried out was divided into several tasks, respecting specifications and adding the synchronization elements necessary for the exchange of data between tasks and with peripherals. He will be able to program his solution using FreeRTOS primitives.

07_O-SCR-AAv3 (15H): At the end of the course/semester, students in the module know how to calculate the fields and the intensity of an electromagnetic wave propagating in an absorbing dielectric medium and in a conductive medium.

07_O-SCR-AAv4 (15H): At the end of the course/semester, students know the characteristics of the propagation of an electromagnetic wave of microwave frequencies in a rectangular metal waveguide.

07_O-SCR-AAv5 (33H): At the end of the course/semester, the student will be able to finely analyze the behavior of widely used components (lines, power dividers, couplers, etc.) in microwave systems, dimension them electrically and/or physically in planar technologies (microstrip, triplicate), as well as precisely analyze the functions obtained by their association.

07_O-SCR-AAv6 (21H): At the end of the course/semester, the student in pairs or threes will be able, based on precise specifications, to carry out a complete study of a component (electrical synthesis and physical dimensioning, simulation, assembly with a production kit, measurement and writing of a study report).

07_O-TSI-AAv1 (12H): At the end of the semester, the student must be able to do the modeling and spectral analysis of real sampling mechanisms, in particular the averaging sampler (or tracker ) and the hold sampler (or hold). The student must know the influence of the choice between these two processes on the spectrum of the sampled signal and take it into account when designing the two filters, the guard filter (upstream of sampling) and the reconstruction filter or interpolator.

07_O-TSI-AAv2 (6H): At the end of the semester, the student will be able to determine the correlation functions (intercorrelation, autocorrelation) and the spectral energy density (DSE) or power (DSP ) of deterministic signals. It must also be able to apply correlation in radar detection to detect the presence of a pattern in a received signal.

07_O-TSI-AAv3 (12H): At the end of the semester, the student must be able to do the modeling and spectral analysis of the principles of modulation and demodulation of amplitude and frequency. The student must know how to analyze and interpret the temporal and frequency representations of analog signals corresponding to the following modulation formats: AM (dual band with DSB carrier, dual band with suppressed carrier DSB-SC, single sideband SSB) and FM (narrow band , wideband). He must also know how to use simulation tools (python, matlab or octave) and the spectrum analyzer to carry out demodulation by envelope detector or synchronous detector.

07_O-TSI-AAv4 (28H): At the end of the semester, the student must be able to design, analyze and implement digital filters of type RII or RIF in response to specifications in a specification. To successfully complete this work, the student must be able to: (1) Translate the specifications into a template. (2) Appropriately choose a filter structure (RII or RIF) and a synthesis method (bilinear transformation, impulse invariance or transfer function sampling) by arguing the relevance of the choices made. (3) Determine the filter coefficients by direct calculation or using a matlab/simulink type rapid prototyping tool. (4) Implement the filter in an interpreted language such as Python, Matlab or Octave and validate its performance against the specified template. He must also be able to study the influence of the frequency distortion implied by the synthesis method. (5) Choose a form (direct, cascade or parallel) of implementation. It must also be able to study the influence of the frequency distortion implied by the quantification of the filter on a finite number of bits (sensitivity to the finite representation of the coefficients). (6) Implement the filter on a microcontroller or DSP type hardware target. (7) Validate the synthesis against the specifications by measurement using a spectrum analyzer.

07_O-TSI-AAv6 (40H): At the end of the semester, the student will be familiar with the challenges of artificial vision and will have acquired the fundamental concepts of processing and analysis of digital images 2D. This concerns: (1) the representation of images in the spatial and frequency domain, (2) contrast improvement by histogram modification techniques (linear and non-linear anamorphosis), (3) denoising by techniques linear filtering (2D convolution operators) and non-linear (filtering of order statistics, image averaging, morphological transformations), (4) restoration by contrast enhancement operations (deblurring), (5) segmentation by contour-based and region-based approaches, (6) texture analysis by frequency and statistical approaches, (7) feature extraction using attribute selection tools, (8) recognition of objects by Hough transform and by machine learning algorithms.

07_O-MSI-AAv2 (20H): At the end of the MSI optional module, a student will be able to understand the notion of Design Pattern. In particular, students will be able to explain and develop a solution by applying one or more Design Patterns

07_O-CMV-AAv7 (14H): Students will be able to write the dynamic system of equations of a discrete oscillating system or a simple continuous oscillating system

07_O-CMV-AAv8 (14H): Students will be able to understand and use a computer program allowing the resolution of a system of second order dynamic equations using the method of modal superposition applied to a case of free and/or harmonic oscillations.

07_O-CMV-AAv9 (14H): Students will be able to analyze a theoretical, numerical or experimental vibration signal and extract the modal parameters using a computer script.

08_SHES-AAV_QQE_optionnel_1_SMQ (18H): In a group, the student will design a strategy for developing a quality management system. In particular, he will be able to evaluate the strengths and weaknesses of a fictitious company, propose and carry out a quality action plan to improve its products in the long term.

08_SHES-AAV_QQE_optionnel_5_Conception_robuste (18H): The student will explain the different stages of setting up an experimental plan. They will also be able to implement robust design analysis using Taguchi's signal-to-noise ratio and quality loss functions. He will be able to carry out a complete robust design process using crossed experimental designs.

08_X-ST8-AAV3 (100H): At the end of the assistant engineer internship, the student will be able to adapt a mathematical or other model to one of the problems to be solved. This model may have been seen in academic training or be provided by management.

07_O-SCR-AAv3 (15H): At the end of the course/semester, students in the module know how to calculate the fields and the intensity of an electromagnetic wave propagating in an absorbing dielectric medium and in a conductive medium.

07_O-SCR-AAv4 (15H): At the end of the course/semester, students know the characteristics of the propagation of an electromagnetic wave of microwave frequencies in a rectangular metal waveguide.

07_O-SCR-AAv5 (33H): At the end of the course/semester, the student will be able to finely analyze the behavior of widely used components (lines, power dividers, couplers, etc.) in microwave systems, dimension them electrically and/or physically in planar technologies (microstrip, triplicate), as well as precisely analyze the functions obtained by their association.

07_O-SCR-AAv6 (21H): At the end of the course/semester, the student in pairs or threes will be able, based on precise specifications, to carry out a complete study of a component (electrical synthesis and physical dimensioning, simulation, assembly with a production kit, measurement and writing of a study report).

07_O-TSI-AAv1 (12H): At the end of the semester, the student must be able to do the modeling and spectral analysis of real sampling mechanisms, in particular the averaging sampler (or tracker ) and the hold sampler (or hold). The student must know the influence of the choice between these two processes on the spectrum of the sampled signal and take it into account when designing the two filters, the guard filter (upstream of sampling) and the reconstruction filter or interpolator.

07_O-TSI-AAv2 (6H): At the end of the semester, the student will be able to determine the correlation functions (intercorrelation, autocorrelation) and the spectral energy density (DSE) or power (DSP ) of deterministic signals. It must also be able to apply correlation in radar detection to detect the presence of a pattern in a received signal.

07_O-TSI-AAv3 (12H): At the end of the semester, the student must be able to do the modeling and spectral analysis of the principles of modulation and demodulation of amplitude and frequency. The student must know how to analyze and interpret the temporal and frequency representations of analog signals corresponding to the following modulation formats: AM (dual band with DSB carrier, dual band with suppressed carrier DSB-SC, single sideband SSB) and FM (narrow band , wideband). He must also know how to use simulation tools (python, matlab or octave) and the spectrum analyzer to carry out demodulation by envelope detector or synchronous detector.

07_O-TSI-AAv4 (28H): At the end of the semester, the student must be able to design, analyze and implement digital filters of type RII or RIF in response to specifications in a specification. To successfully complete this work, the student must be able to: (1) Translate the specifications into a template. (2) Appropriately choose a filter structure (RII or RIF) and a synthesis method (bilinear transformation, impulse invariance or transfer function sampling) by arguing the relevance of the choices made. (3) Determine the filter coefficients by direct calculation or using a matlab/simulink type rapid prototyping tool. (4) Implement the filter in an interpreted language such as Python, Matlab or Octave and validate its performance against the specified template. He must also be able to study the influence of the frequency distortion implied by the synthesis method. (5) Choose a form (direct, cascade or parallel) of implementation. It must also be able to study the influence of the frequency distortion implied by the quantification of the filter on a finite number of bits (sensitivity to the finite representation of the coefficients). (6) Implement the filter on a microcontroller or DSP type hardware target. (7) Validate the synthesis against the specifications by measurement using a spectrum analyzer.

07_O-TSI-AAv6 (40H): At the end of the semester, the student will be familiar with the challenges of artificial vision and will have acquired the fundamental concepts of processing and analysis of digital images 2D. This concerns: (1) the representation of images in the spatial and frequency domain, (2) contrast improvement by histogram modification techniques (linear and non-linear anamorphosis), (3) denoising by techniques linear filtering (2D convolution operators) and non-linear (filtering of order statistics, image averaging, morphological transformations), (4) restoration by contrast enhancement operations (deblurring), (5) segmentation by contour-based and region-based approaches, (6) texture analysis by frequency and statistical approaches, (7) feature extraction using attribute selection tools, (8) recognition of objects by Hough transform and by machine learning algorithms.

07_O-MSI-AAv2 (20H): At the end of the MSI optional module, a student will be able to understand the notion of Design Pattern. In particular, students will be able to explain and develop a solution by applying one or more Design Patterns

07_O-CMV-AAv7 (14H): Students will be able to write the dynamic system of equations of a discrete oscillating system or a simple continuous oscillating system

07_O-CMV-AAv8 (14H): Students will be able to understand and use a computer program allowing the resolution of a system of second order dynamic equations using the method of modal superposition applied to a case of free and/or harmonic oscillations.

07_O-CMV-AAv9 (14H): Students will be able to analyze a theoretical, numerical or experimental vibration signal and extract the modal parameters using a computer script.

09_O-CNO-AAV1 (30H): The student of the CNO module, at the end of the module, will be able to describe the main elements (active and passive components) of the architecture of a WDM optical communication chain (from transmitter to receiver) and to use the main metrics, tools and methods to evaluate transmission quality.

09_O-CNO-AAV6 (21H): The student of the CNO module, at the end of the module, will be able to determine qualitatively, analytically and by simulation the spectral power density and the probability of errors of digital modulations in baseband and on carrier. It will be able to use the information obtained by adapting the signals in terms of waveforms and/or power, to meet the specifications of digital transmission.

09_O-CNO-AAV8 (15H): The student of the CNO module, at the end of the module, will be able to analyze, implement and study the performances (in EVM, SER, BER) of a simple single-carrier (M-QAM, M-PSK) or multi-carrier (CP-OFDM) digital communication chain for a Gaussian or selective additive channel in stationary frequency. The student will also be able to implement some classic algorithms at the receiver level using preamble and pilot symbols (carrier frequency offset correction, synchronization, zero-forcing equalization, linear LMS equalization).

09_O-IAS-AAv2 (20H): At the end of the module, students will be able to name and explain the most appropriate knowledge representation models for the formulation and resolution of characteristic problems varied.

09_O-IAS-AAv4 (30H): At the end of the module, students will be able to implement different tools and existing software libraries linked to AI for the industrial application areas covered.

09_O-MRA-AAv1 (12.5H): At the end of the semester, MRA students will be able to understand and characterize the different spaces in which the robot evolves and describe the models and their associated characteristics, making the connections between them.

09_O-MRA-AAv2 (12.5H): At the end of the semester, MRA students will be able to obtain the direct geometric model of a serial robot, with rotoid and prismatic connections, using either a kinematic diagram, or from the analysis of the axes of a real robot.

09_O-MRA-AAv3 (12.5H): At the end of the semester, MRA students will be able to obtain the direct and inverse kinematic model of a serial robot, with rotoid and prismatic connections, using either a kinematic diagram or by analyzing a real robot.

09_O-MRA-AAv4 (12.5H): At the end of the semester, MRA students will be able to obtain the direct and inverse static model of a serial robot, with rotoid and prismatic connections, using either the geometric model and/or the kinematic diagram of the robot.

09_O-MRA-AAv5 (12.5H): At the end of the semester, MRA students will be able to obtain the dynamic model of a serial robot, with rotoid and prismatic connections, in the form of a system of nonlinear differential equations, using the kinetostatic model and the double recursive Newton-Euler method.

09_O-MRA-AAv9 (18.75H): At the end of the semester, MRA students will be able to synthesize the system and control laws of wheeled mobile robots, based on the model

09_O-REV-AAv1 (12H): Each student must be able to express the necessary calculations, corresponding to sequences of geometric transformations (homogeneous matrices, quaternions), in order to obtain this representation.

09_O-REV-AAv5 (8H): Each student is able to explain the key concepts making it possible to characterize and highlight the Presence in a virtual reality system by considering both methodological and software as well as hardware aspects.

09_O-REV-AAv6 (12H): Each student is able to explain the methods necessary for the implementation of virtual reality systems distributed through a computer network.

09_O-REV-AAv7 (8H): students are able to explain the needs related to the creation of conversational virtual agents

09_O-REV-AAv8 (12H): Each student is able to list the steps necessary for motion capture.

09_O-REV-AAv9 (12H): Each student is able to list the different augmented reality devices and the pose calculation methods adapted to augmented reality necessary to ensure good consistency between the projections of real and virtual objects .

09_O-CCM-AAV1 (12H): At the end of this course, the student will be able to describe and model a controlled system in state representation, for applications in the fields of mechatronics, instrumentation or energy production. The dynamic system may be of varied nature: linear or non-linear, possibly non-stationary, continuous time or discrete time, single-input/single-output (SISO) or multi-input/multi-output (MIMO).

09_O-CCM-AAV2 (8H): At the end of this course, the student will be able to simulate a controlled system in state representation using scientific calculation software and to operate transformations allowing access to various representations of the system (differential equations, state representation, transfer function, transfer matrix).

09_O-CCM-AAV3 (12H): At the end of this course, the student will be able to build a state observer and synthesize a state feedback control observed on a SISO linear system meeting specifications (stability, precision, speed, robustness).

09_O-CCM-AAV4 (12H): At the end of this course, the student will be able to model the uncertainties of modeling a discrete-time dynamic system and the uncertainties observation of the state of the system, with a view to an adaptive estimation of the state which it will carry out by Kalman filtering for the case of linear systems.

09_O-CCM-AAV5 (20H): At the end of this course, the student will be able to linearize a dynamic process or an observation law in order to carry out an adaptive state estimation by extended Kalman filtering (EKF filter) and perform a comparison with an Unscented Kalman filter (UKF).

09_O-CCM-AAV6 (16H): At the end of this course, the student will be able to control a linear system by feedback state according to a quadratic optimization criterion: LQR command or LQG command when the state is only partially observed

09_O-CCM-AAV7 (12H): At the end of this course, the student will be able to identify the equilibrium points and analyze the local stability of a non-linear dynamic system, in the phase plane (for systems of order 2) and by Lyapunov methods

09_O-CCM-AAV8 (42H): At the end of this course, the student will be able to implement, set up and adjust some system control solutions non-linear: linearizing control, control by flatness, control by Lyapunov function,…

10_X-S10-AAv3 (150H): At the end of the engineering internship, the student is able to adapt a mathematical or other model to the problem to be solved, to use reasoning and formal calculation techniques and digital views in progress in order to solve the problem theoretically or by simulation and evaluate the accuracy of the related concrete solution.