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 Êƒ.

### 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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