Explaining Stanford's Applied Math PhD Qualification Exam (PART ONE) 

Time-Stamps: 0:00 Introduction 1:16 Elliptic PDEs/Laplace Equation 2:03 Poisson Equation 2:37 Green’s Function (Elliptic) 4:39 Parabolic PDEs 5:10 Heat Equation 6:14 Green’s Function (Parabolic) 7:33 Random Walks/Brownian Motion 8:25 Connection To Parabolic PDEs 9:26 Hyperbolic PDEs 10:12 Wave Equation 11:00 1-D Schrodinger Equation 11:42 Hamilton-Jacobi Equations 13:25 Conservation Laws 13:51 Shocks 14:38 Weak And Entropy Solutions 15:29 Lax = Oleinik Formula 15:57 Stochastic Modeling 16:19 Brownian Motion (Wiener Process) 17:25 Stochastic Integral 18:21 Ito’s Formula 19:03 Stochastic Differential Equations 19:39 Forward Kolmogorov Equation 20:22 Backward Kolmogorov Equation 20:52 References

Good practice for next year. Thank you Jacob.

i'm self studying my BS degree from a MIT syllabus on math. Maybe one day if i decide to go for self study phd, I can grok something like this for my qualification exam.

Gonna Join this Fall 25 PhD program in ICME Stanford. RU-vid recommendations at times is actually helpful !

Hey Jacob, these videos are really cool and informative. Please do more on differential equations. Thanks

damn i got a degree in applied math/physics and this basically covers the whole degree, and some stuff you'd learn on your own doing undergrad research and shit. do they really test you on everything? and are the questions made to be trivial (ive seen this before so i know how to do it) or is it spend 30 min trying to solve it just to end up where you started?

Am I the only one here who hears dimenxional instead of dimensional? For real though, nice video!

Its a bit weird to call it applied math when this is almost just pde analysis type of stuff. There are many applied math phds where you‘re never gonna have to do any of this

awesome vid!! Can you do the one for physics?

crazy value

Looks very basic for a qualifications exam.

loved the explanation of what a green function is!

I've never heard of such

This is not true, applied math does much more than pdes