"In my free time I do differential and integral calculus." -Karl Marx
Calculus may not have a stellar reputation among secondary school students as does language arts, history, drama, or even physical education; some may also view it as a last option when choosing A-Level subjects.
Nevertheless, for those planning to study or specialise in the fields of economics, medicine, or engineering, the academic discipline of calculus is absolutely essential. So let's start with the basics, what's the meaning of calculus?
What Is Calculus?
Calculus is a branch of mathematics that studies the rates of change and accumulation of quantities.
The study of calculus consists of two essential concepts: differentiation and integration. Differentiation is the understanding of how quantities change, for example, it helps us to determine how fast an object is moving or how a value is changing over time.
Differential calculus is the process of finding the ever-important rate of change. On the other hand, integration looks at the accumulation of changing quantities, such as determining the population of a species or the shape of a building construction. Integral calculus aims to calculate the prime area underneath the graph of a function.
It is essential to mention that calculus is necessary for all forms of maths since it calculates objects that are moving and changing; since the universe is continually changing, we need calculus. It provides us with an essential toolkit for modelling real-world problems and has a wide range of scientific and practical applications.
Differentiation, denoted by the derivative function (dy/dx) represents the instantaneous rate of change of a quantity.
Integration, denoted by the integral function (∫), involves finding the accumulation or area under a curve.
When was calculus first developed?
Calculus was first developed in the 17th century by British scientist and mathematician Isaac Newton, however, the calculus rules, equations, and examples that we know today were further advanced by Gottfried Leibniz. The invention of calculus was a huge step forward in advancing our understanding of mathematical concepts.
In the United Kingdom, the basic of calculus is an important subject that is not studied in the GCSEs but rather as a subject to prepare for further education in the last year of the A-Levels; calculus can also be mastered at a university level.
Where Can You Find a Calculus Tutor?
If you think that you can master any mathematical topic without the desire or need of help from a private educator; hats off to you! Nonetheless, for the rest of us, mere mortals, a maths tutor is a brilliant idea to navigate through the more difficult subjects and to prepare for exams.
However, many young A-Level or Uni students find it quite challenging to find highly qualified, professional, and engaging private tutors from the overwhelming amount of options available today.
For additional support, consider exploring tailored math lessons that break down complex concepts into manageable segments.
Fun fact: in the last two decades the private tuition industry has grown so much that it is estimated that one in four students have been taught by a private educator.
While some may think that overcoming academic difficulties on their own is possible, the benefits of hiring a private tutor for maths subjects like calculus outweigh all the cons. Some prime reasons for hiring a tutor to review calculus include the following:
- Confidence Booster: private tutors quickly learn the academic defects of their pupils and are quick to commend their strengths and help them through their flaws. After a few failed exams, the encouragement of a private tutor is like a breath of fresh air that helps the student build confidence and keep going.
- One-to-One Attention: since teachers in a classroom setting are supposed to follow the course guidelines and move along studying essential information about calculus, there is little time to show specific attention to each student and answer their questions. Therefore, a great advantage of private tutoring is the one-to-one time spent together.
The advantages of private tutoring cannot be refuted; we hugely suggest hiring an online or in-person tutor near you.
In the UK's major cities such as London, Birmingham, Manchester, Glasgow, Belfast, and Cardiff, there are hundreds of maths tutors offering classes that specialise in calculus.
The best online resource to consult is, without a doubt, Superprof. The majority of our tutors are flexible to the hours and availabilities of their students, offer extremely competitive prices that depend on experience or qualifications (£7-70 an hour), and the best part is that the first lesson is always 100% free!
Consider visiting the Superprof website to search for maths/calculus tutors in the city nearest you. If there are no calculus educators nearby on the Superprof site, without a doubt, one can be found that teaches via an online system such as Skype from a more central location such as London.
Get an online maths tutor for your kids here.
Calculus Resources Online
Did you know that studying for any academic discipline has been made easier due to the world wide web? We are living in the digital age, and so many aspects of learning have been facilitated.
Acquiring a broad knowledge of calculus can be quickly achieved by consulting valuable apps, websites, and listening to podcasts.
The Best Calculus Website
The process of finding a highly recommended calculus-based site is like searching for a needle in a haystack; however, the following option proves that the process doesn't have to be too tricky:
- Weebly: without bells and whistles and stunning graphics, Weebly demonstrates that a straightforward approach with fantastic information is sometimes better when learning calculus. The original PDFs on the site were created by educator Philip Lloyd for students and teachers in the United States during their last years of secondary education; equivalent to A-Levels in the UK. Visit the site to scroll through the distinct calculus themes.
The Most Recommended Calculus Apps to Download
Using a mobile app to acquire information about distinct themes has become extremely commonplace in recent years. The application industry is slowly showing cellular phone users that a phone is not just to take selfies and scroll through the pages of Instagram; many intriguing school subjects can be reviewed.
The subsequent applications, one for Android and one for Apple, are the best available as of today:
- Calculus Pro: boasting excellent reviews from users, Calculus Pro is one of the best calculus-based apps on the App Store. While it is only available for iPhone users, Calculus Pro is very user-friendly and touches on various topics such as limits, continuity, differentiability, optimisation, and double integrals. Download now for a small credit card fee!
- Calculus for Beginners: viewed by many Android users as a brilliant refresher to review essential topics before attending further education programmes, Calculus for Beginners boasts a 4.4 out of 5 stars review on the Google Play Store. Though valuable information is featured, it should never be viewed as a replacement for a textbook, instead, an opportunity for on-the-go practice sessions.
Calculus-Based Podcasts
Do you have a relatively long commute to school or university? Does your secular work allow you some time to listen to music?
If so, finding a highly recommended podcast that discusses calculus is the best option available. The following options are informative and free of charge to download:
- Khan Academy Calculus: possessing such a brilliant reputation, the Khan Academy helps students all over the world learn about essential topics such as calculus. On the Player FM website, there are various calculus topics discussed and episodes last approximately 10-14 minutes long.
- The C-Word with Steven Strogatz: produced by and featured on The Numberphile Podcast that is recorded at the Royal Society in London, the C-Word talks about calculus in an engaging fashion. The episode is not recurring yet lasts 51 minutes; listeners are ensured quality since Strogatz has many years of experience.
By reviewing the previously mentioned websites, apps, and podcasts calculus learners become skilled in everything they will do!
Improve yourself with a Maths tutor here on Superprof.
Basic Calculus Equations and Examples
When reviewing the essential topics of calculus, there are specific tips that help students excel and set them apart from the rest.
For example, many tutors, professional educators, and experts in the field of calculus claim that aspects such as not neglecting homework assignments, creating study groups, and revising information during school breaks are the ingredients for success.
Nonetheless, there are many who are unfamiliar with the equations and examples of calculus; what's a limit? How many subgenres of calculus are there? Are derivatives frequently used?
Also, it is essential to state that although for beginners absolute equations of calculus may resemble Mandarin Chinese, they can be reviewed by taking the time to practise specific examples/problems on highly recommended sites.
On many sites, the most basic calculus equations can be divided into groups of limits, derivatives, and integrals.
Consider reviewing and visiting the Tutorial Math Lamar webpage to encounter sample equations and solutions about some of the most complex and straightforward calculus topics.
There you have it dear readers, some of the essential information about calculus. We are confident that by reading this article, the overall fears and worries of studying calculus have subsided and the realisation that it is one of the world's most brilliant subjects becomes more apparent.
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