Hi Brilliant!

Recently many users have started posting great problems in Calculus section (level 3-5). All of them include variety of functions, new ideas, skill, etc. to solve them.

But I feel just being able to solve an integral or summation doesn't make one good at calculus. There is no use of solving complicated integrals/summations when you are not able to apply them properly. For example the problem, Looks Like Gabriel's Horn To Me is an application of functions which are frequently used in the Calculus section. But very few users have solved it.

I asked a user, who recently posted some good problems, whether he was able to apply them or not? He replied he barely knows application of calculus. I was stunned. What's the point of studying so much when you are not able to apply them? I've seen many people eagerly preparing for Brilliant Integration Contest. But only a few of them have covered all the basics.

Some users have not at all gone into the depth of Differential Calculus and have directly done Integral Calculus. This leads to Nothing. I'll give an example: There is a Slam Dunk Contest in NBA. Many eagerly prepare themselves for that contest. But is that contest as valuable as the NBA title? The answer is no. Just being able to dunk perfectly when no one is standing in front of a player will be of no use in the game. Similar is the case in Calculus.

So please make your basics very strong then start applying them. Later move into high level. No one has set a time limit to calculus. So take your own time and become a master.

I hope everyone liked this note.

Thanks.

## Comments

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TopNewestThis is something that I have echoed often, which is that your ability to apply your knowledge is much more important than the depth your knowledge. Someone who knows how to analyze / problem-solve / research, can easily be taught the new knowledge that he needs, and applies his skills in this area. This is especially true in university / workplace, where they do not expect you to have had all of the knowledge going in, but you learn and apply it along the way.

This is why we set up the chapters with as many levels of challenge quizzes as possible (and we're still working on it with the help of the community). For someone who only knows quadratic equations, how far can he push himself to apply it to novel situations? – Calvin Lin Staff · 6 months, 3 weeks ago

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– Aditya Kumar · 6 months, 3 weeks ago

Thanks for sharing your views :)Log in to reply

I learnt how to apply calculus before I actually dive into things like how to integrate and differentiate, which is also a reason why many of my previous problems require computational methods (Because I did not know how to evaluate it, so I just used Mr wolf.) I think that learning both is important, or it would just seem useless to learn. – Julian Poon · 6 months, 1 week ago

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– Nihar Mahajan · 6 months, 1 week ago

So early you gave your opinion :3Log in to reply

– Julian Poon · 6 months, 1 week ago

.__. \(\)Log in to reply

– Nihar Mahajan · 6 months, 1 week ago

Frog with medium mouth.Log in to reply

Great Note. But my basics are clear. I spent 1 year on it. – Rajdeep Dhingra · 6 months, 3 weeks ago

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– Aditya Kumar · 6 months, 3 weeks ago

Cheers you don't come under that category then.Log in to reply

Differential and Integral calculus have great applications in engineering. Many times you have to deal with the situations which can be solved using transforms which is an important part of Integral calculus. There are still many more things which I can't tell here in this short description.

Use of differential calculus is most common. And we all know most probably. – Aman Rajput · 6 months, 3 weeks ago

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@Aman Rajput – Chinmay Sangawadekar · 6 months, 2 weeks ago

Your Hot integral problems are really too tough but yet awesome !!! are they your self constructed problems ?Log in to reply

– Aditya Kumar · 6 months, 3 weeks ago

Yeah that's what I wanted to say. People ignore differential calculus thinking it is easy and of no use.Log in to reply

Thank you for the advice , I have started applications :) – Nihar Mahajan · 6 months, 3 weeks ago

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– Aditya Kumar · 6 months, 3 weeks ago

That's very nice!Log in to reply

@Aditya Kumar I didn't get your views clearly. By application, do you mean applications of already known concepts to solve problems that are generally require knowledge of advance concepts, or do you mean applying (advance or elementary) concepts to real life problems? – Samuel Jones · 6 months, 3 weeks ago

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– Aditya Kumar · 6 months, 3 weeks ago

The latter one :). See the link. It uses one of advanced concept.Log in to reply

Hello @Aditya Kumar !

I have posted some problems which will be really helpful for others to clear their basics...For example , The series of Ignited Integrals can really be helpful to clear the basics of Integral Calc. Btw can you suggest me some good books for differencial equations? – Chinmay Sangawadekar · 6 months, 2 weeks ago

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– Aditya Kumar · 6 months, 2 weeks ago

Piskunov volume 2 is good for diffyLog in to reply

– Dev Sharma · 5 months, 3 weeks ago

Is it E-book?Log in to reply

– Aditya Kumar · 5 months, 3 weeks ago

You'll get a book.Log in to reply

– Chinmay Sangawadekar · 6 months, 2 weeks ago

Gr8 thanks...Log in to reply