Calculus is a branch that derives from mathematics, which studies the resolution of mathematical problems after determining the variables of an equation progressively, increasing each of its values. This is used to determine curves, slopes, the minimum and maximum values of a function, areas and volumes. It will be studied in a certain range or interval. Calculus is useful for application in various disciplines, such as engineering.
What is a calculation
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It is a derivation of mathematics that is studied through the increase of variables in a specific range to determine an area, a volume, the path of a particle, a slope, among other surfaces or objects. A procedure of rules is used in which signs are used to solve problems and their solution expressed in a mathematical language.
The verb "calculate" refers to solving a mathematical problem by means of the different operations that are required with the data that are had to arrive at a result. In other meanings, the term can also refer to a health condition, in which stones develop in an organ of the body; or also the one that is applied to other professional areas.
The etymology of the word comes from the Latin calculus which means "little stone", due to the elements in the form of balls of the abacus with which things were counted. In ancient times stone balls were used to count livestock, each stone representing an animal.
In everyday life it is so important that people usually perform mental calculation in their daily activities, applying it to tasks at home, school or work, and in the work area it is very useful to perform various accounts such as calculation of payroll.
History of mathematical calculation
Its first origins date back to ancient Greece, approximately 2,500 years ago, when they managed to find the area of a circle with the exhaustive method, which consists of approximating a result based on geometry, and the more complex the accounts, the more approximate it will be..
Centuries later, it was developed in the seventeenth century to solve several problems, which were to find the minimum and maximum values of a range; the length of a curve and its tangent at a certain point; the area of a region; the volume of a solid; find the acceleration, distance, and velocity of a body at a random instant.
Brilliant minds such as Aristotle, Plato, Thales of Miletus, Zeno and Pythagoras, laid the first stones in the construction of the calculus as it is known today.
The limits and derivatives, the integrals, the real numbers, the infinitesimals were developed. After a long chain of contributions, it is Sir Isaac Newton and Gottfried Wilhelm Leibniz who are credited with the fundamental theorem of calculus, demonstrating that integration and derivation are inverse processes.
All these contributions contributed to what we know today as differential calculus, which was also developed by contributions on infinitesimal calculus and mathematical analysis, whose study focuses mainly on derivatives. The integral is related to the differential established in your fundamental theorem.
Calculation function
Through this branch of mathematics it is possible to formulate basic concepts for the creation of important laws and principles of different disciplines such as: chemistry, biology, physics, economics, electrical engineering and some others within the social sciences.
Regarding its application, its main function is to determine the solution to a given problem or unknown according to the variables that are handled in its equations.
In various areas, its function is also to predict when an increase or decrease may occur according to the data provided by the stock index, a distance that a particle must travel at a certain moment, determine an unknown based on other data for applications in engineering, among others.
The function of the variables or indeterminates in the algebraic type can be the representation of an unknown to be determined in the problem; that of a constant; represent a numeric range; they represent in the same way vectors, points, among others.
In an equation or problem there can be more than one variable, which are going to be related in some way; and these will be represented by the first letters of the alphabet when it comes to constants, and the last letters will represent unknowns.
In this there is also what is known as a function, which is the relationship of a set called domain (X) and another set called codomain (Y), for each element X there will be a unique value of Y, and each point of correspondence will define a journey, which is known as rank or scope.
Calculation types
Algebraic calculus
This is the type of computation that performs operations with numbers in general through the use of letters to represent any number. This studies the general properties of arithmetic operations so that they can be generalized in case of any value assigned to the "letters".
This type is characterized by taking for granted the unknowns that are in an operation. By combining numbers, letters and symbols, the language used is known as algebraic language, which was created in the Al-Juarismi period (780-850 AD approximately), whose function is to globalize mathematical operations.
An example of this is that if you want to subtract any number from another, it could be expressed as ab, and in each case, both a and b can take any value.
Arithmetic calculation
It focuses on the study of problem solving of numbers with the basic operations of mathematics, which are addition or addition, subtraction or subtraction, multiplication and division. The results can be achieved through instruments, from the use of the fingers to count. This is the first type of mathematical operation that students face at the school stage.
Calculus in the human body
Gallstones
They are solid structures formed by bile that is in a state of crystallization. These can be of two types depending on their origin: due to high cholesterol levels, one of the main factors being the incorrect emptying of the gallbladder or its irregular displacement; or by high levels of bilirubin.
Its appearance implies inflammation in the gallbladder or bile duct, depending on where they are lodged, which is accompanied by intense pain. The size of these formations ranges from that of a grain of sand to that of a golf ball.
There are some factors that can increase the chances of formation of these structures, such is the case of marrow-to-organ transplants, the intake of contraceptive drugs, intravenous feeding, bile duct infections, diabetes, among others.
Kidney stones
They are stones that form in the urine collection area of the kidney, whose sizes can vary from grit to small balls of one or more centimeters. This causes pain in the abdomen; nausea and vomiting; decreased volume of urine and bleeding in it; presence of calcium, phosphate, oxalate, cystine, urate and phosphate, substances that favor the formation of stones.
The pain is usually sudden onset, very severe and crampy (intermittent), worsened by changes in position, radiating from the back, down the flank and into the groin. Predisposing factors may include recent reduction in fluid intake, increased exercise with dehydration, medications that cause hyperuricemia (high uric acid), and a history of gout. It occurs in 1 in 20 people at some point in their life.
Other examples of calculations
Probability calculation
This type allows knowing the possibilities of an event happening. To calculate the probabilities, you must have several data: for example, the possible cases that this event occurs taking into account all the ways in which this could occur and the cases of occurrence, which would be the situations that meet all the conditions for to happen.
The range of values is between 0 and 1 or in percentages: 0 is equivalent to 0%; 0.5 equals 50%; and 1 equals 100%. In an analysis, 0 would be interpreted as an impossible event, while 1 would represent an event that would surely occur.
The formula to calculate the probability of an event is given by: A = Favorable cases / Possible cases. An example could be the degree of probability that a specific option will come out (winning 1 million pesos, for example) when spinning a roulette with 10 options. The favorable case in this case would be that the million pesos come out, while the possible cases would be 10, expressed as follows:
A = 1/10 → A = 0.1, which can also be translated as a 10% probability that the winning option will come out.
Statistical calculation
Statistics is responsible for obtaining, organizing and analyzing a set of data to be able to explain situations, trends and even to be able to predict future events. For this, the one that is based on simple assumptions is used.
In statistics, this has the purpose of determining the probability of an event occurring, which would be the number of times it has taken place under certain circumstances or conditions.
In statistics it is used to determine the mode, the median and the mean, which are the values to be determined in the universe of data provided for the conclusions of the study. Mode is understood to be the data that most repeats in a set of data collected for a statistical study; the median is the central value of the data, for which the data must be ordered; and the mean or average is the measure that is used the most and is easier to calculate with equations.
Economic calculation
It refers to the theory in economics that states that the use of goods and services, their production and distribution can take place appropriately in an environment of private property, since their presence is necessary for the formulation of prices, which will serve as instrument to account for the granting of limited resources for a specific purpose.
This is applied by socialist companies in a planned way when they must confront expenses, to deduct profitability and the responsibilities that they must fulfill as an organization and with its personnel. This seeks to ensure compliance by the parties involved with the highest amount of resource expenditures.
Settlement calculation
It is defined as the payment that corresponds to the worker for the voluntary termination of the employment relationship with his employer, which can be given either by his resignation from the company, the completion of a contract, by justified dismissal, lack of the boss and disability or death of the employee.
The settlement calculation includes the pay received for the days worked, and the equivalent compensation in terms of bonuses, vacations, bonuses, commissions and other remuneration contemplated in the employment contract; and in the case of having worked for a period greater than 15 years, what is known as the seniority premium is included.
It is important to mention that it is not the same as the settlement calculation, since this is the one carried out in the event that the worker does not have responsibility for the termination of the contract with his employer.
The reasons that may cause this are the deterioration of salary and / or benefits, sexual harassment from the boss or one of its members, or that he is obliged to engage in any activity that goes against his principles. This amount includes three months of salary, 20 days of salary for each year worked, a seniority premium of 12 days for each year.
Integral calculus
It is the division of mathematics that integrates or performs the inverse of the derivation, whose application aims to determine the surface of an area, the volume of a region and solids of revolution (or the volume resulting from the rotation of a plane taking a line as the central axis).
The physicist Isaac Newton (1643-1727) and other great scientists such as René Descartes (1596-1650) and Archimedes (288-212 BC), contributed to the creation of the fundamental theorem of integral calculus that states that the derivative (speed of an object for all moments of the same in a time interval) and integration are inverse.
What is a Spreadsheet
It is a program that allows you to enter numerical data, which can be calculated automatically according to a series of formulas that the software has.
The data must be arranged in a table made up of cells, where the figures will be emptied, organized in a matrix of rows and columns. These programs allow you to graph functions from accounts made by equations.
Among the best known are the Google spreadsheet, Microsoft Excel, PlanMaker, KSpread Apache OpenOffice Calc, Corel Quattro Pro, among others.
Christmas bonus calculation
In Mexico, the calculation of the bonus corresponds to an estimate of 15 days of salary that the employer must grant to its employees on an annual basis, on a date prior to December 20. The easiest way to calculate it is by dividing by two the monthly net income received by the worker.
In the case of workers who have provided services for a period of less than one year and who already have to collect a bonus, the result of their monthly income must be taken by two (the total amount of the bonus), divided by 365 days a year.
This last amount must be multiplied by the number of days worked during that year (example, if it is three months, it corresponds to 90 days) and that must be the amount corresponding to that employee's bonus.
