Analysis I and algebra

Presentation

Program (detailed contents):

Analysis:

• Number series, sequences and series of functions, power series, Fourier series
• Norms vector spaces

Algebra:

• Block diagonalization of matrices
• Euclidean spaces (projection, isometry)

Organisation:

Analysis and algebra lectures take place in parallel throughout the first semester to highlight the links between both subjects.

Main difficulties for students:

Students confuse sequences and series, linear applications and symmetric bilinear forms. They have difficulty distinguishing the different kinds of convergence, and tend to manipulate vectors as real numbers. Calculations and bounds are often difficult to most of them.

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

- Determine the different kinds of convergence for number series. Series of functions, power series or Fourier series.

- Find the block diagonalization matrix of an endomorphism, manipulate scalar products and understand the notion of orthogonality in Euclidean spaces. Express quadratic forms as sums of squares.

Needed prerequisite

Lectures of mathematics of first year (I1ANIF11, I1ANMT11,  I1ANMT21).

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...