Points, Vectors, and Functions Examples

Unlike the typical college junior that shows up to their morning class wearing pajamas and their retainer, some functions care what they look like in the mirror. These functions, called even or odd...

With an understanding that vectors are simply mathematical equivalents of mythological hybrid beasts, we'll investigate their parts to see if we can understand them better. Surely, with the help of...

Since we know all about the bodies, err, magnitudes of vectors, we now need to look at the directions of vectors. We can equate the direction of the vector to the head of the griffin or the minotau...

Quiz time. Already? Yep.What's one apple plus another apple? Two apples. What's two oranges less one orange? One orange. What's one griffin plus one minotaur? Any mythology buff could tell you it's...

We've been through apples, oranges and mythological creatures unlike anyone has ever seen. But we still don't have a quick way to compare the magnitude of a vector before and after we scale it.To d...

Now that we've managed to capture a few mythological beasts and have squashed them inside our laptop for processing, we want a picture of it. After all, all of that work is a tall tale until you co...

Graphing parametric equations is similar to graphing vector functions.One way to graph parametric equations is to find points for certain values of t, graph those points, then play connect-the-dots...

We can describe trajectories of things with parametric equations.Before we go forward, we should review parabolas via Super Mario Brothers. When Mario jumps, we can parameterize his trajectory d(x,...

One of the first shapes we learned as a toddlers was the circle. It probably didn't take long to realize that pizza is shaped this way. Now we'll discuss the unit circle, the circle with radius equ...

If circles equal pizzas, then lines equal hot dogs. Welcome to Calculus Analogies 101.What kind of toppings can we put on hot dogs to suit our tastes?Sample ProblemBegin with mustard and ketchup, t...

It's a hot summer evening. Bob has been training for a triathalon and needs a major calorie intake. He finished his dinner of pizza and hot dogs, but he still has room for dessert, so he eyeballs t...

It's time to get friendly with our graphing calculators. First, we need to understand how to graph polar functions by hand. This is one of the many instances in calculus where it's helpful to...

The best way to graph polar functions is by using a graphing calculator or a computer program. We can wave our hands and pull a rabbit out of a hat. That's because there aren't as many rules about...

Polar function plots may leave your head spinning like you got off the Tilt-a-Whirl ride at the amusement park. But using them, it's possible to model that Tilt-a-Whirl ride, and they make some of...

We need one more tool to solve for intersections of polar functions. We need to know how to solve a system of two equations.We can find where two rectangular functions y = f (x) and y = g(x) i...