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

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 Applied Math Ph...   Link To Stanford Math PhD Qualifying Exam Syllabus: https://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 #math #phd #education #stanford