Saturday, 22 February 2014

Calculus - Awesome Mathematics

This is going to be a long one. Better grab something to eat.

Calculus has remained my favourite topic since JEE. It's the best, the most logical and the most beautiful topic for me. It has it's own beauty. It's a mixture of everything - co-ordinate geometry, algebra, vectors and what not. It's because of my interest in calculus that I performed good in our calculus course. It's extremely important from the point of engineering.
Coming back to JEE, 
Here is a chapter wise discussion of JEE calculus.

Functions : forms the framework of calculus. Understand this concept well otherwise studying calculus will be a tough time for you. Common questions are :

  • finding domain/range of a given function : students commit silly mistake here
  • given a domain and range, finding the number of one-one, onto, etc functions
  • plotting graph and finding number of intersection points of 2 or more functions
study this chapter well, especially graph plotting. It's going to help you a lot.
Practice a number of problems of finding domain/range. There are tricks like :

  • no negative number inside a square root.
  • no division by zero
  • no negative number zero inside log
  • base of log is not equal to 1 etc etc.
They expect you to know these basics. A good practice is to cross check your answer from the options available.

Limits : Most important part. Entire calculus is based on finding limit of a function. L'Hopital's rule is extremely important. Apply it as much as you can. You might also give a try to series expansion but I avoided it because most questions of series expansion can be solved if you are good at L'Hopital's rule. So, I never needed it. However, it is advisable to remember the exponential and logarithmic series.
Questions from this chapter are usually straight forward and simple. You just have to figure out the zero by zero form or the infinity by infinity form and apply L'Hopital's rule.
The variety of questions is large.

Continuity : another important topic. This chapter can be solved if you are accurate and quick at drawing graphs of functions. Continuous functions have many interesting and important properties like "intermediate value property", invertibility etc. Understand them and apply them.

Differentiation : One of the easiest chapter. Doesn't need much effort. Learn the formulas of differentiation - quotient rule, product rule, chain rule, implicit differentiation, differentiation of exponential and logarithmic functions, higher order derivatives. Practice enough questions.

Application of derivatives : Most-most-most important chapter because maximum number of questions are asked from this topic. Rolle's theorem, Lagrange's mean value theorem, concept of maxima-minima, increasing and decreasing functions, inflexion points, etc are really really important. Practice as many questions as you can from these topics. Be prepared to see maximum questions in JEE from this topic. If you are weak at it, then better do something otherwise you will face trouble. This chapter basically is the application of all that you studied in the previous chapters and JEE is all about applying concepts.

Integration : Relatively easy chapter. You won't find many questions in JEE from indefinite integrals. There are a number of formulas to be remembered from this chapter. The formulas are extremely important because you will sometimes need them in definite integration.

Definite integrals : most important topic of integral calculus. There will be a good number of questions from this chapter. Most questions will be based on the properties of definite integrals rather than just applying fundamental theorem of calculus to a definite integral.
Practice enough questions from this topic.

Differential equations : A relatively simple and interesting chapter. Need a good amount of practice and some memorizing skills. Learn the known methods of solving the standard differential equations and you will enjoy this topic.

Books : Arihant differential calculus, Arihant integral calculus (Both by Amit M. Agarwal) are the best books for this topic. They will cover almost everything (except one topic - inflexion points which you may cover from somewhere else). Solve all the subjective and objective problems of the book. You may choose to ignore the extremely long ones because they are meant for olympiads etc.

Revision : Revise from the standard revision packages in the market. FIITJEE GMP or Resonance rank booster or the one provided by your coaching will be sufficient.

Final word : Calculus needs a lot of cramming. There are a number of standard methods and techniques that you are expected to remember. You won't derive the formulas in exam. Just understand them at home and then learn them by heart.
Practice a number of problems especially from application of derivatives and definite integrals. These are the favourite topics and definitely there will be questions from them. You can't afford to lose marks in calculus because it is one of the easiest topic.
Enjoy calculus.

76 comments:

  1. Aman,
    Is it worthwhile to study finding of limits from "first principles" method. Its part of NCERT 11th syllabus (no L'Hospital" rule there). I mean can they ask conceptual questions from this area ?
    (Conceptual in the sense questions other than to just find the limit, but to apply the concept in another situation etc)

    ReplyDelete
    Replies
    1. Everything given in NCERT is worth studying.
      You never know how the questions will be framed

      Delete
  2. hey dint u go for arihant for vectors nd 3d ?

    ReplyDelete
  3. the books that you referred for Biomolecules and Polymers?

    ReplyDelete
    Replies
    1. This is not the right place to ask this question.
      Please post your doubt on the organic chemistry page

      Delete
  4. Hey aman, I am not very good at indefinite integration so can I afford to leave its jee part and just study the board level.

    ReplyDelete
    Replies
    1. Definitely not.
      If you are appearing for JEE 2014, then better learn the standard formulas given in Arihant book.
      if you are for JEE 2015, then start solving arihant integral calculus and solve each and every problem

      Delete
  5. @Aman
    Is integration as a limit of a sum part of jee advanced syllabus??

    ReplyDelete
    Replies
    1. Of course. That's the definition of integrals

      Delete
    2. Hi Aman what about ml Khanna for calculas

      Delete
  6. Do you suggest solving "PROBLEMS.IN.CALCULUS.OF.ONE.VARIABLE by I.A.MARON" ? Is it helpfull??

    ReplyDelete
  7. Replies
    1. To be mentioned in "blog feedback/suggestions" post

      Delete
  8. From which source did you get test papers to practice at home? Are Arihant Practice sets a good option?

    ReplyDelete
    Replies
    1. Fiitjee provided me enough test papers.
      I don't know about arihant

      Delete
  9. IS (A Textbook of Differential Calculus for JEE Main & Advanced) and (Arihant differential calculus) same book??

    ReplyDelete
  10. which is better (A Textbook of Differential Calculus for JEE Main & Advanced) OR (Arihant differential calculus) ??

    ReplyDelete
  11. 1st of all this blogsopt is really cool.
    i have solved about 150 questions of each calculus chapter from target exercise of amit m agarwal. what else can i do to get full marks in calculus in advance?

    ReplyDelete
    Replies
    1. Please mention the year in which you are appearing for JEE

      Delete
    2. what i mean, should i stick with the basics or should i go for high level problems from new pattern sk goyal?

      Delete
    3. depends on you completely

      Delete
  12. can you give a link to the book "Arihant Differential Calculus"

    ReplyDelete
    Replies
    1. google it
      Or purchase from the market.
      Note that you won't get the old book which I used.
      Now you will get a new edition book meant for JEE advanced rather than IIT JEE

      Delete
    2. I did the same before asking not only from Google but even from Arihant's website and it showed only one book tittled "A Textbook of Differential Calculus for JEE Main & Advanced" but you said above that you used a different book that is why I am asking you to please share the link

      Delete
    3. Actually the new book must be the revised edition.
      Go ahead and purchase it
      They must be same

      Delete
    4. Hi Aman,

      This is Confusing.As stated there are two versions of the same book by the same author. Hence I request you to share the correct title and help me choose the right book.

      Links
      Skills in mathematics by Amit Agarwal

      http://www.flipkart.com/skills-mathematics-integral-calculus-jee-main-advanced-7th/p/itmdv8y27n2vphgj?pid=9789351418443&otracker=from-search&srno=t_4&query=amit+m+agarwal&ref=1272b583-dde4-41a1-9adc-c4f842c98b04

      And
      Textbook of Mathematics by Amit Agarwal
      http://www.flipkart.com/textbook-integral-calculus-jee-main-advanced/p/itmdvcpgjdeeeu3x?pid=9789350943960&otracker=from-search&srno=t_13&query=amit+m+agarwal&ref=c68c88ca-97db-42f5-a368-3e464b8de395

      Thanks for Your Time,
      Adway

      Delete
    5. Hi aman I have a doubt , I have already bought calculus book by g. Tewani ,so should I now go for arihant's IC & DC

      Delete
  13. This comment has been removed by the author.

    ReplyDelete
  14. how long shall calculus go ..!>... more than 5 months??.... how much was is ur fiitjee??

    ReplyDelete
  15. hey. i am a jee- 2015 aspirant. i am in fiitjee coaching. for integral calculus, is arihant integral calculus amit agarwal really necessary or if i solve fiitjee package, archive and one other good practice book enough.? i am having this doubt as i dont think i'll be able to complete it. i just went through my friend's copy of the book and it was huge.. so ur advice?

    ReplyDelete
  16. This comment has been removed by the author.

    ReplyDelete
  17. This comment has been removed by the author.

    ReplyDelete
  18. is cengage tewani a good book for calculus or refer other book

    ReplyDelete
  19. Is GN Berman a good book for calculus

    ReplyDelete
  20. is the book you recommended this
    http://www.flipkart.com/skills-mathematics-integral-calculus-jee-main-advanced-7th/p/itmdv8y27n2vphgj?pid=9789351418443&otracker=from-search&srno=t_4&query=amit+m+agarwal&ref=1272b583-dde4-41a1-9adc-c4f842c98b04

    or this
    http://www.flipkart.com/textbook-integral-calculus-jee-main-advanced/p/itmdvcpgjdeeeu3x?pid=9789350943960&otracker=from-search&srno=t_13&query=amit+m+agarwal&ref=c68c88ca-97db-42f5-a368-3e464b8de395

    ReplyDelete
  21. i am aiming for jee 2015 ... but my maths concepts is very weak.... i m doing self study at home from fiitjee rsm... can you suggest me ideas to strengthen up my concept.

    ReplyDelete
  22. Hi Aman. My daughter will be starting class 11 in a couple of months. I want to help her in preparing for calculus for iitjee. Towards that end, I am solving all questions in arihant's differential and integral calculus. I plan to take her through all the questions. My query: will this be enough as far as calculus for iitjee is concerned? She will be having her fiitjee classes though. Your reply will be really helpful. Thanks in advance!

    ReplyDelete
  23. This comment has been removed by the author.

    ReplyDelete
  24. This comment has been removed by the author.

    ReplyDelete
  25. Aman, I jus t finished my class 10 and I am new to calculus.I am studying in a school which has IIT classes for class 11 and 12. What should I do during this summer holidays? Your reply would be very useful to me.

    ReplyDelete
  26. Aman, I jus t finished my class 10 and I am new to calculus.I am studying in a school which has IIT classes for class 11 and 12. What should I do during this summer holidays? Your reply would be very useful to me.

    ReplyDelete
  27. Will tmh suffice for calculus if I have one year in hand

    ReplyDelete
  28. Which book is best for differential calculus

    ReplyDelete
  29. I started solving calculus problems but I am unable to solve almost 90% of them.

    I haven't joined any coaching....

    I am following cengage and preparing for jee 2016...

    Plsss. Help me

    I think I am quite weak in maths!!!!!

    ReplyDelete
  30. HI Aman, I am having problems in solving the solved problems of Integral Calculus by Amit M Agarwal. Though I have completed from the NCERT level but still if we see at the level of Amit M Agarwal book, most of the solved problems are not being solved easily by me. Can you please suggest any strategy to discard the problem

    ReplyDelete
    Replies
    1. Well, do not discard the problems if you are aiming high.
      Learn what the problem aimed to teach you

      Delete
  31. Hello! Can you please tell when is the right time to start doing calculus. Is it better to go with FIITJEE or start by own. By which month should I be starting it.... **Presently in class XI. Completed whole of conic section.**

    ReplyDelete
    Replies
    1. Good question. I'd recommend reading basics of calculus from school level books (RD Sharma if you are in CBSE and ML Agarwal if you are in ICSE).
      It always helps to know basics of calculus because you will be using quite a bit of calculus in physics (kinematics)

      Delete
  32. What is the approx. weightage of Functions,Applications of Deriavatives and Definite Integrals in JEE Advanced?

    ReplyDelete
  33. What is the approx. weightage of Functions,Applications of Deriavatives and Definite Integrals in JEE Advanced?

    ReplyDelete
  34. Hi Aman , I have enrolled in 2 yr coaching . They are making us solve basic problems in the class itself.

    At home , i am only solving the examples + target ex problems of differential calculus by amit aggrawal . plus selected previous year problems . Would it suffice ?

    Thanks



    ReplyDelete
  35. Hi Aman . I'm preparing for jee 2016. have completed solving every calculus question from amit m agarwal,as well as 37 years iitjee. But this time fiitjee aits questions really banged me totally. Now I am not so much confident about calculus. Please suggest what to do.

    ReplyDelete
  36. Hey aman! I am facing troubles in limits. It's taking too much of my time( i haven't completed it in about 2 weeks) is it worthwile to linger on to it?? Or shall i move on and cover it during revision

    ReplyDelete
  37. Bhaiya I am currently in class 11 taking coaching in aakash. In maths currently limits is going on and I am facing difficulties in solving my aakash package. Please help me in getting grip on this topic...
    Or will u suggest to leave it and do that in class 12?

    ReplyDelete
  38. Aman sir, from tomorrow calculas is going to start in my coching so please will u suggeat me which book or source is best for qstns of jee

    ReplyDelete
  39. Sir do you know a good way for mastering integral calculus

    ReplyDelete
  40. HI Aman. Though i have completed almost whole of the mathematics but still i feel some difficulty in solving very hard or subjective type problems. Presently I am also completing TMH Jee Advanced book, what else can I do in order to become pretty good at the topics (especially like integration). Please help...

    ReplyDelete
  41. Hey I am in class 12 and I have not done well in class 11 jee maths preparation. I am a student of resonance and want to ask you that can I start doing TMH mathematics from now for both class 11 and 12 or it is late
    Please reply fast

    ReplyDelete
    Replies
    1. TMH is not recommended for beginners. Start with say RD Sharma

      Delete
  42. Aman Bhaiya
    I am using Cengage series for maths.
    Are they worth solving, or as u said arihant series?
    I am JEE 2017 candidate
    Thanks bhaiya

    ReplyDelete
  43. Aman bhaiyaa im jee 2017 aspirant and am pretty weak at indefinite should i leave it and focus on definite or i need to get thorough with it

    ReplyDelete
  44. Is M.L Khanna IIT MATHEMATICS good for IIT JEE ADVANCED

    ReplyDelete
  45. Is M.L Khanna IIT MATHEMATICS good for IIT JEE ADVANCED

    ReplyDelete
  46. Baiya what are the prerequisites before learning calculus?

    ReplyDelete
  47. I am currently in class 10th and want to learn calculus.Which book should I use? Thanks

    ReplyDelete