"The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking." -John von Neumann
Have you ever been so bored in math class that you started to question the entire existence of mathematic equations and rules? After this, have you started to slowly resent those who are responsible for giving us a clearer understanding of maths?
If so, you are not alone. Maths was by far my worst academic subject throughout primary and secondary school. I just couldn't seem to understand the main points and the entire logic of mathematics. Hence, the reason I'm a writer and not a mathematician!
Nonetheless, enough about me, maths are widely regarded as the academic subject UK-based students have the most trouble with, in general; yet there are many ways to remedy the solution.
We highly recommend learning more about the basics of a specific maths branch to appreciate the fact that its invention or development has helped people understand important matters more effectively; that is what we're going to do with calculus!
In today's article, we will examine how calculus is one of the most essential mathematics subjects in the universe.
A Brief History of Calculus
"The only way to learn mathematics, is to do mathematics." -Paul Halmos
The previously mentioned quote could not be any truer! Upon staring at mathematical problems in a textbook or worksheet of equations, they may look mindboggling and impossible to complete. Nevertheless, maths are studied in all schools around the world to improve the numeric skills of pupils.
When analysing a topic as complex as maths, it is of the utmost importance to separate each branch or section so that readers/learners can grasp each topic effectively.
Therefore, we shall consider one of the maths most intriguing yet complex branches known as calculus.
What is calculus?
It is important to state that calculus is defined as the study of rates of change. Calculus is essential to all forms of maths since it calculates objects that are moving and changing. Before the invention of calculus, only static objects could be mathematically calculated. Nevertheless, the universe is constantly changing and transforming; therefore, calculus is necessary!
Calculus was developed in the latter half of the 17th century by two very intelligent mathematicians: Gottfried Leibniz and Isaac Newton.
As soon as Newton developed calculus, he used it right away to understand physical systems such as how particles, stars, and matter actually move about and change in actual time. Although Isaac Newton is credited for first inventing calculus, Leibniz is recognised for having created the basic notions used in calculus.
Leibniz introduced the aspect of using basic math functions such as plus, minus, times, and division while employing functions and integrals to calculate rates of change. By following these tools, mathematicians were able to calculate indispensable things such as determining the exact slope of a curve.
Calculus was implemented to understand maths better and replace the static geometry introduced by the Greeks years before.
When is Calculus Studied During the Education System in the UK?
Calculus is necessary; there is no way around this fact. It must be studied to understand so many natural elements that are bound to change. In a world of constant transformation, calculus stands as an anchor to help us understand the things unknown.
Also, it is a little known fact that calculus is used in multiple of the world's most important secular fields. Sectors that make use of calculus include physics, engineering, economics, statistics, and medicine among others.
Since calculus is such an important subject, it can be studied in schools all across the world at a secondary or further education level.
In the United Kingdom, since calculus is a relatively difficult subject, it is studied during the AS or A2 Levels at the age of 16-18 for those who want to continue learning additional topics to prepare for further education programmes. It is important to mention that calculus used to be analysed during the last GCSE years; however, it is more of a specific academic discipline that is best suited for those who want to enjoy a career in a scientific or mathematical field.
Also, for those who didn't have the opportunity of studying A-Level calculus, we greatly suggest hiring one of Superprof's brilliant maths tutor to learn all about the rules that make calculus one of mathematics most important branches.
Are there different types of calculus?
Read the following subheading to become more familiar with the distinct kinds of calculus studying by people all around the world.
Types of Calculus
By analysing the distinct types of calculus, learners become accustomed to which ones they rather study and the functions it handles. Modern calculus has two types of categories that are studied by the world's most brilliant minds.
Therefore, without further ado, we will examine differential and integral calculus; both are distinct and require time to assimilate.
It is essential to state that differential calculus is the process of finding the ever-important rate of change of a variable compared to another variable. Differential calculus studies the derivative, according to MIT, which sets it apart from integral calculus.
The bases of differential calculus are to find the speed of a moving object or the slope of the curve; essentially things that change often. Many mathematical amounts used in physics can be variables and the most common example of this is the variable between distance and time.
Before calculus was invented, especially differential calculus, finding the variables of distance and time was only possible by cutting the time into smaller and smaller pieces. Why? So that after awhile the average speed over the smaller time would get closer and closer to the actual speed at a point in time; can you imagine how long that must have taken?
Thank goodness for calculus!
What about integral calculus? What makes it different from differential calculus?
The main purpose of integral calculus contrasts the principles of differential calculus and seeks to find the quantity where the rate of change or in other words, it is the process of calculating the area underneath the graph of a function.
The best way to complete integral calculus correctly is by dividing the graph into very many small pieces and then draw very thin rectangles under each piece; seems simple enough!
Without using too many technical and fancy words, integral calculus is used to figure out the total size of lengths, areas, and volumes. Integral calculus is truly an important aspect of maths that is necessary in the world today.
Essential Tips to Pass Calculus With Flying Colours
Does the mere thought of calculus send shivers down your spine and keep you up at night? Do you have no idea how to improve your overall results in calculus and feel discouraged every time attending class?
Don't be afraid; there are many tips and tricks that can be implemented that can bring your exam results in calculus from zero to hero!
Therefore, without any further delay, the following are the best pieces of advice from qualified mathematics experts about how to pass calculus and actually enough the subject:
- Study, Study, and Study: by studying and making a conscious effort to review essential topics of calculus, students are setting themselves up for success. Be ready to dedicate a few hours every week to assimilating the basics of calculus; this will make sure that you are up to date with all the aspects of calculus.
- Get a Study Partner: find a student or multiple students in your calculus class to study with each week; by doing so you share your strengths and weaknesses with each other. Spend time talking about how to solve calculus problems and go through them together.
- Find Helpful Online Resources: when you do not have the possibility of studying with others, a tutor to provide assistance, or after class times when a teacher cannot be consulted, we highly recommend finding trusted online resources. The best calculus sites are set to aid pupils to complete calculus exercises that immediately show their results and help them get better.
- Hire a Tutor: we cannot stress the importance of private, after-school, tutoring sessions. The best calculus educators guide struggling students through aspects of maths that they simply do not understand. 100% worth the investment, private tutors are on the rise and for good reason.
By putting into practise the previously mentioned advice, we are certain that A-Level or university grade students will ace their impending calculus exams.
There you have it, dear readers, fundamental information about the bases of calculus; it really doesn't have to be such a painful subject to examine!