Here I am, in front of the Red Burn. It's a beautiful symbol of my University. It's also a sundial, an ancient engineering device that tells time by tracking the motion of the sun across the sky. Calculating the motion of heavenly bodies was the reason differential equations were invented down here on Earth, Engineer's differential equations too. Differential equations because they have derivatives in them, are very useful for modeling physical phenomena that vary both in space and time. Different cues also show up in our every day lives. Let me show you some examples today. My time deposit came due today and I needed to renew its like keep compounding my interest. I've been investing my family's money for many years now. I'm looking forward to a wealthy retirement. Let's see how well my compound interest formula has worked. Wow, thank you compounding. I should tell my wife how much money we have. I just got an email from my good friend Rami. That crazy guy has gone sky diving again. Let's see how is skydiving looks. Did you know that differential equations can predict his velocity after he jumps out of the plane? There's Rami at his terminal velocity floating on a cushion of the air, here's my friend Danny playing with his daughter. Let's go say hey. Hey Danny, how's it going? Great. I can put Jisela really high. High. Another example of differential equations. Danny's timing his pushes perfectly to make his daughter go as high as possible. That's resonance. Hello daddy? Voila. Wow, so nice. Are we celebrating something? I went to the bank today. Our compound interest formula is working really nicely. We almost have enough money to retire. Wow. This great. Do you still want to go visit all the parks in United States? Yeah, sure. I'm in. Cheers. Cheers. Nice, that's the resonance frequency of the wine glass. You know someone can break that glass if they sing at that frequency? Remember to wear safety glasses. Pretty cool, don't try that one at home. Many of the laws of nature are expressed as differential equations. Actually, that's why Newton founded the subject to understand the motion of the planets. Engineers also need to know about differential equations. Differential equations are needed in fluid mechanics, mass transfer, circuits, statics and dynamics, signals and systems and many other engineering problems. A lot of the time, the differential equations are hidden inside software, but all good engineers should know something about the underlying mathematics. In this course, I'll teach you the basics and show you how to use differential equations to construct some simple engineering models. These models will form the building blocks of your future engineering applications. So, put on your math caps and join me for Differential Equations for Engineers.