differential calculus - meaning and definition. What is differential calculus
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What (who) is differential calculus - definition

SUBFIELD OF CALCULUS
Increments, Method of
  • The graph of an arbitrary function <math>y=f(x)</math>. The orange line is tangent to <math>x=a</math>, meaning at that exact point, the slope of the curve and the straight line are the same.
  • The graph of <math>y=x^2</math>, with a straight line that is tangent to <math>(2,4)</math>. The slope of the tangent line is equal to <math>4</math>. (Note that the axes of the graph do not use a 1:1 scale.)
  • The mean value theorem: For each differentiable function <math>f:[a,b]\to\R</math> with <math>a<b</math> there is a <math>c\in(a,b)</math> with <math>f'(c) = \tfrac{f(b) - f(a)}{b - a}</math>.
  • The derivative at different points of a differentiable function
  • The dotted line goes through the points <math>(2,4)</math> and <math>(3,9)</math>, which both lie on the curve <math>y=x^2</math>. Because these two points are fairly close together, the dotted line and tangent line have a similar slope. As the two points become closer together, the error produced by the secant line becomes vanishingly small.
  • The graph of a function, drawn in black, and a tangent line to that function, drawn in red. The slope of the tangent line equals the derivative of the function at the marked point.
  • The graph of <math>y=-2x+13</math>

differential calculus         
¦ noun Mathematics the part of calculus concerned with the derivatives of functions.
Differential calculus         
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve.
Boolean differential calculus         
SUBJECT FIELD OF BOOLEAN ALGEBRA DISCUSSING CHANGES OF BOOLEAN VARIABLES AND FUNCTIONS
Boolean Differential Calculus; BDC (mathematics); BDK (mathematics); Boolescher Differentialkalkül; Boolean calculus of differences; Boolean difference; Transition operator (Boolean differential calculus); Potential variable (Boolean differential calculus); Pulse variable (Boolean differential calculus); Potential variable; Pulse variable; Homogeneous potential-pulse circuit; Algebraic theory of the logical operation of electric circuits; Partial differential of a Boolean function; Derivative of a Boolean function; Invariance of a Boolean function; Variance of a Boolean function; Differential of Boolean function; Partial differential of Boolean function; Derivative of Boolean function; Invariance of Boolean function; Variance of Boolean function; Differential of a Boolean function; Boolean derivative; Boolean differential; Total Boolean derivative; Boolean total derivative; Partial Boolean differential; Boolean partial differential; Boolean differential operator; Partial Boolean derivative; Boolean partial derivative; Total Boolean differential; Boolean total differential; Boolescher Integralkalkül; Boolean integral calculus; Boolean Integral Calculus; Logic Differential Calculus; Logic differential calculus; XBOOLE
Boolean differential calculus (BDC) (German: (BDK)) is a subject field of Boolean algebra discussing changes of Boolean variables and Boolean functions.

Wikipedia

Differential calculus

In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve.

The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point. For a real-valued function of a single real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point.

Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration.

Differentiation has applications in nearly all quantitative disciplines. In physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of the velocity with respect to time is acceleration. The derivative of the momentum of a body with respect to time equals the force applied to the body; rearranging this derivative statement leads to the famous F = ma equation associated with Newton's second law of motion. The reaction rate of a chemical reaction is a derivative. In operations research, derivatives determine the most efficient ways to transport materials and design factories.

Derivatives are frequently used to find the maxima and minima of a function. Equations involving derivatives are called differential equations and are fundamental in describing natural phenomena. Derivatives and their generalizations appear in many fields of mathematics, such as complex analysis, functional analysis, differential geometry, measure theory, and abstract algebra.

Examples of use of differential calculus
1. My own science O–level included trigonometry, advanced algebra and differential calculus, and related them to physics, engineering, statics and dynamics.
2. It is easier, and more fun, to "discuss" Birdsong or Talking Heads than – say – to master differential calculus or those other hard topics that the young British foot is determinedly marching away from, year on year.