What is calculus?
In the most general sense, calculus is the act of calculating – that is, following a procedure to obtain the result of an operation. From a more mathematical approach, it explains the algorithmic process to get the result of symbolized variables that are known in advance.
This discipline follows a structure of steps based on knowing certain data whose numerical value may or may not be known. In addition, it offers a response to the arithmetic operations of addition, subtraction, multiplication, and division, though unlike algebra: it draws on the same procedures but does so in a more abstract way, substituting numbers for letters.
Calculus is also useful for determining areas, volumes, curves, slopes, and the maximum and minimum values of a function, which is why it is closely linked to other scientific disciplines such as mathematics, physics, and engineering.
What terms are related to mathematical calculation?
- Function: the relationship between two sets, where the first set is given a single element of the second, meaning its value depends on that given.
- Variables: amounts that can have an indefinite number of changes generated by different conditions.
- Constants: Unlike variables, a constant has a fixed value that does not change.
- Derivatives: the term used to calculate the answer to a function by altering its initial value.
- Increment: the difference between two values of a variable.
- Limit: this term is attributed to a variable when it approaches a constant value without becoming equal to it, with the value changing according to a set of factors.
What are the branches of calculus?
There are different forms of calculus, each with its own characteristics, structure, and theorems. The main branches include:
- Infinitesimal calculus: the study of limits, derivatives, integrals, and infinite series.
- Differential calculus: establishes the change of an object according to its variables and focuses mainly on the study of movement, speed, and acceleration.
- Integral calculus: calculates a value when the acceleration in the area where it is located is known.
How is calculus applied in other fields or disciplines?
Mathematical calculus explains many phenomena and processes that surround humankind. Modern technology would not be possible without this discipline, which can be applied to nature, as well as to economics, administration, and physics. Basically, every scientific approach draws on equations that, in turn, involve functions and derivatives, and their analysis is done by using calculus tools.
For example, in engineering, calculus makes it possible to measure structures and areas; in environmental fields, calculus can be used to count and study the growth of various organisms; in electronics, it is used to calculate current loads or discharges, as well as their times; in accounting, it makes it possible to determine the profits or losses that may be generated by different projects.