Error functionIn mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: Some authors define without the factor of . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real.
InterruptIn digital computers, an interrupt (sometimes referred to as a trap) is a request for the processor to interrupt currently executing code (when permitted), so that the event can be processed in a timely manner. If the request is accepted, the processor will suspend its current activities, save its state, and execute a function called an interrupt handler (or an interrupt service routine, ISR) to deal with the event.
Computational physicsComputational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline (or offshoot) of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics - an area of study which supplements both theory and experiment.
Interrupt handlerIn computer systems programming, an interrupt handler, also known as an interrupt service routine or ISR, is a special block of code associated with a specific interrupt condition. Interrupt handlers are initiated by hardware interrupts, software interrupt instructions, or software exceptions, and are used for implementing device drivers or transitions between protected modes of operation, such as system calls. The traditional form of interrupt handler is the hardware interrupt handler.
Homogeneous differential equationA differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.
Trigonometric functionsIn mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
Computational scienceComputational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes Algorithms (numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve sciences (e.
Non-maskable interruptIn computing, a non-maskable interrupt (NMI) is a hardware interrupt that standard interrupt-masking techniques in the system cannot ignore. It typically occurs to signal attention for non-recoverable hardware errors. Some NMIs may be masked, but only by using proprietary methods specific to the particular NMI. An NMI is often used when response time is critical or when an interrupt should never be disabled during normal system operation.
Interrupt requestIn a computer, an interrupt request (or IRQ) is a hardware signal sent to the processor that temporarily stops a running program and allows a special program, an interrupt handler, to run instead. Hardware interrupts are used to handle events such as receiving data from a modem or network card, key presses, or mouse movements. Interrupt lines are often identified by an index with the format of IRQ followed by a number. For example, on the Intel 8259 family of programmable interrupt controllers (PICs) there are eight interrupt inputs commonly referred to as IRQ0 through IRQ7.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Jacobi elliptic functionsIn mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for .
Exact differential equationIn mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in physics and engineering. Given a simply connected and open subset D of R2 and two functions I and J which are continuous on D, an implicit first-order ordinary differential equation of the form is called an exact differential equation if there exists a continuously differentiable function F, called the potential function, so that and An exact equation may also be presented in the following form: where the same constraints on I and J apply for the differential equation to be exact.
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
Delay differential equationIn mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e.
Programmable interrupt controllerIn computing, a programmable interrupt controller (PIC) is an integrated circuit that helps a microprocessor (or CPU) handle interrupt requests (IRQ) coming from multiple different sources (like external I/O devices) which may occur simultaneously. It helps prioritize IRQs so that the CPU switches execution to the most appropriate interrupt handler (ISR) after the PIC assesses the IRQ's relative priorities. Common modes of interrupt priority include hard priorities, rotating priorities, and cascading priorities.
Even and odd functionsIn mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function is an even function if n is an even integer, and it is an odd function if n is an odd integer.
Bessel functionBessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation for an arbitrary complex number , which represents the order of the Bessel function. Although and produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of . The most important cases are when is an integer or half-integer.
Interrupt latencyIn computing, interrupt latency refers to the delay between the start of an Interrupt Request (IRQ) and the start of the respective Interrupt Service Routine (ISR). For many operating systems, devices are serviced as soon as the device's interrupt handler is executed. Interrupt latency may be affected by microprocessor design, interrupt controllers, interrupt masking, and the operating system's (OS) interrupt handling methods. There is usually a trade-off between interrupt latency, throughput, and processor utilization.
TimerA timer is a specialized type of clock used for measuring specific time intervals. Timers can be categorized into two main types. The word "timer" is usually reserved for devices that count down from a specified time interval called a countdown timer, while devices that do the opposite, measuring elapsed time by counting upwards from zero, are called stopwatches. A simple example of the first type is an hourglass. Working method timers have two main groups: hardware and software timers.
Theta functionIn mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function.
