Why do Engineers students study so much calculus ?
There are many answers to this one !
1. "We had to suffer now its your turn !" (grizzled old Professor)
2. "As part of a government plan to keep underdesirables (e.g. mathematics lecturers) off the street" (cynical student)
3. "So much !!!! In my day, we were doing triple integration by the time we left primary school" (mathematics Professor in early stages of dementia)
Here is my answer. Engineering students should study calculus because , firstly, it provides them with a powerful tool to analyse the physical world and , secondly, because is a beautiful topic in itself, a triumph of imagination and analysis. Differential calculus, which I would describe as the mathematics of change, is incredibly useful for analysing the movement of fluids, the flow of heat, the rates of chemical reactions, the effect of changing electrical/magnestic fields, the movements of machines and numerous other engineering examples. Integral calculus, which I would describe as the mathematics of accumulation, allows to calculate area and volumes of complex shapes, centroids and moments of structures, accumulated energy and heat, and generally the overall effect of any varying process.
The fact that both forms of calculus are directly related to each other (i.e. one is the inverse operation of the other) is also one of the most profound and useful intellectual insights of all time. For example, this means that gradient of a tangent line to parabola (i.e the instanteous rise of the curve) is 2x, given y = x2. If we graph this gradient function (g = 2x), the area under that curve is the anitderivative (x2). In other words, the mathematics of change can also be used to describe the mathematics of accumulation. This is not only true for this simple example but for any function that you care to think off. Accumulation is the mirror image of change. Bravo Mr Newton and Mr Leibniz - who both worked this out in the 17th century, though there is still much debate about who was actually first to make the breakthrough (see "A Tour of the Calculus" by Berlinski for an entertaining overview of this topic).
The advent of symbolic computer programs and, more recently, CAS calculators has taken much of the pain from University calculus. This technological advance has shifted the emphasis from memorizing algebraic routines towards using calculus as a tool to analyse a problem.