Mathematical methods are integral to the study of electronics.

Mathematics in Electronics

Electrical Engineering careers usually include courses in Calculus

Calculus

Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

 (single and multivariable

Multivariable calculus

Multivariable calculus is the extension of calculus in one variable to calculus in more than one variable: the differentiated and integrated functions involve multiple variables, rather than just one....

), Complex Analysis

Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...

, Differential Equations (both ordinary

Ordinary differential equation

In mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....

 and partial

Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

), Linear Algebra

Linear algebra

Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...

 and Probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

. Fourier Analysis and Z-Transforms

Z-transform

In mathematics and signal processing, the Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation....

 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.

Basic applications

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

• Faraday's law of induction
  Faraday's law of induction
  Faraday's law of induction dates from the 1830s, and is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators...
  
  : 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
  Gauss's law
  In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:...
  
  : 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 or the sum of total current at a junction is zero
• Kirchhoff's voltage law: the directed sum of the electrical potential differences around a circuit must be zero.
• Ohm's law
  Ohm's law
  Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...
  
  : the voltage across a resistor is the product of its resistance and the current flowing through it.at constant temperature.
• Norton's theorem
  Norton's theorem
  Norton's theorem for linear electrical networks, known in Europe as the Mayer–Norton theorem, states that any collection of voltage sources, current sources, and resistors with two terminals is electrically equivalent to an ideal current source, I, in parallel with a single resistor, R...
  
  : 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
  Thévenin's theorem
  In circuit theory, Thévenin's theorem for linear electrical networks states that any combination of voltage sources, current sources, and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. For single frequency AC systems the 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
  Millman's Theorem
  In electrical engineering, Millman's theorem is a method to simplify the solution of a circuit. Specifically, Millman's theorem is used to compute the voltage at the ends of a circuit made up of only branches in parallel.It is named after Jacob Millman, who proved the theorem.-Explanation:Let ek...
  
  : 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
  Analysis of resistive circuits
  A network, in the context of electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, every component in the network. There are a number of different techniques for achieving this...
  
  .

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

• Circuit analysis

Components

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

• Electronic components

Signal analysis

• Fourier analysis. Deconstructing a periodic
  Wave
  In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
  
   waveform into its constituent frequencies; see also: Fourier theorem, Fourier transform
  Fourier transform
  In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
  
  .
• Nyquist-Shannon sampling theorem.
• Information theory
  Information theory
  Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
  
  . Sets fundamental limits on how information can be transmitted or processed by any system.