![]() So if I want to know x as aįunction of time- a suitably vibrant color- so x as aįunction of time is going to be what? Well, we're going to assume Get the equations and see what the graph looks like. Videos, if you want to know where the equations come from. Problem, and I won't go deep into the physics. Happens to this car as it drives off the cliff? So this is a bit of a physics And let's say the car's rightĪt this point, right about to drive off the cliff. Right here on the cliff, that's at x is equal to 10. Point- well, we know that this is a 50 meter high cliff. The path of this car as it falls off of the cliff? So let's set up a littleĬoordinate axis here. And it's driving off of thisĬliff at 5 meters per second. ![]() Sitting on the cliff, it's driving off of it. Let's make this cliff, Iĭon't know, let's say it's 50 meters high. Wikipedia has a pretty good blurb about the math uses of "parameter." You can also use the parameter to find a unifying function that does directly relate x to y, as Sal hinted at. This is much more useful and intuitive than looking at the graphs of y(t) and x(t) separately. The car is moving through time equally "in both directions." This allows us to graph (x, y) coordinates to show the position of the car, as Sal showed. In the y-direction, however, its position is changing exponentially with time. the graph of its function is a straight line. In the example, the car's position in the x-direction is changing linearly with time, i.e. Parametric equations are used when x and y are not directly related to each other, but are both related through a third term. What makes them parametric is that they share a parameter. Each of the functions in the example are 'normal,' separate functions. ![]() It's tempting to say so, but parameter has a special meaning in this context. So if you want to get into any of those fields, expect to run across these at some point. Parametric equations and many other mathematical ideas are the foundations of calculus. You represent these changes, if they are the motion of something in a game, or the growth of a disease, or the sway of a building in an earthquake to determine if you have designed in sufficient bracing, or the population of the planet, or the business projections for a company, or so on and so forth. Anything that changes for whatever reason is the topic of calculus. The more you get into higher levels of math, the more you find it applies to all sorts of jobs.Ĭalculus is the study of CHANGE.
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