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.