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

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 Two of Two, covering the computational section. Please like and subscribe for more videos!

Twitter: @jacobrintamaki

Link To Part One:    • Explaining Stanford's Applied Math Ph...  

Link To Stanford Math PhD Qualifying Exam Syllabus: https://mathematics.stanford.edu/acad...

References:
Larsson and Thomée, Partial differential equations with numerical methods, Springer.
E, Li, and Vanden-Eijnden, Applied stochastic analysis, AMS.
Mallat, A wavelet tour of signal processing, Academic Press.

Time-Stamps:
0:00 Introduction
1:13 Finite Methods (Difference, Element, Volume)
1:24 Finite Difference Methods
1:41 Laplace and Poisson
2:45 Heat Equation and Wave Equation
3:42 Elliptic Equation In Divergent Form
4:50 Finite Element Methods
6:11 Finite Volume Methods
7:09 Scalar Conservation Laws
7:56 Entropy Solution
9:14 Conservative Schemes
10:11 Godunov Scheme
10:59 Gradient Flow/Descent Methods
11:26 Gradient Flow
12:37 GD, SD, MBGD
14:24 Connection With Optimization
15:00 Hamiltonian Flow
15:35 Basic Symplectic Operators
16:42 Monte Carlo Methods
17:17 Metropolis Algorithm
19:00 Variance Reduction
19:35 Importance Sampling
21:02 The Euler-Maruyama Method
22:10 The Milstein Method
22:29 The Feynman-KAC Method
24:09 Wavelets
25:07 Multiresolution Scheme
25:41 Conjugate Mirror Filters
26:19 Orthogonal Wavelets
27:37 References

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