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Optimization  AO101  
1. SummaryThe objective of this course is to provide an overview of both theoretical and practical aspects of a field in applied mathematics whose applications are various in mechanics, economics, finance, industry, ...
This is an introduction to the theory of differentiable nonlinear optimization (with an emphasis on quadratic optimization problems). The first chapter introduces fundamental mathematical concepts that will be very helpful in analyzing any optimization problem: modelling, a concept of local / global solution, differential calculus, and basic elements of convex analysis.
In the next chapter, we will analyze the questions of existence and uniqueness of a minimum. Then will arise the question of characterization of optimal solutions. This characterization will be given as optimality conditions (Euler inequality). It will be first described in a fairly general framework where the set of constraints is convex. Then the optimality conditions will be made more precise in the case of linear equalities or inequalities.
Another part of the lectures will be dedicated to the numerical algorithms for quadratic optimization problems (gradient algorithms, conjugate gradient, projected gradient, Uzawa algorithm).
2. Acquired SkillsTo be able to discuss existence and uniqueness properties of optimal solutions for nonlinear optimization problems (mainly quadratic problems) To be able to state the optimality conditions in cas of optimization problems with constraints (equality or inequality forms, ...) To be able to implement numerically descent methods for solving optimization problems with/and/without constraints. To be able to analyse the convergence rate for optimisation methods.
3. Programme des séances
1. Existence d'un minimum. Convexité, différentiabilité (1h cours + 2h TD) 2. Conditions d'optimalité (Equations d'Euler). Problème de moindres carrés (1h cours + 2h TD +DM) 3. Méthodes numériques pour le cas sans contraintes. Systèmes linéaires(1h cours + 2h TD) 4. Conditions de minimalité pour le cas avec contraintes (1h cours + 2h TD +DM) 5. Mise oen oeuvre de quelques méthodes numériques pour le cas avec contraintes. (3h TP noté) 6. Analyse de convergence des méthodes numériques: cas avec contraintes (1h cours + 2h TD) 7. Examen Ecrit (3h)  1.75 ECTS Professor(s):

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Dynamical Systems  AO102  
The course constitutes an introduction to the study of ordinary differential equations and control theory. The main objective is to present various concepts of stability whose importance, for many problems, is comparable with that of the effective knowledge of the solution.
The course is composed of two parts.
The first one is devoted to differential calculus: differentiability, fixed point theorems,...
The second part treats linear ordinary differential equations, with constant coefficients initially, then with general coefficients.
The last part is devoted to the study of the stability of nonlinear ordinary differential equations. One shows how it can be reduced in certain cases to the study of the stability of linear ordinary differential equations, using a technique known as of linearization.  1.75 ECTS Professor(s):

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Signal processing  ES101  
This course introduces the main basic signal processing tools used in electronics. After a brief presentation of the linear systems principles, the problematics of digitization (sampling theorem, etc.) as well as the quantization noise phenomena will be adressed. The various transforms usually applied to the digitized signals will be presented, notably the Discrete Fourier Transform and the corresponding fast algorithms (FFT). The digital filtering will then be set out. The methods of analysis and synthesis of the FIR and IIR filters wil be detailed. In the second part of the course, the issues of the stochastic processes and their statistical characterization wil be tackled in a rather intuitive manner. The course will end with a small student project, allowing them to put in practice their theoretical knowledge in the domain of audio signals (they'll have to restore signals intentionally perturbed).  2.5 ECTS Professor(s):

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Digital and VLSI Design: Components and Systems  ES102  
The unprecedented development over the last three decades of information and communication technologies is mainly based on the continuing exponential growth in the complexity and speed of digital electronic systems. If the transport industry had developed at the same pace, we would now be crossing the Atlantic in just a few seconds at a price of a few cents. The course ambition is to provide the scientific and technological knowledge that link the electron  in its Silicon crystal  with the software program running on a microprocessor. Looking at computer science from the electronics viewpoint is a way to make it less artificial  therefore less confusing  for the engineer. Grounded on some solidstate physics, different forms of logic  combinatorial, sequential, programmed  are reviewed, from elementary CMOS VLSI implementation to exploitation within a processor or applicationspecific hardware. The course then moves on to computer arithmetics and computer architecture, up to a look at the internal operation of a C compiler.  2.5 ECTS Professor(s):

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Algorithmics and Programming (in Python)  IN101  
1. Description
The objective of this course is firstly to study different data structures and advanced algorithms and also to enrich the computer development skills.
2. SkillsThe IN101 course aims at making the student able to:
 formulate algorithms from problem descriptions  implement algorithms in a programming language (the programming language being Python)  learn and apply several algorithms and representations frequently used in computer science (sorting, linked lists, trees)  formulate and implement algorithms autonomously
3. ProgramThe detailed program.  1.75 ECTS Professor(s):

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C Programming  IN102  
This courses aims at learning the C language and the lowlevel mechanisms it makes explicit conversely to some other higherlevel languages like Python seen in IN101 (compilation, typing, memory structure, pointers, ...).  1.75 ECTS Professor(s):

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Operating system and programming  IN103  
This courses aims two objectives: * Learn some algorithmic datastructures not explored in IN101 / IN102. * Use the former point to explain and implement (in a simplified way compared to real systems):  the (some) roles of an operating system,  the (some) mechanisms allowing to go from a source code to a running program.  1.75 ECTS Professor(s):

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Computer Science Project  IN104  
This course, last in the series of four computer classes, aims to introduce students to the design and implementation of a computer program.
This course builds on the knowledge acquired especially in the course on programming and algorithmics (IN101 / IN102) and in the first contact with the realization of an IT project in the course of Matlab (IN103).
The course itself has three objectives:
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Probability and statistics: an introductory course  MA101  
The aim of this course is to present some tools to analyse the huge quantity of data an engineer has to face during his work, and how to use some simple models to help him take decisions, or at least evaluate their risks in random environnement.
In this course, we introduce the basic notions of probability and statistics: random variables (discrete and continuous), the strong law of large number, the theorem of central limit, estimation, confidence regions and tests in a parametric framework. This course is highlighted by many examples from different fields: mathematics, biology, physics,...  3.5 ECTS Professor(s):

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Elementary tools of analysis for partial differential equations  MA102  
This course constitutes an introduction to the functional analysis and its applications to the study of the linear partial differential equations. The aim of this course consists in familiarizing the students with some of the essential ideas on which the study of the simplest models of physics and mechanics are based. Our purpose is not only to provide methods for the solution of these equations, but also to bring to a better comprehension of the modelled phenomena.
The course is composed of four parts:
The first part is devoted to elementary concepts of topology, to the concepts of convergence in spaces of functions and to the essential theorems of integration. These results form the essential technical base on which the remainder of the course is based.
The second part is devoted to the distributions, which generalize the functions, and to the principal operations which they support: derivation and multiplication.
The third part introduces the Fourier transform, first for integrable functions, then for squareintegrable functions.
The fourth part relates to the application of the variational method to the study of the linear partial differential equations, within the framework of particular Hilbert spaces, which are the Sobolev spaces. In particular, this method makes it possible to bring an answer to the questions of existence and uniqueness for the considered problem.  3.5 ECTS Professor(s):

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Introduction to partial differential equations discretization  MA103  
This lecture mainly deals with finite difference schemes to approximate main partial differential equations of physics (elliptic, parabolic and hyperbolic PDE). There are few objectives :  to introduce from simple examples some fundamental properties of solutions  to give the basics of finite difference schemes (explicit and implicit)  to give notions of consistancy, stability and convergence  1.75 ECTS Professor(s):

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Functions of one complex variable  MA104  
The theory of holomorphic functions which was developed in the 19th century under the leadership of Gauss, Cauchy, Riemann ... constitutes one of the first successes of the analysis. Its power and simplicity are such that holomorphic functions are found in almost every field of pure or applied mathematics, since the numbers theory (Riemann hypothesis), spectral theory, differential equations and partial derivative. They also constitute a particularly important tool in physics (asymptotic expansions), control (Laplace transform, location of poles) or fluid mechanics (perfect fluids, stability).
The course aims to describe the fundamentals of the theory and its typical applications. Essentially varied exercises focused on applications will allow to taste all the salt and gain a new understanding of some of the formal calculations of physical, mechanical or automatic.  1.75 ECTS Professor(s):

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Incompressible Fluid Dynamics  MF101  
This lecture is a basic introduction to the subject of fluid mechanics and in particular we deal with incompressible flows. The conservation laws are derived to obtain for newtonian, incompressible flows the Navier Stokes equations. In order to get a better understanding of the physics of fluid flows, energy considerations (Bernoulli) and production of vorticity are discussed. We focus then on perfect fluids before introducing the concepts of boundary layers.  3.5 ECTS Professor(s):

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Incompressible Fluid Dynamics  MF102  
The second part of this lecture is devoted to the effect of viscosity. The boundary layer on a flat plate is studied in the framework of matched asymptotics expansions. The Blasius and Falkner Skan solutions are derived. Finally, an introduction of instability temporal theory in the particular case of Kelvin Helmholts instability is presented.  0 ECTS Professor(s):

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Incompressible Flows : Third Part  MF103  
1. DescriptifPractical exercises and laboratory lectures as a complement of MF101 and MF102. Students, per group of 2, will choose one practical exercise subject among the list below. The laboratory lecture, addressed to all the students, consists in 3 demonstration experiments of 1 hour each. So, a student will attend to 1 practical exercise (3.5 hours) and the laboratory lecture (3.5 hours).
PRACTICAL EXERCISES (TP) T.P. N°1 : BÉNARDVON KARMAN INSTABILITY T.P. N°2 : THE SWELL T.P. N°3 : CAVITATING WAKE T.P. N°4 : AIRFOIL T.P. N°5 : BOUNDARY LAYER T.P. N°6 : BLUFF BODY T.P. N°7 : PLANE JET
DEMONSTRATION EXPERIMENT (LECTURE):  FREE SURFACE. Gravity waves, swell, wave breaking, soliton, hydraulic jump.  FLOW COMPLEXITY. Newtonien and nonnewtonien Fluids, instability and turbulence.  LIFT. Origin of the lift, Prandtl eddy, wingtip vortex, stall and control.  0 ECTS Professor(s):

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Continuum mechanics  MS101  
This course is an introduction to the whole courses of Mechanics. It is composed of two parts : The first part, devoted to kinematics, includes primarily the Lagrangian description and the eulerien description of the continuum media. The concepts of strain tensor and strain rate tensor are in particular presented. Within the framework of the infinitesimal transformations, the notion of compatibility of the strains is given and the determination of the corresponding displacement is carried out. The second part is relative to the description of efforts. After the conservation of mass, we introduce the dynamic evolution; first the fundamental law, then, the Principle of Virtual Powers (PPV) which allows an interesting introduction of the stress tensor and the local partial derivative equations governing the dynamic evolution of the continuum.
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Linear Elasticity  MS102  
This lecture series is a short introduction to linear elasticity under the hypothesis of small strains and quasistatic transformations.
In the first lecture, the generalized Hooke's law is presented, with particular emphasis to the behavior of isotropic solids. In the two following lectures, the general formulation of the problem of linear elasticity is presented. The two basic methods (method of displacements and method of stresses) are presented and illustrated by various examples, for simple cases where exact solutions can be found: tractioncompression, torsion, plane flexion.
Lectures 4 and 5 are devoted to the variational formulation of linear elasticity, based on the principle of virtual work. This method allows to obtain approximate solutions and forms the basic framework of numerical resolution (Finite Elements Method).
The last chapter is aimed at introducing the fundamentals of beam theory. This illustrates a case of high practical importance, when dealing with slender structures.  1.75 ECTS Professor(s):

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Quantum and statistical physics  PA101  
1. Description
Quantum physics is one of the greatest intellectual adventures in the history of humanity. Given the experimental evidence that the phenomenological processes at the microscopic level could not be explained by the concepts of classical physics, the scientists at the beginning of the last century had to create a new theory, which took the name of quantum physics. The impacts of such a theory has been enormous, and spread from philosophy to technological applications, such as semiconductor devices or lasers, and of course to theoretical physics. Quantum physics is the quintessence of modern physics, as it allows to explain all the physical phenomena at the elementary level.
The knowledge acquired in this course are essential for engineering students in order to attend specialized courses in many different fields, as this course is a real introduction to modern physics used in most of modern technologies. The knowledge of quantum physics is indispensable to every engineer.
This course will be based on video materials. In particular, the first six sessions of this course will be based on the Massive Open Online Courses (MOOC) "Introduction à la physique quantique" available on the France Digital platform:
https://www.funmooc.fr/courses/ENSTA/73001S02/session02/about
The last six sessions will rely on SPOC (Small Private Online Courses) videos.
Moreover, in this course we will systematically use electronic voting boxes distributed beforehand, which will enable the students to check their understanding of the concepts treated at each session.
2.Expertiese to acquire
Being able to implement the main notions of quantum physics, also using the Dirac formalism.
Being able, through knowledge of the fundamental principles of quantum physics:  to study the dynamical behavior of a quantum system;  to predict the results of a measurement process on a quantum system;  to analyze the state of a quantum system after the measurement.
3. Program of lectures
1. Introduction to quantum physics. Experiments and birth of quantum physics.
2. Analytical mechanics, Lagrangian and Hamiltonian formalism, Poisson's hooks, fundamental equation of dynamics.
3. First and second postulates of quantum physics.
4. Dirac formalism.
5. Third postulate of quantum physics and measurement.
6. Representation "x" and representation "p" and Heisenberg inequality.
7. Midterm exam in QCM format.
8. Correction of the midterm exam and presentation of an experiment on a quantum system.
9. Angular momentum
10. Spin.
11. Hydrogen atom.
12. Conference on the applications of Quantum Physics.
13. Final exam.
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Introduction to statistical physics  PA102  
After the course of quantum mechanics, these lectures are a presentation of the classical theory of classical and quantum perfect gases. One of the objectives is to construct the microscopic basis of this theory after the first macroscopic approach introduced in "classes preparatoires". These serie of lectures could arrive as a conclusion of the general course of physics in first year of EnstaParistech or it could appears as one of the first initiation to more advanced optional lectures in second year (Interacting systems and plasma physics).  1 ECTS Professor(s):

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Workman Internship  SIMI  
The workman internship is mandatory and is part of the engineer curriculum. During the internship the intern should have the opportunity to discover the company’s environment and organization, to understand the constraints of a workman job in a company and to discover the skills he/she will have to develop along the three years curriculum. The student should be in charge of an execution work with specific tasks to accomplish and expectations in terms of quality and delivery times. The student should be part of a workers’ team either in a foreign or French company. The internship should require no previous skill and the intern should occupy an operator position. It is absolutely essential that the internship’s work content be operational. It should not be a jobshadowing experience.
SKILLS TO BE ACQUIRED OR DEVELOPED: To complete an entry level task (shop or factory floor) and experiencing the constraints that impact operational staff. Discover the organizational structure of the company. Obtain an understanding of working conditions of entry level staff, of the importance of human relations, the impact of hierarchy, the circulation of information, and overall the diversity and complexity of the social context of the enterprise.  0 ECTS Professor(s):

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