Objectives of general skills

• Understand the theoretical and methodological fundamentals in science and engineering to solve problems involving these disciplines
• Identify, describe and explain basic scientific and mathematical principles
• Select and rigorously apply knowledge, tools and methods in sciences and engineering to solve problems involving these disciplines
• Communicate in a structured way - both orally and in writing, in French and English - giving clear, accurate, reasoned information
• Argue to and persuade customers, teachers and a board both orally and in writing
• Use several methods of written and graphic communication: text, tables, equations, sketches, maps, graphs, etc

UE's Learning outcomes

Recall, interpret and apply all the studied definitions and properties; recall, explain, justify and formalize demonstrations; manipulate the concepts of logic; exploit theoretical results;
In Algebra: solve systems of linear equations; calculate a distance, a norm, a scalar product; orthogonalize a matrix; calculate the eigenvalues and eigenvectors of a matrix;
In Analysis: integrate functions from Rn to Rm (with or without change of variables); compute line and surface integrals (including the use of vector analysis theorems); use power series to solve differential equations.

UE Content

In Algebra: distances, norms and scalar products, orthogonal projections; eigenvalues and eigenvectors; properties of particular square matrices.
In Analysis: introduction to measure theory; multiple integrals (Fubini theorem, change of variables); line and surface integrals; vector analysis theorems (Green, Stokes and Ostrogradski); conservative fields; constrained optimization; numerical sequences and series; power series; power series for differential equations.

Prior experience

Sans objet