Slope Fields, Equilibria, and Solutions to ODEs - Ordinary Differential Equations | Lecture 1

This is the first lecture in this video series on ordinary differential equations (ODEs). In this video we go over many of the basic concepts for analyzing ODEs, all while working through a single motivating example. In particular, we use physical laws to derive an equation for the motion of a falling object and then use this differential equation to discuss important concepts such as equilibrium solutions, sketches of slope fields, and even produce general and particular solutions. These are all fundamental concepts in ODE theory and using our derived model we can demonstrate them not in theoretically, but interpret them physically.

This course is taught by Jason Bramburger for Concordia University.

Follow @jbramburger7 on Twitter for updates.

[DebarghaRay-rk]

My brain is hamburgered.Amzing job btw

[lukassimon]

amazing video. Thanks for explaining everything in such a slow speed and going over things multiple times. That really helps!

[wcemkfd]

Man, your classes are just AMAZING! Thank you for sharing.

[bluestudio]

Does Jason write all this stuff BACKWARDS on a piece of grass? I'm impressed

[liliac]

Thank you for this, it was really helpful ♥️

[mmesomaemmanuelanukam]

When we assume v(0) is 0, isn't D = 49 instead of -49? Or is it possible for D to be positive and negative at the same time?

[mmmbacon]

I lost something when you exponentiate - you silently drop the absolute sign around (v-49). Then later you replace e^C with any real number D (whereas I don't see how D could be negative following this definition). I guess these two things are related. In reality negative D is essential to ensure asymptotic behaviour on both sides of equilibrium. Can you fill-in the gaps?

[LooseOrangeJuice]

Nice video but the stereo mix is distracting when you move your head around. I would recommend bouncing your audio to mono for videos like these because your voice should be front and center anyway.

[alijraisheh]

Wouldn’t drag force be proportional to velocity square?

[forughghadamyari]

Please introduce a resource for this subject