TATM51	Transform Theory, 5,3 ECTS-points /Transformteori/ Advancement level: C
	Aim: The course deals with Fourier and other orthogonal series, as well as Fourier, Laplace and z-transforms. It is intended to give proficiency in analytic functions such as is necessary for treating problems in electrotechnology and physics. It is also a prerequisite for the course on Partial Differential Equations. Prerequisites: TATM 06, Calculus Y; TATM 50, Theory of Analytic Functions. Course organization: Teaching is done in lectures and problem classes. Course content: Linear transformations of functions. Convolution. Fourier series. Convergence theorems. Convolution formulas. Parseval's formula. Orthogonal systems of functions. Bessel's inequality. Completeness. Fourier transforms. The inverse transform. Calculation rules. The convolution formula. Parseval's formula. Sine and Cosine transforms. Laplace transforms, particularly the one-sided Laplace transform. Domains of convergence. the inverse transform. Calculation rules. Convolution formulas. Stability of (systems of) differential equations. Discrete Fourier transforms with inverse transforms. Poisson's formula and the sampling theorem, the z-transform with its inverse transform, calculation rules and convolution formulas. Introduction to distributions, particularly "Dirac functions" and their derivatives, as well as their transforms. Course literature: A compendium published by the Institute.
TEN1	Written examination, 3,5 p.

Course language is swedish.