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.
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?
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
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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. UA-cam recommendations at times is actually helpful !
Hey Jacob, these videos are really cool and informative. Please do more on differential equations. Thanks
Will do
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?
I will be going over exam questions on the weekend! That should hopefully answer a lot of your questions. :)
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
loved the explanation of what a green function is!
Looks very basic for a qualifications exam.
crazy value
awesome vid!! Can you do the one for physics?
I've never heard of such
This is not true, applied math does much more than pdes
Lol