Damned good question. I never learned the answer until third year Calculus. I sat and stewed on this one for quite a while, but I think I can answer it without using numbers or equations. As much as I loved the math, particularly after a short Asian woman really laid it out for me in my last year of college, I must remind everyone that it's been a few years, so check me Sue. Here goes.

These graphs we see all the time -- bell curves, marketing graphs, even the daisies, all represent real data. In addition they can all be represented by an algebraic equation. Maybe we started with the equation and then we plugged in values to get the graph. Maybe we started with some data points, connected the dots and looked for an equation that best fits the curve. It's one thing to look at a simple graph and learn something from it, but quite often, we need to know some real specific things that aren't available by just looking. What I want to do here is jump quickly to an example and then describe the use of Calculus through the example.

Say Michael is sitting in his car at a red light that turns green, and he jams on the accelerator. Picture the speedometer moving up -- 10, 20, 30 ...

What's happening? -- I'm accelerating, but at a constant rate. So each second I'm going 10 mph faster than the last. --My velocity is increasing in a linear manner. 10, 20, 30 ... --The distance that I'm travelling is increasing exponentially.

Stick with me, now and picture three graphs representing acceleration, velocity, and distance during the time traveled. --The graph for acceleration would look like a straight horizontal line. Acceleration is how fast we are increasing rate of travel. Since we always go 10mph faster each second, we get a graph of the number 10 --The graph for velocity would be a straight line moving up at a 45 degree angle from the lower left (0,0) to the upper right (90,90). Velocity is the distance covered each second. 90mph is as fast as my car will go. --The graph of the distance would be a parabola. The line starting low and horizontal, then shooting up vertically.

Calculus is about rates, and rates of rates, and rates of rates of rates, ...etc. If I ask Mr. Algebra to look at the bottom graph of distance over time and tell me my velocity 3.2 seconds after the light turned green, he scratches his head, looks for paper, looks for the algebraic equations describing distance and velocity, and starts plugging in values. Miss Calculus knows that velocity is the rate of change of distance over time. So she turns a quick trick on the equation called taking the derivative, and ends up with the equation that Mr. algebra had to go look up. This is the equation for velocity and its graph is the graph described above. If she wanted the acceleration, she would take the derivative of the equation for the velocity and voila. She could also go the other way by starting with the acceleration and turning the opposite trick of derivation, which is called integration. Pages of work for Mr. algebra, but three easy equations, each created from the last for Miss Calculus. Mr. Algebra is only concerned with getting answers, but Miss Calculus knows about asking the right questions in different ways.

Most algebra books present equations to solve the problem. Calculus tells where those equations came from.

2 times Pi times the radius gives the circumference of a circle -- one dimension
Pi times the radius squared gives the area of a circle -- two dimensions
4/3 times the radius cubed gives the volume of a sphere -- three dimensions

Three unrelated equations to Mr. Algebra, one central concept to Miss Calculus. Those three equations are each derived, or integrated from the other.

To try to readdress your questions, I found Calculus easy, but only after that little Asian woman laid it out the way she did. Calculus is rarely taught well. Just writing this makes me remember how beautiful it can be, how elegant. It also makes me remember how hard it was in the beginning. I consider it an unfortunate circumstance that I never get to use it at any of my jobs. Your instructor's statistics notwithstanding, I demonstrably make more money having taken Calculus, but alas, I've never used it since college.

Except today.

--M!chael