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Regardless of the college course to be chosen, there will certainly be some subjects that will be too famous to take away the sleep and tranquility of students’ lives, especially freshmen.In courses of the area of exact the differential and integral calculus is the great villain. Known for being an extensive subject (in some courses we have calculation I, calculation II and calculation III), this matter is one of the first responsible for failures and delays in courses, especially in engineering.But you do not have to despair. With correct study and focus on the most important parts, it is possible to be approved and, more importantly, to learn all the content passed on by teachers.Interested in the subject? Want to eliminate this nightmare of your life? So, continue reading this article and get to know 6 important concepts about differential and integral calculus. Do not waste time!
1. Differential and integral calculus
First, one must be aware of the concept of differential and integral calculus. Thus, it can be affirmed that this type of knowledge was developed from algebra and geometry, fundamental subjects for the continuity of a course of exact.
The purpose of the calculation is to study and analyze rates of variation of quantities and the accumulation of quantities. Simply put, you can analyze the slope variation of a line and the area below a given solid.
The differential and integral calculus was developed by the physicist Isaac Newton, who counted on the help of Gottfried Wilhelm Leibniz in independent actions. Therefore, it is said that this knowledge is widely applied in mathematics, classical physics, modern physics, chemistry and also in economics.
In other words, where there is certain movement or growth, at certain acceleration, the calculation can be applied.
Surely you have heard of this word and know its meaning. But can you really understand the concept of infinity? Infinity is one of the most difficult concepts to be understood by students and students of mathematics.
To begin with, we must remember that infinity is not a number and, mathematically speaking, there is no concept of infinity. There are infinite sets, infinite limits, infinite limits, and so many others, but infinite numbers do not exist.
Pay attention: When your teacher writes that a certain limit equals infinity, it is making a serious notation error. The concept of equality can only be applied to real numbers and, as already pointed out, infinity is not a real number.
The calculation is widely used for the analysis and manipulation of very small, infinitesimal quantities. These infinitesimals were always considered numbers, infinitely small.
In an imaginary number line, for example, it would be a position where it is not zero, but is “zero” away from zero. Although it is somewhat complex, infinitesimal is one of the most important concepts.
It should be noted that no number other than zero is an infinitesimal, after all its distance from zero is positive. Also, any number that is multiple of an infinitesimal will also be an infinitesimal number.
The concept of infinitesimal arose in the nineteenth century, but since its understanding is very complex and its use made no sense, it was left out. Years later, in the twentieth century, this concept returned to the surface and was replaced by the limit.
The limit is the first concept we have learned in the study of differential and integral calculus. Limits are used to describe the values of a function, using a specific point and analyzing it in terms of the values presented in near points.
As in infinitesimals, the limits are restricted only to the behavior of small numbers, but using ordinary numbers. Now, you can understand why we hear so much the phrase “calculate the limit of x, with x tending to infinity”, is not it?
Another extremely important concept in differential and integral calculus is the concept of derivatives. This knowledge is passed on after the student has consolidated the entire study of algebra.
Derivatives are more advanced studies, responsible for definition, ownership and applications when analyzing the displacement of a graph. To find the derivative, we must carry out a process called differentiation.
The integrals are responsible for the study of definitions, applications and properties of two main concepts: defined integrals and indefinite integrals.
Defined integrals are those in which we insert a given function and get a number in response. This number is able to give us valuable information, such as the area between the graph of the function and the x-axis. It may even be said that the limit of the sum of the areas of the rectangles, called Riemann’s Sum, is the technical explanation of integr indefinite integrals, also known as antiderivatives, have the opposite process to derivation. That is, F is an indefinite integral of f, when f is a derivative of F (case is common in calculus for a function and its indefinite integral). We can use a classical example to facilitate its understanding. Consider that a distance (D) traveled at a given time (t). If velocity (V) is constant, we need only multiply V and t to know the value of D. But if velocity is variable, a more comprehensive method is needed to determine the distance. One way is to use the approximation of the distance traveled by the segmentation of time, in small intervals of time. Then we can multiply the time, in each one of the intervals, by one of the speeds present in that interval and, after doing the Sum of Riemann of the approximate distances in each interval. The basic concept is: if only a small amount of time passes, the speed will practically remain the same. Thus, it becomes easier to determine the distance. A little tricky, is not it? Complementary classes, videos and other forms of learning should be sought, always seeking to facilitate the understanding and understanding of these important concepts.In this article we seek to list some important concepts of differential and integral calculus, but we must improve and seek to understand all the necessary knowledge for that matter. It may be interesting to look for new study methods such as using online classes. There are some companies that offer knowledge in several areas, helping students to be approved in the subjects and, more importantly, to understand the subject that should be studied. Worth knowing, is not it?