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.
• Read research articles in at least one discipline of mathematics.
• 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.
• 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.
• Have sufficient knowledge of English for basic scientific communication.
• Adapt to different contexts.
• Demonstrate thoroughness, independence, creativity, intellectual honesty, and ethical values.
• Skill 6: Have acquired professional skills in relation to the objective defining the degree.
• Have gained expertise and specialised knowledge in a field of mathematics in order to enter fully into the world of research.
• Demonstrate intuition and creativity to tackle new mathematical problems.
• Expose high-level mathematical results to a specialised audience.
• 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.
• Appropriately use bibliographic resources for the intended purpose.
• Present the objectives and results of a project orally and in writing.
• 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.
• Have sufficient knowledge of English for basic scientific communication.

Learning Outcomes of UE

At the end of the instruction, the students will be able to:
• explain what is a differential equation with boundary conditions;
• determine their solutions in simple cases;
• prove the equivalence with the weak form and the variational form, as well as the Lax-Milgram theorem;
• implement the finite element method for elliptic equations.

Content of UE

Classification of partial differential equations (PDE).
Weak formulation, Lax-Milgram theorem
Variational formulation, direct method of the calculus of variations
The method of finite elements: Galerkin approximations, errors, convergence, practical advice for implementation
<em>The precise content will depend on the students' objectives.</em>

Prior Experience

Not applicable

Type of Assessment for UE in Q1

• Presentation and works
• Practical test

Q1 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q2

• Presentation and works
• Practical test

Q2 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

• Presentation and works
• Practical Test

Q3 UE Assessment Comments

Not applicable

Q1 UE Resit Assessment Comments (BAB1)

Not applicable