Differential

Differential may refer to:

Mathematics

Differential (infinitesimal)

The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in the variable x. The idea of an infinitely small or infinitely slow change is extremely useful intuitively, and there are a number of ways to make the notion mathematically precise.

Using calculus, it is possible to relate the infinitely small changes of various variables to each other mathematically using derivatives. If y is a function of x, then the differential dy of y is related to dx by the formula

where dy/dx denotes the derivative of y with respect to x. This formula summarizes the intuitive idea that the derivative of y with respect to x is the limit of the ratio of differences Δy/Δx as Δx becomes infinitesimal.

There are several approaches for making the notion of differentials mathematically precise.

Differential (mechanical device)

A differential is a particular type of simple planetary gear train that has the property that the angular velocity of its carrier is the average of the angular velocities of its sun and annular gears. This is accomplished by packaging the gear train so it has a fixed carrier train ratio R = -1, which means the gears corresponding to the sun and annular gears are the same size. This can be done by engaging the planet gears of two identical and coaxial epicyclic gear trains to form a spur gear differential. Another approach is to use bevel gears for the sun and annular gears and a bevel gear as the planet, which is known as a bevel gear differential.

Overview

In automobiles and other wheeled vehicles, the differential allows the outer drive wheel to rotate faster than the inner drive wheel during a turn. This is necessary when the vehicle turns, making the wheel that is traveling around the outside of the turning curve roll farther and faster than the other. The average of the rotational speed of the two driving wheels equals the input rotational speed of the drive shaft. An increase in the speed of one wheel is balanced by a decrease in the speed of the other.

Forensic science

Forensic science is the application of science to criminal and civil laws. Forensic scientists collect, preserve, and analyse scientific evidence during the course of an investigation. While some forensic scientists travel to the scene to collect the evidence themselves, others occupy a purely laboratory role, performing analysis on objects brought to them by other individuals. In addition to their laboratory role, forensic scientists testify as expert witnesses in both criminal and civil cases and can work for either the prosecution or the defense. While any field could technically be forensic, certain sections have developed over time to encompass the majority of forensically related cases.

Etymology

The word forensic comes from the Latin term forēnsis, meaning "of or before the forum." The history of the term originates from Roman times, during which a criminal charge meant presenting the case before a group of public individuals in the forum. Both the person accused of the crime and the accuser would give speeches based on their sides of the story. The case would be decided in favor of the individual with the best argument and delivery. This origin is the source of the two modern usages of the word forensic – as a form of legal evidence and as a category of public presentation. In modern use, the term forensics in the place of forensic science can be considered correct, as the term forensic is effectively a synonym for legal or related to courts. However, the term is now so closely associated with the scientific field that many dictionaries include the meaning that equates the word forensics with forensic science.

Public speaking

Public speaking (sometimes termed oratory or oration) is the process or act of performing a presentation (a speech) focused around an individual directly speaking to a live audience in a structured, deliberate manner in order to inform, influence, or entertain them. Public speaking is commonly understood as the formal, face-to-face talking of a single person to a group of listeners. It is closely allied to "presenting", although the latter is more often associated with commercial activity. Most of the time, public speaking is to persuade the audience.

Overview

In public speaking, as in any form of communication, there are five basic elements, often expressed as "who is saying what to whom using what medium with what effects?" The purpose of public speaking can range from simply transmitting information, to motivating people to act, to simply telling a story. Good orators should not only be able to engage their audience, but also able to read them. The power of a truly great presenter is the ability to change the emotions of their listeners, not just inform them. Public speaking can also be considered a discourse community. Interpersonal communication and public speaking have several components that embrace such things as motivational speaking, leadership/personal development, business, customer service, large group communication, and mass communication. Public speaking can be a powerful tool to use for purposes such as motivation, influence, persuasion, informing, translation, or simply ethos.