Objectives

The courses in this Unit can be broken down into two disciplines: mathematics, and computer science. The Unit plays a transverse role with respect to the other units, inasmuch as it provides instruments for solving sets of abstract problems, models describing phenomena in physics, mechanics, economics, management, etc. Mathematics provides a rigorous framework for the numerical analysis and resolution of such problems. Computer science concerns modeling and processing data with a view to using machines.

MATHEMATICS

Mathematics is to be understood here in the widest sense, including as it does many aspects concerning numerical analysis and scientific calculation in general.

In 2nd year, the core program comprises 2 basic modules in particular:

1 - Fourier transforms and distributions:

This is taking the 1st year course a little further: the study of the theoretical or numeric aspects of models defined by partial differential equations is extended to multidimensional domains, and new instruments such as distributions are brought into play.

2 - Numeric analysis:

This presents classical numeric methods for solving linear systems.

The form and content of both courses are adapted for double-degree students admitted on qualifications.

COMPUTER SCIENCE

The 2nd year computer science course follows on from 1st year's, which focused on algorithmics and the structure of data implemented in imperative structured programming in language C. 2nd year goes into the paradigm of object oriented programming implemented in C++.  

The 2nd year core program comprises 2 modules:  

1 - an Object Oriented Programming foundation course, teaching the fundamental concepts (encapsulation, inheritance, composition, polymorphism, genericity, etc.). The concepts are illustrated in C++ class exercises.  

2 - an Object Oriented Programming lab transfer module in the form of a mini-project to create a serious application dealing with all aspects of the software life-cycle, from the study of the problem to the validation and integration. The application is to be performed in C++ under Unix.  

The unit also offers 7 advanced modules and 7 optional courses over the two disciplines.

Content

2nd YEAR
Basic modules
LSb2.1 - Partial differential equations, theoretical and numerical analysis
LSb2.2 - Numerical analysis
LSb2.3 - Object oriented programming

Advanced modules
LSa2.1 - Numerical analysis of ordinary differential equations
LSa2.2 - Partial differential equations
LSa2.3 - Practice of numerical methods
LSa2.4 - Computer language processing
LSa2.5 - Algorithm and reasoning
LSa2.6 - Process-based software development

Practical modules
LSt2.1 - Object oriented programming lab

Optional modules
LSo2.1 - Theoretical and practical aspects of the finite element method
LSo2.2 - Nonlinear problems in mecanics and physics
LSo2.3 - Stochastic processes and applications
LSo2.4 - Image analysis and indexing
LSo2.5 - Information systems
LSo2.6 - Server-side web technology
LSo2.7 - Operating systems