Here is a link to a short, 15 min, introduction to differential equations: http://youtu.be/kIKp8rLjsHY Here is a long video recorded in Blackboard Collaborate: https://sas.elluminate.com/p.jnlp?psid=2012-06-27.1134.M.415E25ABC3437BC9A4A0FBE3CC971C.vcr&sid=837

We live an a world of rapid change. But, even when technology and culture once shifted through time more slowly, everything around us still changed over time. Winds blew, plants grew, prey moved, the moon drifted across the sky, all displaying change. Differential equations give us mathematical tools to model the changes that we observe. […]

Here you can find information about differential equations: \(\frac{dy}{dx}=f(x)\) \(\frac{\partial^2u }{\partial x^2 }=\frac{1}{c^2}\frac{\partial^2u }{\partial t^2 }\) \(y''+k\sin(y)=0\) If \(\frac{dy}{dx}=ky\), then \(\displaystyle y=\sum_{n=1}^\infty \frac{(kx)^n}{n!}\). A falling body with air resistance proportional to the square of velocity \(m\dot{v}=mg-kv^2\) The Total Differential:

\[ df(x,y)=\frac{\partial f}{\partial x} dx+\frac{\partial f}{\partial y} dy\]