# Differential Calculus for JEE Maths

Differential calculus forms an integral part of the JEE Maths syllabus. Not only does it form a separate branch by itself, but also has its uses in other fields. In this article we will discuss what you need to know, and what is the best book for calculus for IIT JEE (or books). Because if you have a good grasp on the concepts of differential calculus, you will score well in JEE Maths.

## Syllabus

The syllabus for differential calculus in JEE Maths is vast. A fair number of questions in JEE Mains, as well as JEE Advanced, are taken from differential calculus. Being a highly method-based and technique-based topic, it is one of the most scoring chapters in IIT JEE Maths.

The chapters that constitute JEE Maths differential calculus are as follows.

### Functions

Functions form the skeleton of differential calculus. They provide the framework for calculus to develop. A good understanding of the fundamentals will help you get a clear picture of calculus. You should have an idea about the mathematical definition of functions, and the different kinds of mapping such as injection, bijection, and surjection.

A typical question deals with the calculation of domain and range for a given function. So be sure to practice a lot of questions on domain and range calculation. It will develop your intuition for differential calculus.

Inverse functions is another hot topic that demands your attention. Problems based on it generally require a deeper understanding of functions and their properties. An effective approach is the graphical analysis of functions. You will be able to solve questions in comparatively less time with graphs. A good book for graphs in JEE Maths is “Play with Graphs” by Amit M. Agarwal.

### Limits

It is essential that you thoroughly understand the concept of limits. It is a fundamental idea which is used extensively in differential calculus. You should be able to calculate limits for most of the functions which are given to you.

Try out all the problems with different methods. It will help you comprehend the idea of limits in a much better way. L’Hopital Rule is the most important technique for evaluation of limits, so become competent enough to apply L’Hopital Rule.

The other method that comes in handy is the series expansion for limit evaluation. You should remember the exponential series, the logarithmic series, and the trigonometric series for cosine and sine functions.

### Continuity

The idea of limits is a prerequisite to continuity. Here, the concepts that you learn in functions become important. You will be able to solve most of the problems if you are quick at drawing accurate graphs. It is a good idea to keep the properties of continuous functions and the theorems associated with them in the back of your mind.

### Differentiability

This is a relatively easy chapter. You can crack it if you remember the differentiation formulas and practice a sufficient number of questions on them. You are not expected to derive formulas during exam hours–so do not forget what you learn.

The only thing that demands your attention is the definition of the derivative. I highly recommend that you remember it. Some problems from other chapters can be solved quickly and easily if you know what a derivative is.

### Application of Derivatives

This is the most important chapter. It sums up everything you have learned so far. Some of the important tools that you must know are maxima and minima, inflection points, Rolle’s theorem, Lagrange’s mean value theorem, increasing and decreasing function, concavity of a function, convexity of a function, and approximating the value of a function.

Image by Tashatuvango

Prepare this chapter thoroughly. The JEE likes to test your preparedness on this topic, so practice as many questions as you can. You can also use the concepts from other disciplines of mathematics. A few problems may require geometrical insight. The bottom line is that the problems may easily be solved with a creative approach, so don’t restrict yourself to one specific train of thought.

### Differential Equations

Image by hafakot

This topic forms a major part of differential calculus, but fortunately, its share in JEE Maths syllabus is limited. It requires a good amount of practice and a little memorizing skill. You should know some of the standard forms of differential equations and their standard solutions.

Some of the forms that you should remember are:

• variable-separable differential equations
• homogeneous differential equations
• exact differential equations
• how to calculate the integrating factor for a given differential equation

The above shows the order in which differential calculus should be taught. An important thing to note is each chapter derives itself from the concepts learned in chapters prior to it. So, it is advised you do not have any weak links in these chapters.

## Best Book for Calculus for IIT JEE

There are a lot of books available on differential calculus for JEE. The books by RD Sharma and HC Verma alone may not be enough for the JEE Main. Arihant series (“Differential Calculus” by Amit M. Agarwal) is one of the best books for calculus for IIT JEE. It covers all the concepts in detail and abounds with objective as well as subjective questions. There are past year questions as well, which gives you an idea of how the JEE tests its candidates. Each chapter includes a large number of solved examples and illustrations which are sufficient for your JEE preparation. If you like challenges, it also offers very long questions which are meant for Olympiads.

Another best book for calculus for IIT JEE is Arihant’s “Play with Graphs” by Amit M. Agarwal. This book gives insight into the graphical nature of problems. It is relatively short and will provide you with a set of tools that will help you solve some of the questions efficiently.

Some other books that you may read are “Cengage Calculus” by G.Tewani and “Mathematics for IIT JEE” by R.D Sharma. Another book that qualifies as a best book for calculus for IIT JEE, and which you may find interesting is “Calculus in One Variable” by I.A. Maron. It presents a large number of theorems and formulas on differential calculus. Before you try this book, you should be aware of the fact that “Calculus in One Variable” is not JEE specific. Therefore, there may be some concepts which are not a part of the JEE syllabus.

With all these books, you will have more than enough on your plate. I suggest that you stick with one book that you find the most interesting and easy to read.

## Revision

There are a number of standard revision packages available from different coaching institutes. You can try FIITJEE Grand Master Package or Resonance Rank Booster. It is pretty good for revision during the final months of JEE preparation.

Some of the test series offered by coaching institutes contain thought-provoking problems on differential calculus. It is a good idea to try them out. Don’t forget to solve the previous years’ questions on differential calculus.

In some topics of differential calculus, students are prone to make silly mistakes. Limit calculation and domain/range finding are a few of them. Be mindful of such errors. Practice as many problems as you can and always verify your answers.

Differential calculus in JEE Maths needs a methodical thought process. There are a lot of standard methods and techniques that you need to remember. Deriving them during exams will be a waste of time as well as effort. You will do well if you memorise each and every one of them. Although you do not need to know the derivations of the theorems in differential calculus, a bit of knowledge about some of them will do you no harm.

Some of the techniques learned in differential calculus can also be applied in algebra as well as coordinate geometry. At times, such an approach will drastically reduce the time it takes to solve problems.

Apart from your ability to solve the problems, you should also focus on improving your time. You should do it once you have completed all the chapters and developed enough confidence in your accuracy. Do not sacrifice your accuracy for time. Differential calculus constitutes a big part of the JEE Maths syllabus. So, it is advised not to ignore this chapter.

Lastly, while you prepare for your JEE, keep a positive attitude and try to stay happy. All the best!