Mathematical methods in electronics

Mathematical methods are integral to the study of electronics.

[edit] Mathematics in Electronics

Electrical Engineering careers usually include courses in Calculus (single and multivariable), Complex Analysis, Differential Equations (both ordinary and partial), Linear Algebra and Probability. Fourier Analysis and Z-Transforms are also subjects which are usually included in electrical engineering programs.

Of these subjects, Calculus and Differential equations are usually prerequisites for the Physics courses required in most electrical engineering programs (mainly Mechanics, Electromagnetism & Semiconductor Physics). Complex Analysis has direct applications in Circuit Analysis, while Fourier Analysis is needed for all Signals & Systems courses, as are Linear Algebra and Z-Transform.

[edit] Basic applications

A number of electrical laws apply to all electrical networks. These include

• Faraday's law of induction: Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil.
• Gauss's Law: The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.
• Kirchhoff's current law: the sum of all currents entering a node is equal to the sum of all currents leaving the node.
• Kirchhoff's voltage law: the directed sum of the electrical potential differences around a circuit must be zero.
• Ohm's law: the voltage across a resistor is the product of its resistance and the current flowing through it.
• Norton's theorem: any two-terminal collection of voltage sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
• Thevenin's theorem: any two-terminal combination of voltage sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.
• Millman's theorem: the voltage on the ends of branches in parallel is equal to the sum of the currents flowing in every branch divided by the total equivalent conductance.

• See also Analysis of resistive circuits.

Circuit analysis is the study of methods to solve linear systems for an unknown variable.

• Circuit analysis

[edit] Components

There are many electronic components currently used and they all have their own uses and particular rules and methods for use.

• Electronic components

[edit] Complex numbers

• Complex numbers

[edit] Signal analysis

• Fourier analysis. Deconstructing a periodic waveform into its constituent frequencies; see also: Fourier theorem, Fourier transform.
• Nyquist-Shannon sampling theorem.
• Information theory. Sets fundamental limits on how information can be transmitted or processed by any system.