Moving charge A magnetic field changes the direction of a moving charged particle, but it doesn't do work.
Magnets; Charges in motion The magnetic force acting on a moving charge can be expressed in terms of a magnetic field. Similar to how the electric force can be expressed in terms of an electric field.
Current; Ohm’s law Ohm's law is the linear relation between the potential and the current.
Capacitors The capacitance of two conductors to store energy only depends on their geometry. Adding a dielectric increases the capacitance.
Energy density Another way to find electrostatic potential energy.
Potential The work per unit charge required to go from infinity to point P.
Gauss’ law Gauss' law relates the electric field through a closed surface with the charge contained within that surface.
Electric field The electric field is defined as the force per unit charge in space.
Coulomb’s law The electric force between two particles decreases with the inverse square of the distance, just as the gravitational force.
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.