Have you ever wondered what’s on the Applied Math PhD Qualification Exam At Stanford?
Well this video is going over that! This is Part One Of Two, covering the analytical section. Please like and subscribe for more videos!
Twitter: @jacobrintamaki
Link To Part Two: • Explaining Stanford's ...
Link To Stanford Math PhD Qualifying Exam Syllabus: mathematics.stanford.edu/acad...
References:
- Evans, Partial differential equations, AMS.
- Øksendal, Stochastic differential equations: an introduction with applications, Springer.
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
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