MATEMATIKChalmers 0pt

kurskod= TMA361

Engelska namn= Fourier Analysis

Ges av= md

Svenska namn= Fourieranalys TM3 (för IKMVZ)

Antal poäng= 4

Beskrivning= This course presents the theory and application of Fourier series and integrals. It covers the following topics: Examples of initial-boundary value problems for partial differential equations (PDEs), the method of separation of variables, periodic and general Fourier series and their convergence theorems, linear spaces, scalar product and norms, orthogonal sets, Bessels inequality, Parsevals formula, completeness, Sturm-Liouville problems, eigenfunction expasions, method of separation of variables for solving PDEs, techniques of solving inhomogeneous problems, some examples of physics, Bessel functions, Solving problems in cylindrical coordinates, orthogonal polynomials (Legendre, Hermite, Laguerre polynomials), Solving problems in spherical coordinates, Fourier Transform (calculus, convolution, Plancherel formula, applications to solve PDEs), Laplace Transform (calculus, applications to, both ordinary and partial, differential equations), and an introduction to generalized functions.

Förkunskaper= The participant is presumed to have

(i) a solid background in calculus of one and several variables,

(ii) knowledge of the elementary theory of linear ordinary differential equations,

(iii) an acquaintance with the complex number system and the complex exponential function.

Mål= To give a solid background for the students to solve, e.g., partial differential equations using the ideas from modern analysis without getting bogged down in the technicalities of rigorour proofs.

Språk= depends on audience (swedish or english)

Bok= Fourier Analysis and its Applications, G. B. Folland, Wadsworth & Brooks/Cole, 1992.

Obligatorisk= Compulsary for TM studies

Teaching staff=

Examiner and Lecturer: Mohammad Asadzadeh, mohammad@math.chalmers.se

Termin= Period I in Fall

Bedömning= Written exam

Limited number of places.