These booklets in English have their focus on showing how theoretical results on Fourier series and Fourier transforms can be applied
in applications and examples with the help of the computeralgebra system Mathematica.
Thus, no proofs of used theorems and properties are given in the text. Instead, it is demonstrated how to comprehend properties and applications
of Fourier Series and Transforms with the help of Mathematica, which frees us from time-consuming own calculations and gives us the opportunity
to understand the subject matter with clear illustrations.
The texts incorporate insights from many years of lectures delivered to students of applied mathematics, physics, electrical engineering,
and communications engineering at Technische Hochschule Nürnberg Georg Simon Ohm, starting in their second semester.

Fourier Analysis and Distributions

A First Course with Applications

Rolf Brigola

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Theoretical basics on Fourier series, Fourier transform, z-Transform and Distributions
Numerous application examples for theoretical physics, electrical engineering, system theory and signal processing
Potentials, Waves, Heat propagation, FEM, DFT, DCT, trigonometric Interpolation, Chebychev polynomials, numerical Integration after Clenshaw-Curtis,
Linear Differential Equations with Constant Coefficients, analog und discrete linear Filters (Lowpass, Highpass, Bandpasss, Bandstop, FIR-, IIR-Filter),
z-Transform, Sampling theorem, Sampling and the Principle of OFDM, Heisenberg’s Uncertainty Relation, Time-Frequency Analysis, Wavelets, Hydrogen Atom
127 Exercises with solutions, 175 Figures with Illustrations

 

Fraunhofer Diffraction at a Rectangle, a Circular Wave, Typical WLAN Spectrum, Potentials of Two Charges, Shape of a Hybridized Water Molecule

Additionally, a downloadable paper on the Laplace Transform for Initial Value Problems.