The history of calculus
People, even from the ancient times, were always intrigued by the term of infinity. Even now, when there are many uses for it, it still holds some mysteries. From this term, alongside with limits and infinite partitions, the calculus was born.
The definition of a definite integral is derived trough the area of the region bounded by the graph
Let be any function and its antiderivative. The set of all antiderivatives of is called indefinite
One of the basic problem of mathematics in its beginning was the problem of measurement of lengths,
In this lesson we will apply the knowledge about the first and second derivative of a function on the ...
Let be an open interval. The function is: 1.) increasing on if () , 2.) strictly increasing on if ()
Firstly, we will observe the limit of a function on a intuitive level. Consider the function
The concept of continuity of a function is intuitively clear, however, very complex. Less formal, if
Geometrically, the problem of finding the derivative of the function is existence of the unique
For convergent sequence we can also notice many other important properties...
Let's first try to notice some important characteristics of sequences...
In geometric sequence every member that starts from the second is equal to the first member...
In arithmetic sequence every member of that sequence is equal to the previous one...
Infinite sequence of numbers is a sequence that has infinitely many members...
Most people were discouraged by this part of math because it simply seemed ridiculous, and the popular opinion was that there is no such thing as infinity. Since people didn’t accept this idea for a long time, calculus didn’t evolve as fast. One of the first sentences that accepted the idea of infinity was found in ancient Chinese text Zhuanzhi.
“When there is a rod of length one feet and you cut away half of it per day, it can last forever.”
Calculating surface of some figure was always very interesting. Some figures were simple to calculate. People simply divided the character into many parts they knew how to calculate and then simply add their surfaces together. The most headaches caused surface of a circle. As you know, you can’t divide circle into squares or triangles because you’ll always have bits of surfaces missing or bits of surfaces going over the circle. This is where the idea of limit came to its existence.
In the 17th century, people started to embrace the idea of infinity and limits as well as their important rule in the development of mathematics. Two most important mathematicians were Isaac Newton and Gottfried Liebniz. If you are interested in mathematics as a science, you’ll be hearing about them a lot.
After some small improvements in that field, many new theorems and definitions emerged. Many problems that were unsolvable before were solved with ease and this is why calculus was developed so quickly. People were so occupied with new theorems and new applications that sometimes they didn’t see into everything there was about their subject. Because of this, full applications of calculus were fully developed in the 19th century.
How to learn calculus?
Calculus may not be one of the easier parts of math but problems in this part can be easily visualised. Everything you do can be drawn and imagined. It is also great because it is not monotonous and you can always find different and fun tasks. When learning calculus it is important to be patient and practice a lot. If you are a beginner at it, there isn’t many rules you have to follow so it’s not hard to get a hang of it.
Why is this important for you?
There are many different parts of calculus with various applications. You will use derivations for finding tangents, motion, optimization; integrals for volumes, area between two curves, length of a curve and many more. If you are not that interested in advanced math, think of learning this anyway. Calculus isn’t that hard to learn, but it will help you a lot in your real life problems. You will learn how to visualize and break down a problem.