I remember a sentence in the intro to Dr Goodman's calc text, it went something like this..."Developing a taste for calculus is like developing a taste for black olives. Some of you will never get it. But for those who do, they will be the first mountain in your mathematical career. There will be other mountains, both higher and steeper, but this is the one you will remember the most, and the one with the sweetest view from the top."

Arithmetic is the science of specific amounts. Algebra is the science of general amounts. Calculus is the science of changing amounts.

I flunked Calculus I, took it again and passed it with a C. After I came back from the Navy I took it a third time for a refresher and the best I could do was a B. I took 4 calculus courses and never aced one of them. But when I finally put Dr Goodman's book away, I felt a greater sense of accomplishment than when I earned my degree.

But the book of nature is written in Differential Equations. In DE you use calculus like you used algebra when you were doing calculus, and arithmetic when you were doing algebra.

One of the proudest moments in my life was when my wife finished her Calculus IV course at DeAnza (she had never graduated from high school when I married her).

Computers can certainly solve calculus problems, but doing calculus "on paper" can actually create new problems, new equations.
Most physical laws are expressed as differential equations. Bear with me for a moment here...

Newton defined a force as the derivative of momentum. Momentum p
is mass m times velocity v. That's human genius; here, calculus takes over

So F = dp/dt = d(mv)/dt

and by the chain rule

= m(dv/dt) + v(dm/dt)

dv/dt, the derivative of velocity,
is just the acceleration, so the first term is just F = ma, Force = mass times acceleration.. The second term drops out because the derivative of the mass is 0. Mass does not change. At least, not until Einstein came along. There are no numbers there at all, just abstract quantities, but not only does it show us how to calculate the force on a rocket (where the mass changes as propellant is consumed) but it even hints at the relativistic case where the moving mass itself DOES change.

The point is calculus just doesn't solve problems, it gives us a way to think about problems, and rephrase them, and even suggest answers. When I first realized that I freaked. That is POWER.