Welcome to the course page for Calculus. Here, I will compile everything related to this course that my students will require.
Course name : Calculus(MAT-1000-1)
Timings : Monday and Wednesday, 8:30 AM - 10:00 AM.
Classroom Number : AC-02-LR-107.
Syllabus : Our aim is to start by defining the real numbers, on which calculus will be performed. So first, we will lead up to the real numbers naturally,while seeing the integers and rational numbers along the way. Having reached the real numbers, we will then explore how calculus helps us understand the notion of infinity. This will be done by defining sequences and series, which provide a standard mechanism to deal with infinitely many quantities.
We will then move to functions on real numbers, which are the fundamental objects on which calculus is performed. We will try to understand functions from a graphical point of view as well, by seeing how to draw/sketch graphs of functions.
Then, we come to the notion of limits and continuous functions, which are very natural examples of functions that can be studied under the umbrella of calculus.
Then, we come to one of the fundamental operations of calculus : the differentiation operation. We define differentiable functions, and then look at the advantage of how differentiation helps constrain functions : this would include e.g. the mean value theorem.
Having studied differentiation in detail, we now move to integration, defining carefully the theory of Riemann integration. We then study various definite integrals, understanding along the way techniques to solve them. Finally, the fundamental theorem of calculus completes the discussion.
Recommended Books (as per Mathematical Handbook) :
Elementary Analysis, by K.A. Ross.
Calculus, by Michael Spivak.
Calculus, by Stewart.
The assignments for this course can be found in this folder.
The lecture notes for this course can be found in this folder.
The final exams and a hard problem sheet can be found in this folder.