Hello.
I think you missed something while writing your question there is not properly clear that what you exactly want to know , is it the definition of Calculus?
Or is it about which Calculus part you study in class 11? .
Still I am answering by considering these all ,hope this may clear you complete doubt:

What is calculus?
It is a branch of mathematics that deals with the particular method of calculation or reasoning, in this basically if we go with its application then we can have its proper deep definition which say that in order to dealing with the minimum smallest part or maximum  largest part of the system we use calculus , it helps to find out the minimum or maximum part of the system or any expression of system.

What are the types of calculus?

There are basically two types of calculus or we can say parts which we focus during our class 11 and 12th .

• Differential calculus.( Dealing with the calculation of smallest part of the expression of any system ).
• integral calculus (dealing with the calculation of of largest part of the expression of the system).

What Calculus we study in class 11 and 12 ?

the answer of this question vary according to the board in which you are studying .
as I have seen that in ICSE board you basically focus on some integral part also which you do not in CBSE  in class 11, and this also vary in various state boards.
In a more general way if we consider NCERT books then this thing do not vary ,it is same for all if it is followed by these all boards strictly as in CBSE it is strictly followed.
so in NCERT of class 11 you only focus on the basic part of the differential calculus along with the limit concept and in class 12 you mainly focus on the intermediate level of differential calculus and basic integral calculus along with the applications. while it turns to the advanced in graduation and super advanced in the post graduation if you go with mathematic course.

best of luck.