Calculus becomes easy and fun if you begin with Basics, which is provided by this book. I used this for my preparation too. For practice and concepts, this book is excellent and then you should try the previous year papers of JEE.
Calculus has certainly an appreciable weightage in JEE. Following books should help you develop the skills and intuition to tackle the problems asked.
|Amit M Agarwal
|Tata McGraw Hill
|Differential Calculus for
jEE MAIN AND ADVANCE
First of all, I would recommend you to learn all the formulae of differential calculus. Because if you don’t learn it then at every single or two steps you may take a pause. This should not happen. Every formula should be on your tip.
You just have to do one thing after this. And that is Practice. Solve as many problems as you can. So that you will come across the types of problems that can be asked on differential calculus. And then with practice, you can learn it.
Continuity, Differentiability– Another easy chapter but is asked heavily in entrance exams. There is little theory in this chapter and to get acquainted with it practice problems and learn to solve problems via the Graphical method. The Graphical method is a time saver in exams because basic method via the first principle or so requires time but if you are quick at drawing graphs you can simply look for sharp points or abrupt changes in the graph
Application of Derivatives– Probably the most important chapter in the whole JEE mathematics. Contains a very large number of concepts. Concepts like subtangent, subnormal, Maxima Minima, Monotonicity, Rolle’s theorem, Lagrange’s Mean Value Theorem, Cauchy Mean value theorem, and Intermediate value theorem are very much important. This topic mixed with Integration is used for making some of the best problems in Calculus. Give this chapter extra time because I’m sure you won’t be able to apply theorem’s in problems easily.
Integration– Another important but easy chapter if you have practiced sufficiently. Moreover, remember that if you are good at indefinite integrals then definite integrals will become a child’s play. Practice indefinite integration from a variety of sources. If you master indefinite integrals then just learn the properties of definite integration you will sail through most of the problems quite easily.
The area under the curves– Important chapter but confusing too. Identifying the correct region is the key. Sometimes the calculations are very lengthy hence questions of an area must be done at the end of the paper If you struggle to draw graphs of function then there is no way you can be good at finding areas of bounded regions. so mastering functions are the basic key mastering area
Differential Equation– Probably the easiest chapter of whole calculus. Understand the concept of degree and order nicely. JEE Syllabus has a very limited part of differential equations including linear differential equations, variable separable method, Bernoulli’s equation, Exact differential method, etc. Just Solve some standard problems you will be with.
Integral calculus is a vast and important topic for both JEE mains and advanced. Approximately 2–4 Questions are expected from this topic in JEE mains and advanced from this topic. 2–4 weeks should be sufficient for a student to prepare for this topic.
Following are some tips for the same:
First, go through your NCERT book and solve some questions from that. This will help you learn all the formulas and also their application. This will prepare you for your board exams too.
After learning all the basic concepts and formulas you can go through some JEE level books like Mathematics for Joint Entrance Examination JEE (Advanced): Calculus by Cengage Publication or Mathematics textbooks from Arihant Publications. The theory in these books is good and after reading the theory, you should be able to solve the questions related to this topic easily.
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