Calculus. This word is enough to bring out the deepest fears of a student or is enough to put Sheldon Cooper at ease. Calculus is defined as the branch of mathematics that studies the continuous change of anything concerning another element. Calculus is generally divided into differential calculus and integral calculus. Differentiation and Integration form the crux of calculus and are opposites of each other. Let us see know how hard is calculus.
While math in itself is seen as a difficult subject for many, calculus pushes math back in this regard. Calculus is difficult for some people as it is placed at a higher conceptual level than other mathematical concepts. The difficulty level of calculus varies from person to person and can’t be generalized. Despite the varying capacities of each person, the majority of learners find calculus hard. Not only is calculus on a higher difficulty level, but it is also abstract when compared to other mathematical concepts.
To all the haters of Calculus, you may have to grit your teeth and learn it, because many fields rely heavily on calculus. Physics is one such, whose puppeteer is calculus. Calculus is used not only in the scientific fields but also in commerce and marketing, to analyze growth and other statistics.
What is Calculus?
The word “Calculus” means “small pebble” in Latin. The Romans used these pebbles for counting and that is what calculus is named after. Although Sir Isaac Newton is credited for the invention of calculus, many great mathematicians and physicists over time have contributed to the development of calculus as we know it today.
As mentioned before, calculus is the study of changes and comprises derivative and integral calculus. The derivative part of a function defines the rate of change at a specific point. Meanwhile, the integral component shows the accumulation of discrete and small values of a function over a range.
How did Calculus come up to be so important?
Back in the seventeenth century, mathematicians Gottfried Leibnitz and Isaac Newton came up with the concept of calculus to make sense of the change in motion. Their invention not only helped them but all mathematicians, astronomers, physicists, and scientists to help them in understanding the motion of planets, stars, and other cosmic objects better. Not only this but it is also used in analyzing population growth, climate change, and even in the creation of video games! To sum up calculus, it is the study of the rate of change of anything and this is imperative to study because nature is always changing and things in nature are always changing as well.
Why is Calculus hard for some students?
The main reason for calculus being hard for some learners is that the conceptualization is higher than other concepts previously dealt with in mathematics. Some learners find memorizing formulae a little hard as well. Apart from this, calculus problems also tend to have applications of trigonometry, algebra, geometry, logarithms, limits, and others. This means that when doing a calculus question, not only would one have to know the concepts of calculus but have to be good at other concepts. The applications of trigonometry, limits, and logarithms extend to a broad base in calculus.
Calculus is not perfected by memorizing the formulae but with a deep and critical understanding of the concepts and the applications of the same.
Applications of Calculus in real life
Calculus has many practical applications, ranging from stock markets to rocketry. It may not be obvious as we are not solving calculus problems every moment of our lives, but the technology that we use to solve our problems are all equipped with calculus formulae and algorithms to make the work easier for us.
In chemistry, the radioactive decay time of elements can be predicted by calculus. Calculus is one of the most important concepts to know in structural engineering. Astronomers use calculus to determine the position of cosmic objects and to determine the stats of a rocket as well.
The most obvious application of calculus is in engineering where it is very prevalent. In the field of medicine, calculus is used to predict bacterial growth, epidemiology, cardiology, pharmacology, neurology, and entomology among others. Calculus proves to be very helpful in monitoring weather data, economics, stock markets, population growth, birth and death rates, and simulations for video games. It would be a surprise for many of you when you know that calculus is also used in harmony and acoustics in music!
Is it important for me to be good at calculus?
Well, yeah. That is because when you are aiming for a career that depends on calculus (which is most careers), calculus is inevitable. Even in other places where your career isn’t directly dependent on calculus, there are implications of calculus. Being good at calculus would also help in the development of other skills like problem-solving and presence of mind since you learn where to use what formula or concept at. It also helps you in mastering the other basic concepts of math like trigonometry, functions, and limits. Other than being important, it is good if one is good at calculus and knows where to apply it.
Can calculus ever be easy for me?
The answer to this is also yes. That is because all that you need to master calculus is diligence and hard work. Remember how the division was hard for us and now it is one of the easiest things in life, as easy as having your meals? That was because we were all repeatedly shown the concept and were able to familiarize ourselves with it over a long period. Similarly, familiarizing oneself with calculus by repeated practice will make calculus easy to understand and easy to solve.
How can I master calculus?
Perfecting anything is not possible without everyday hard work and endurance. Solving problems every day would go a long way in the process of mastering calculus. But before trying to master calculus, it is better to study and revise the earlier concepts of math and brush through the prior knowledge that you have already since math is a subject that builds on prior knowledge.
It would also help when you can visualize and picture the problem you have at hand before solving it. Drawing a diagram would help in most cases and that is the first big step. Most errors in calculus happen because the question is misunderstood, so reading the problem more than once and taking time to understand it would be a great thing to do before attempting to solve it.
Another part of the problem-solving process where the most error occurs is the application of a particular formula or concept in the problem. Taking time to think of the best way to go about solving the problem would be a huge step in the right way. Sometimes, problems in the field of calculus tend to mislead the learner and they might have to restart the problem again in a different way. This is normal and errors in calculus occur often. Avoid getting discouraged by them because as a learner, it is important to make mistakes.
Some tips to learn calculus
- Apart from everyday practice, a good study timetable can help in being regular.
- Staying curious about the implications and trying to spot real-life applications will make the study process more interesting and exciting.
- When you come across an error, you can use online tutorials or online problem solvers to help you solve the problem, but try that out only after you have manually tried the problem multiple times and are not able to arrive at the correct solution.
- Use online question banks and quiz platforms initially and then go on to give yourself tests.
- Eventually, try timing the time you take to complete a set of questions and try to improve upon that.
- Try to form your questions and solve them.
- But most importantly, be patient with yourself and give yourself time to learn and master any subject. Calculus is quite a tough nut to crack and you will have to use your resources smartly.
- Internalizing information and not dealing with them at the last minute is very important if you want to master calculus.
- Try to have sticky notes that you can use to revise your formulae at a glance and as always, using different colors to write will make the information stay in your mind.
Calculus has numerous applications in almost all fields. It may be challenging for you as a student, with a proper plan and hard work, calculus can be an easy concept and will help you get over your fear of calculus.
How long does it take to learn calculus?
This depends entirely on each individual as the grasping capacity of individuals may vary. But the general time it takes to have an idea of one concept in calculus can take anywhere between four to six months.
What are the most important things to know in calculus?
The most important parts of calculus are the definitions, theorems, and formulae as they help in solving all the problems. Revise them regularly as no matter how advanced the concept is, the definitions and theorems would still be basic and simple.