Objectives of Programme's Learning Outcomes

• Have integrated and elaborate mathematical knowledge.
• Mobilise the Bachelor's course in mathematics to address complex issues and have profound mathematical expertise to complement the knowledge developed in the Bachelor's course.
• Use prior knowledge to independently learn high-level mathematics.
• Research mathematical literature in an efficient and relevant way.
• Carry out major projects.
• Independently carry out a major project related to mathematics or mathematical applications. This entails taking into account the complexity of the project, its objectives and the resources available to carry it out.
• Give constructive criticism on the quality and progress of a project.
• Work in teams and, in particular, communicate effectively and with respect for others.
• Appropriately use bibliographic resources for the intended purpose.
• Present the objectives and results of a project orally and in writing.
• Apply innovative methods to solve an unprecedented problem in mathematics or within its applications.
• Appropriately make use of computer tools, as required by developing a small programme.
• Communicate clearly.
• Communicate the results of mathematical or related fields, both orally and in writing, by adapting to the public.
• make a structured and reasoned presentation of the content and principles underlying a piece of work, mobilised skills and the conclusions it leads to.
• Adapt to different contexts.
• Have developed a high degree of independence to acquire additional knowledge and new skills to evolve in different contexts.
• Critically reflect on the impact of mathematics and the implications of projects to which they contribute.
• Demonstrate thoroughness, independence, creativity, intellectual honesty, and ethical values.

Learning Outcomes of UE

At the end of the instruction, the students will be able to:
* prove the existence an uniqueness (both local and global) of solutions of ordinary differential equations (ODE);
* solve linear ODE;
* linearize ODE;
* build standard numerical methods for ODE and implement them;
* possess an expertise in building moderate sized programs.

UE Content: description and pedagogical relevance

Cauchy problems: existence, uniqueness, linearization, continuous dependence, matrix exponential, method of variation of constants.
Numerical methods: consistency, order, convergence
A large part of the time will be devoted to a personal or group project.

Prior Experience

Differential and integral calculus of several variables, basic numerical analysis.

Type(s) and mode(s) of Q1 UE assessment

• Oral presentation - Face-to-face

Q1 UE Assessment Comments

The course is taking place on both semesters with continuous evaluation.

Method of calculating the overall mark for the Q1 UE assessment

Not applicable

Type(s) and mode(s) of Q1 UE resit assessment (BAB1)

• N/A - Néant

Q1 UE Resit Assessment Comments (BAB1)

Not applicable

Method of calculating the overall mark for the Q1 UE resit assessment

Not applicable

Type(s) and mode(s) of Q2 UE assessment

• Oral presentation - Face-to-face

Q2 UE Assessment Comments

The course is taking place on both semesters with continuous evaluation.

Method of calculating the overall mark for the Q2 UE assessment

Not applicable

Type(s) and mode(s) of Q3 UE assessment

• Oral examination - Face-to-face

Q3 UE Assessment Comments

Not applicable

Method of calculating the overall mark for the Q3 UE assessment

Not applicable