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So I have started learning Calculus!

Hello Everyone!

After a long wait, now I have started learning Calculus. Being a beginner I am not aware of what topics should I master before learning Calculus, (for example, trigonometry). So I need help. Please tell which topics I should be already prompt in , in order to start a Calculus course. Please provide a brief list of the topics.

Looking forward for your help,

Swapnil Das

Note by Swapnil Das
2 years, 3 months ago

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Another thing: The order in which you must learn Calculus is as follows:

  • Limits

  • Differential Calculus

  • Integral Calculus

Do not leave any of these sections above until you understand every single thing and are quite confident about them. Only then should you proceed to the net section.

Secondly, do not look at even a single Calculus problem on Brilliant (regardless of levels). People of all levels post problems of all levels here and subsequently even the simplest looking problem can turn out t be quite complex. Borrowing one of my mother's axioms, do not walk until you learn to crawl. \[\]I remember that after I learnt the basic properties on Differentiation, I tried to solve problems here. Obviously, they were above my level and I just got confused. Also, the problems are not in a particular order and thus you should not try them at first.\[\] I suggest you first solve problems in books (once through with the basics of Calculus, the Class 11 RS Agarwal - much as I despise it - is a good book to start slightly more advanced Calculus from). Once you complete it, you will be able to solve the Level 1-2 (and some Level 3 problems) problems on Differentiation with ease. Ishan Dasgupta Samarendra · 2 years, 3 months ago

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Hello Swapnil. \[\] I remember when I first learnt Calculus, I was very confused. One of the hardest things about Calculus is the way it becomes really abstract. This is the root cause behind mainly problems faced by many students. I didn't do things in the order I should have and started off with books which were above my level. I sincerely hope that does not happen to you since it is quite a mess that I have had to get out of. \[\]

In order to start with Calculus, one must be thorough with a lot of things. Some of the topics which come to my mind are as follows:\[\]

  • An good grasp of functions, their notations, as well as properties of special functions (such as the exponential function, the logarithmic function, the modulus function and so on so forth.

  • Trigonometry (this is of paramount importance) - however, this becomes really, really long. Note that you \(\text{do not}\) need to know how to solve Trigonometric Equations. You need to know how to manipulate Trigonometric Identities.

  • Series and their notations.

  • And of course a basic knowledge of Set Theory (you just need to understand what a Set is, and what an Interval is).

  • Another thing is that you must understand the meaning and the reason why you are doing whatever you do in Calculus. You must understand why certain properties work and why you do whatever is done. Without this, you will just get more and more confused, or will learn it in a completely mechanical, useless way. Also, if you do not understand something, please do not try to figure it out on your own. You might create theories which will be completely wrong. This happened to me when I was trying to understand a property regarding Integrals. In order to understand, I created a theory which went against the basic definition of Integration!

  • Which reminds me, I cannot stress enough on the need to know the precise definitions of each and every term in Calculus. Trust me, I have realized the value of this the hard way.[]

This is an excellent site to get started with.the basics. I would recommend that you first complete everything in this Calculus I course before you start with any other sources.

Two last suggestions to round it off:

  • However boring or however easy a certain section may be, it is of paramount importance that you understand each and every word. You must do everything in a sequence. One common problem is that students become carried away if they can do something and jump off to much higher concepts. I cannot tell you what a foolish decision this is. \(\text{ You MUST do everything in the correct sequence without skipping a single concept}\).

  • If possible, get a Calculus teacher who could guide you. S/he would be the best way to start learning Calculus.

Wishing you all the very best in your endeavor. Ishan Dasgupta Samarendra · 2 years, 3 months ago

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@Ishan Dasgupta Samarendra So sir should I start learning from the site you gave or books? Swapnil Das · 2 years, 3 months ago

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@Swapnil Das I would recommend the site. This is because the site also explains the conceptual meaning of a limit,or a derivative and so on so forth.Till date I haven't seen a single Calculus book (for beginners) which does this properly. Also, this would help you get familiar with the basic properties in Calculus before you move onto higher levels.\[\] Another thing is that you must also learn the pre-Calculus topics that have been given in the site. Take as much time as you want. Do small portions, but do it everyday. This way, you will retain everything too. Ishan Dasgupta Samarendra · 2 years, 3 months ago

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@Ishan Dasgupta Samarendra Well, I wanted to ask you a personal question, please don't answer if you don't want to.

At what age did you learn calculus? Swapnil Das · 2 years, 3 months ago

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@Swapnil Das I began earnestly 4-5 months back. Ishan Dasgupta Samarendra · 2 years, 3 months ago

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@Ishan Dasgupta Samarendra Another Question, Am I very late to learn Calculus? Swapnil Das · 2 years, 3 months ago

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@Swapnil Das You're on the earlier side in fact! But remember, the important thing is not how early you learn, but how well you learn. Ishan Dasgupta Samarendra · 2 years, 3 months ago

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@Ishan Dasgupta Samarendra I am really privileged to gain your guidance. Thank you! Swapnil Das · 2 years, 3 months ago

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@Swapnil Das Come on, you're paying me too many compliments! You're always welcome. Ishan Dasgupta Samarendra · 2 years, 3 months ago

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@Ishan Dasgupta Samarendra If you don't mind, What do you really want to become? Swapnil Das · 2 years, 3 months ago

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@Swapnil Das Honestly, I have no idea. My passion however is Maths (Calculus in fact!). Ishan Dasgupta Samarendra · 2 years, 3 months ago

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@Ishan Dasgupta Samarendra I am extremely indebted to gain your reply, Sir. Thank you very much for your help. Swapnil Das · 2 years, 3 months ago

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@Swapnil Das Oof! I'm not Sir! And you're welcome. I'm glad I could help:) Ishan Dasgupta Samarendra · 2 years, 3 months ago

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@Swapnil Das You should start up with derivatives. Try to understand what is the rate of change of something with respect to another. And don't forget to get good with the formulas of \(\sum { n } ,\sum { { n }^{ 2 } } \). If you find it interesting. You will learn calculus in no time. Rohit Ner · 2 years, 3 months ago

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@Rohit Ner Thank you for your help. Swapnil Das · 2 years, 3 months ago

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@Mehul Arora please reshare my note.:-) Swapnil Das · 2 years, 3 months ago

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Hi Swapnil! Although I am also a beginner in Calculus, But I strongly think that you should Learn Basic Summations Before starting Calculus. After you learn those, You can easily solve Level 2-3 Summation problems :D Mehul Arora · 2 years, 3 months ago

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@Mehul Arora Can you please tell me, Sir, from where and how should I learn them? Swapnil Das · 2 years, 3 months ago

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@Swapnil Das Search them online. Type "Basic Summation Formulas"

And, From the next time, Kindly refer to me as Mehul. Mehul Arora · 2 years, 3 months ago

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@Mehul Arora Thank you very much! Do you have any other advice? BTW is learning set theory of any use? Swapnil Das · 2 years, 3 months ago

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@Swapnil Das Actually, I don't personally know. I have myself only learnt those summation formulas, and I will learn those product- type formulas soon.

P.S. According to me:- Set theory is of no use xD :P Mehul Arora · 2 years, 3 months ago

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@Mehul Arora Thank you for your time! Please reshare this note so that experts and more people can help. Thanks again!

@Mehul Arora Swapnil Das · 2 years, 3 months ago

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. Nihar Mahajan · 2 years, 3 months ago

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@Nihar Mahajan Errr....., you mean indices? Swapnil Das · 2 years, 3 months ago

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