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.

Content of UE

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 of Assessment for UE in Q1

• N/A

Q1 UE Assessment Comments

It's a year course with continuous evaluation and/or an evaluation in June.

Type of Assessment for UE in Q2

• Presentation and/or works
• Oral Examination
• Written examination
• Practical test

Q2 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

• Presentation and/or works
• Oral examination
• Written examination
• Practical Test

Q3 UE Assessment Comments

Not applicable

Type of Resit Assessment for UE in Q1 (BAB1)

• N/A

Q1 UE Resit Assessment Comments (BAB1)

Not applicable