Tuesday, 14 July 2020

Calculus 3



Calculus 3, calculus is also called infinite calculus, which means the mathematical study of continuous change, in the same way, that geometry means the study of shape, in which the science of algebra means the study of mathematical operations in general, so calculus is a branch of mathematics that studies variables and how they change By looking at them in infinitely small pieces ie infinite.

This science is divided into differential science that studies rates of change and inclination of curves, and integration science that studies the accumulation of quantities, and areas under levels and curves that are also between them, and these two branches are related to each other through the basic theory of calculus.

The science of differentiation

This science mainly searches for finding derivatives for different functions, and Isaac Newton and Leibniz have separately built laws to find formulas that represent the tangent value of the curve for a curve, where the rate of change in the function of the conjugation (f) x is known as the conjugation derivative and symbolized by the symbol (f ′). (x), and finding a conjugation derivative is called a derivation.

The rules for doing this are the basis for differentiation and integration, as the derivative can represent the slope of the tangent line, or the acceleration of a moving particle, by deriving the coupling of its velocity with respect to time, and the velocity of an object can be reached by deriving the coupling of the distance with respect to time, and the derivation can represent any other quantities, here The great power of the differential.

The science of integration

In integration, operations are performed in a completely opposite way, since integration is a reverse process of derivation. Integration of a particle's velocity in relation to time determines its exact location, just as the derivatives are found from calculating the slope, the integration is found from calculating the spaces, for example, the area below the speed-time curve represents the distance That the body cut.

The integral is divided into a finite integral and unlimited integral, and the symbol for the conjugation with the capital letter (F) x represents the integral, whereas the conjugation with the lowercase letter (f) x denotes the derivative, which is entered into the integral process, and in this indication that the lower case that represents the derivative is derived from The uppercase letter representing integration, uppercase and lowercase letters have been used to denote integration and derivatives of functions throughout the ages.

The product of unlimited integrals is a conjugation in the form of (F) x in addition to the boundary C that represents the integral constant, and the finite integration is defined by mathematical values ​​and numbers, where the mathematical functions enter the integral and output with a fixed number, while the integration signal is ʃ.

Calculus applications


Physics:

In physics, all concepts in classical and electromagnetic mechanics are connected through calculus. An example of the use of this science is its use in Newton's second law of motion, since historically the word "change of motion" has been mentioned which indicates that the change in body momentum is equal to the force obtained Affecting the body in the same direction, which is currently expressed as the resultant force is equal to the mass of the body times its acceleration, and the laws of Einstein's theory of relativity and Maxwell's theory of electromagnetic fields are expressed in the language of calculus.

Chemistry:

To determine rates of reaction and radioactive decay.

Biology:

It is used specifically in the population density dynamics, from birth and death rates to population change rates.

Maths:

It can be used in conjunction with other mathematical disciplines, for example, it can be used with linear algebra to find the linear approximation best suited to a set of points within a specific field.

Analytical engineering:

It is used in studying graphs of some functions, and to find values, maximum, minimum, slope values, and turning points in conjugations.

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