Please enable JavaScript.
Coggle requires JavaScript to display documents.
Calculus, , integral | Definition, Symbol, & Facts | Britannica.…
Calculus
Applications
-
-
-
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.
-
Main concepts
Differential Calculus
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.
Integral Calculus
Integrals can be categorized into two types namely definite integral and indefinite integral. However, integration is the reverse process of differentiation.
Limits
Are values that a function or sequence “approaches” as the index or input “approaches” some specific value may be finite or infinite.
Multivariable Calculus
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.
Defining it
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.
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.
Integrals
An integral is a numerical value that equals to the area under a graph of a certain function for a specific interval.
-
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.
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.
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.
-
-
-
Andrea Martínez Fuentes, Andrea Flores Canales, Daniela Mendoza Lozano