Discrete transfer functions (unfinished) Transfer function in the Z-domain let us determine the discrete system response characteristics without having to solve the underlying equations.
Inverse Z-transform (unfinished) The inverse Z-transform, can be evaluated using Cauchy's integral. Which is an integral taken over a counter-clockwise closed contour C in the region of converge of (z)
Z-transform proofs Proofs for Z-transform properties, pairs, initial and final value. Includes derivative, binomial scaled, sine and other functions.
Z-transform and proofs (unfinished) Derives the Z-transform using the Laplace transform. Includes stability criteria and region of convergence where the z-transform is valid.
Laplace in mechanical systems Analyzes springs, resistance and mass in mechanical systems using Laplace transforms to solve the ordinary differential equations.
Laplace transform and proofs The Laplace transform turns differential equations in time, into algebraic equations in the Laplace domain thereby making them easier to solve.
Fourier transform The Fourier transform takes a time-domain signal and decomposes into the frequencies that make it up,
Euler’s formula Proofs Euler's formula using the MacLaurin series for sine and cosine. Introduces Euler's identify and Cartesian and Polar coordinates.
Impedance Derives the formula for impedance of common passive electronic components using the models for energy storage of those parts.