Techniques de Fabrication - Exercices corriges

B. CONTENT OF COURSES


| | | | |
| | | | |
|General computer science 1 | |
|Code: IG1-1 1 |ECTS credits: 2 |Semester: 1 | |
| |Professor: Mr PAILLE J. | | |



COURSE PLAN




Presentation of the course - General remarks on computer science

- History, computer architecture, programs
- Possibilities, limits and perspectives of computing systems

Mathematical tools for computer science

- Logic, numeration and coding of numbers
- Notion of algorithms and evaluation of complexity

Structured programming

- Revision on Pascal language, manipulation of files
- Writing, programs documentation tests

Operating systems

- History, role of an operating system
- Presentation of the UNIX and DOS systems
- Control under UNIX and DOS, shell scripts, communications under
UNIX
- Administration and security under UNIX,- the future

Documentation

- How do we get information ?, How do we inform ?

Project management

- The analysis - design - implementation cycle
- Presentation of a method of analysis
- Presentation of the project

Office tools

- Spreadsheet, word processing

Networks

- Network architecture and model - Study of the ISO model

Databases

- Databases management systems models, manipulation languages,
presentation of Oracle




ASSESSMENT


- 6 applications of 2 hours 30


| |General Physics | | |
|Code: IG1-2 |ECTS credits: 3 |Semester: 1 | |
| |Professor: Mr NOAT | | |

COURSE PLAN

Introduction
- Presentation of « modern physics »
- Dimensional analysis
- Orders of magnitude in physics
From classical mechanics to restricted relativity
- Introduction: classical principle of relativity / Measurement of the
wind of ether
- Postulates of relativity
- Relativist transformation: Lorentz transform / Speed transformation
- Consequences: Relativity of simultaneity / Dilation of temps / Lengths
contractions / Movement energy and quantity
- Relativist effects: Radiation of a moving particle / Doppler effect
Quantum physics
- Introduction: the quantum world / Waves and particles
- Wave/particle duality: Is light a wave ? / Is an electron a particle ?
- New concepts : Neither wave, nor particle: quantons / Notion of
quantum state
- Wave mechanics: L2 space/ Postulates of quantum mechanics / "Free"
quanton / Quanton in a potential / Spin / Identical quantons
Structure of matter
- Atoms: Hydrogen atom/ Helium atom / Complex atom / Periodic
classification of elements
- Molecules: molecular links / molecular spectrum
- Revision on statistical physics
- Solids: crystalline structures / electronic structure

ASSESSMENT

- 3 applications of 2 hours 30.
- 1 written exam of 2 hours 30.



|General Mathematics |
|Code: IG1-3 |ECTS credits: 2 |Semester: 1 |
| |Professor: Mr CHAQUIN | |


COURSE OBJECTIVE


Equip students with the necessary mathematical tools and methods to study
the basic technical and scientific subjects in engineering (fluids
mechanics, structures mechanics, acoustics, signal processing, numerical
analysis, technological subjects...). The aim of this course is to spare
the teaching of these mathematical tools and methods common to all these
courses to the professors who teach these basic subjects.


COURSE PLAN



Complex analysis

Complex functions of complex variables, holomorphy, Cauchy theorem,
Cauchy integral, multiformity, notion of Riemann surface, analyticity,
Taylor series, Laurent series, residuals, integral calculation by the
method of residuals, Jordan formula.

Harmonic functions

Definition, theorem of the 2 H, properties, average, maximum principle,
Poisson theorem, Dirichlet problem.

Special functions

Euler functions of the 1st species, Legendre polynomes, Weber-Hermite
functions, Tchebychev polynomes, Bessel functions.

Fourier series

Definition, Fourier series of a locally summable function, of a
distribution, convergence, revision on Hilbertian bases, Bessel-Parseval
theorem, harmonic analysis.

General remarks on PDE of the 2nd order

Types of PDE, canonical forms, classification, homogeneity, existence and
uniqueness of solutions, initial value problems, separation of variables,
modal method.

Green's function

Introduction, principle of solution of a PDE, fundamental solutions,
application to Laplace's equation in IR.

Integral equations

General remarks, major types of integral equations, application to the
solution of PDE, example on Laplace equation and Helmholtz equation,
methods to solve integral equations: method with Laplace transform, case
of degenerated nucleus for homogenous or non-homogenous equations,
numerical methods (collocation, double projection).

Variational methods

General remarks on variation calculation, Euler theorem, equivalence
between a physical problem and a variational principle, examples, method
of Ritz, introduction to the finite element method.


ASSESSMENT


- 3 applications of 2 hours 30
- 1 written exam of 3 hours


BIBLIOGRAPHY


- Analyse réelle et complexe par W. RUDIN (Masson)
- Compléments de mathématiques par A. ANGOT (Edition de la Revue
d'Optique)
- Méthodes mathématiques pour les sciences physiques par L. SCHWARTZ
(Hermann)
- Introduction to integral equations with applications par J.J. JARRY
(Pure and applied mathematics)


|Integral Calculus |
|Code: IG1-4 |ECTS credits: 2 |Semester: 1 |
| |Professor: Mr J.P. COUPRY | |


COURSE OBJECTIVE


- Building the so-called "LEBESGUE" integral calculation method :
In the specific case relating to functions defined in IR, with values
in IR, compared to the Lebesgue measure in the general frame of
measured spaces (Ritz theorem, Hölder and Minkowski inequalities. L1 et
L2 spaces, Fubini, Stokes, Ostrogradski and Green change of variable
formula)
- Translations. Convolution. Fourier transform in L1 and Fourier
Plancherel transform in L2. Laplace transform
- Brief study of some classical operational spaces Co, Cc, S, D.
Introduction to the notion of distribution and tempered distribution.
Laplace derivative and transform of a distribution. Introduction to
the notion of Green's function.


ASSESSMENT


- 3 applications of 2 hours 30
- 2 written exams of 2 hours 30


BIBLIOGRAPHY


- Analyse réelle et complexe, Walter RUDIN, Editions Masson
- Calcul intégral (maîtrise mathématiques C2), A. GUICHARDET, Editions
Armand Colin


|Differential Calculus |
|Code: IG1-5 |ECTS credits: 2 |Semester: 1 |
|Professor: Mr GUILLERMIN |

COURSE OBJECTIVE

Give students the basics of differential geometry that will allow them to
go deeper into this subject later, if need be.
This presentation allows to define some mathematical elements often used in
physics, such as tensors, metric invariants, differential forms, mobile
bases. The aim is to exempt the professors who teach courses using
differential geometry concepts from presenting these tools in detail.

COURSE PLAN


Euclidian spaces

- Coordinates systems .
- Change of coordinates.
- Euclidian space (Curve in the Euclidian space - Quadratic forms and
vectors).
- Riemann's spaces (Riemann's metrics).

Théorie des surfaces

- Geometry of surface in space (Coordinates on a surface - Tangent plan
- Metric on a surface - Surface area).
- Second fundamental form (Curvature of curves on a surface - Invariants
quadratic forms).

Tensors

- Examples of tensors.
- General definition of a tensor.
- Algebraic operations on tensors (Permutation of indices - Contraction
of indices - Tensorial product).
- Tensors of the (0,k) type (differential notation of tensors with lower
indices - Alternate stress tensors of the (0,k) type - Outer product
of two differential forms - Exterior algebra).
- Tensors in Riemannian space (indices up and down - Initial value of a
quadratic form - The operator - Tensors in the Riemannian space).
- Effects of an application on tensors (Restriction of lower indices
tensors - Tangent spaces applications).

Differential calculation on tensors

- Differential calculation on alternate tensors (Gradient of an
alternate tensor - External differential of a form).
- Alternate tensors and integration theory (Integration of differential
forms - Stokes formula).
- Covariant derivation (Euclidian connection - Covariant derivation of
tensors of any rank - Derivation and metrics - Parallel transport of
vectors - Geodesic - Connections associated to metrics).

ASSESSMENT


- 4 applications of 2 hours 30.
- 1 written exam of 3 hours.

BIBLIOGRAPHY

« Leçons sur la Géométrie des espaces de Riemann » E. CARTAN, Éditions
Gauthier-Vil