"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them."
Calculus is full of these analogies-- the idea of rates of change, the derivative, the idea of accumulation, the integral, and the idea of approximation.
These are everywhere.
If I were to change this temperature, if I were to sort of turn up the dial and see what happens as the temperature increases, how might that affect an ecosystem?
How might it affect the population?
How might it affect all sorts of different things all over the course of the planet?
One of the biggest reasons we use continuous models is so we can use calculus, because calculus is so important to the underpinnings of some of the key principles in economics.
When you see an X-ray image, you're basically seeing a map of [? p. ?] It would be better if we could have a map of mu, so we would have a map of the attenuation at every single point in the body.
For us, the goal is to try to see how we can obtain this formula from this more complicated formula.
The concepts that you can study in pure mathematics, without any interest in physics.
You'll apply and refresh concepts and tools that you've learned or are learning now in single variable calculus.
By the end of the course, you'll understand some of the diverse ways
that calculus is applied every day, and we hope you'll feel more comfortable making sense of mathematical models, harnessing the powerful language and tools that calculus offers to analyze the world around us.