Derivatives and their generalizations appear in many fields of mathematics, such as complex analysis, functional analysis, differential geometry, measure theory, and abstract algebra.ĭerivative The graph of an arbitrary function y = f ( x ) y=f(x). Equations involving derivatives are called differential equations and are fundamental in describing natural phenomena. In operations research, derivatives determine the most efficient ways to transport materials and design factories.ĭerivatives are frequently used to find the maxima and minima of a function. The reaction rate of a chemical reaction is a derivative. 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 = m a equation associated with Newton's second law of motion. 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. 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.ĭifferential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration.ĭifferentiation has applications in nearly all quantitative disciplines. 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. The process of finding a derivative is called differentiation. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. It is one of the two traditional divisions of calculus, the other being integral calculus-the study of the area beneath a curve. If you want more Calculus topics covered, let me know which ones.In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. The Method of Undetermined Coefficients.Exact Equations and Integrating Factors.Homogeneous Differential Equations ( Homogeneous Functions).First Order Linear Differential Equations.In our world things change, and describing how they change often ends up as a Differential Equation: an equation with a function and one or more of its derivatives:
#Meaning of differential calculus series
Fourier Series and Fourier Series Grapher.Solids of Revolution by Disks and Washers.Integral Approximations Calculator and Graph.Graphical Intro to Derivatives and Integrals.Integration can be used to find areas, volumes, central points and many useful things.
Concave Upwards and Downwards and Inflection Points.
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