Mathematical engineering techniques 2

This course is a continuation of S5.
Introduction to additional mathematical tools useful to the electronics engineer.
Chap 1 Bessel functions.
Chap 2 Functional spaces.
Chap 3 Functions of the complex variable
Chap 4 Introduction to distribution theory

Mathematics module - I of the first semester

Chap 1 Bessel functions.

Solving differential equations by integer series
Case of the 1st kind Bessel equation. Properties.
Applications (FM modulation, tubular OEM guide, circular conductor skin effect, etc.)

Chap 2 Functional spaces.

Euclidean spaces of functions
Hermitian spaces of functions
Orthogonal bases in L2(a,b) spaces
Applications (Orthogonal polynomials, Chebyshev's in particular, filter approximation function, etc.). )

Chap 3 Functions of the complex variable

Analyticity property.
Algebraic and transcendental functions.
Laurent series.
Integration in the complex plane. Residue theorem.
Z-transform, definition and properties.
Applications.

Chap 4Introduction to distribution theory

Regular and singular distributions (Dirac, comb, Pf 1/x), definitions and properties.
Fourier transform in the sense of distributions.
Applications, including Poisson relation, Hilbert transform, frequency causality criterion.

- Polycops de cours et de TD
- Mathématique du signal par H. Reinhardt (Dunod)
- Walter Appel Mathématique pour la physique et les physiciens, HetK Editions, Paris
- Auliac Guy, Avignant Jean, Azoulay Elie Techniques mathématiques pour la physique, Ellipses