Calculus

Defining it

Derivatives

Integrals

Applications

Derivatives represent the rate of change of a function with respect to a determined variable.

An integral is a numerical value that equals to the area under a graph of a certain function for a specific interval.

It studies the rates of change caused by time or other reference variables, this in order to gain a better and clearer understanding of the meaning of an operation as a part of a problem.

Theorems

The Mean Value Theorem for Integrals says that a continuous function on a closed interval takes on its average value at some point in that interval. We state this theorem mathematically with the help of the formula for the average value of a function.

It can be useful to obtain the original funtion of a derivative.

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integral | Definition, Symbol, & Facts | Britannica. (2022). In Encyclopædia Britannica. https://www.britannica.com/science/integral-mathematics
derivative | Definition & Facts | Britannica. (2022). In Encyclopædia Britannica. https://www.britannica.com/science/derivative-mathematics
BYJU'S FutureSchool. (2021, December 5). The Applications of Calculus in Everyday Life (Uses & Examples). BYJU’S Future School Blog; BYJU’S Future School Blog. https://www.byjusfutureschool.com/blog/the-application-of-calculus-in-everyday-life/#Economics
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Bolton, B. (2002). Calculus - an overview | ScienceDirect Topics. ScienceDirect. https://www.sciencedirect.com/topics/mathematics/calculus
‌L.B. (2019). What is the difference between a derivative and an integral? | Wyzant Ask An Expert. Wyzant. https://www.wyzant.com/resources/answers/602205/what-is-the-difference-between-a-derivative-and-an-integral
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Ferrao, L. (2022). Applications of Calculus: Finance, Graphics, Architecture & More. Retrieved 9 April 2022, from https://www.embibe.com/exams/real-life-applications-of-calculus/

Evaluate survey data to help develop business plans

Determine the amount of materials necessary to construct curved structures

Calculus is used in epidemiology to know the spread rate of an infection.

To launch an exploratory probe, it allows each of those variables to accurately take into account the orbiting velocities under the gravitational influences of the sun and the moon.

Integral and differential calculus are used in electrical engineering for calculating voltage or current through a capacitor.

Set the minimum payments due on credit card statements at the exact time the statement is processed.

Differential calculus is used in biology to obtain the bacterial growth rate.

Andrea Martínez Fuentes, Andrea Flores Canales, Daniela Mendoza Lozano

It study it by modeling and using the ´rates of change´ equations that will allow the physical system to be represented, an analysis made and a solution formed under defined conditions.

Main concepts

Differential Calculus

Integral Calculus

Limits

Multivariable Calculus

Are values that a function or sequence “approaches” as the index or input “approaches” some specific value may be finite or infinite.

It deals with the rate of change of one quantity concerning another. The derivative of a function at a certain point describes the rate of change of the function at that input.

Integrals can be categorized into two types namely definite integral and indefinite integral. However, integration is the reverse process of differentiation.

Is the extension of calculus functions of one variable to calculus with functions of several variables. Also, the differentiation and integration operations will be performed on functions involving several variables, rather than just one.

Relationships

The derivative and integral are linked in that they are both defined via the concept of the limit: they are inverse operations of each other: and they are both fundamental to much of modern science as we know it.

That a derivative and an integral are opposites of each other. A derivative, is the slope of a function at any given point. An integral, is the area under the curve over a certain interval.

The Evaluation theorem states that if we can find an antiderivative for the integrand, then we can evaluate the definite integral by evaluating the antiderivative at the endpoints of the interval and substracting.