TNG014	Transform Theory, 6 ECTS-points /Transformteori/ Advancement level: B
	Aim: The course aims to provide the fundamental knowledge needed to treat problems within such areas of engineering as signal analysis and automatic control. At the end of the course the students should (i) be familiar with the classical integral and discrete transforms and (ii) be able to apply transform methods to solve differential and difference equations and systems of such equations. Prerequisites: TNG001 Calculus in One Variable, TNG010 Multivariable Calculus, TNG002 Linear Algebra Supplementary courses: TNG015 Signals and Systems Course organization: The course is given in the form of lectures and tutorials. Course content: Orthogonal systems of functions: scalar (inner) product; concepts of the norm and completeness; the Gram-Schmidt orthogonalisation process. Fourier series: Fourier coefficients, convergence, Bessel's inequality, Parseval's formula, general trigonometric Fourier series. Integral transforms: the Fourier transform, cosine and sine transforms, the two-dimensional Fourier transform, the Laplace transform. Transform inversion using tables. Convolution and Parseval's formula. Calculation rules. Applications: solution of ordinary and partial differential equations and systems of differential equations. Discrete transforms: the discrete Fourier transform (DFT), the fast Fourier transform (FFT), the z-transform. Convolution. Calculation rules. Applications: solution of difference equations and systems of difference equations. Course literature: To be announced.
TEN1	A written examination, 2 p.
UPG1	Compulsory assignment presentations and/or class tests, 2 p.

Course language is Swedish.