Math 442 Schedule

 Date Sections Lecture Notes Homework Other readings Videos/software 1/18(R) 1.1, 1.2 Lecture 1 Homework 0 (do not turn in) differential equation  PDE(wiki) PDE(scholarpedia)  millennium problems  Survey article Applications of PDE: image processing climate Tsunami developmental biology finance econnomics socio-economic sciences Wolfram Alpha 1/23(T) 1.2 Lecture 2 Homework 1 (due Jan 26) Matlab: plotting a solution of 1st PDE Diffusion (intuition) Diffusion 1/25(R) 1.3 Lecture 3 Laplace operator in polar/spherical coordinate spherical coordinates  Divergence 1/30(T) 1.3 Lecture 4 Homework 2: (due Feb 2) Diffusion Molecular diffusion  diffusion coefficient Fick's law Fourier's law heat equation Laplace operator Matlab(transport equation): pulse 2/1(R) 1.4,1.5,1.6 Lecture 5 ODE reference Wave equation  vibrating string vibration of drum Jean le Rond d'Alembert  continuity equation Vibration of strings 2/6(T) 2.1 Lecture 6 Homework 3: (due Feb 9) 1st order linear ODE 2nd order linear ODE Matlab(wave equation): plucked string  hammer 2/8(R) 2.2 Lecture 7 Joseph Liouville Youtube (calculate integral of exp(-x^2) solution of diffusion equation and wave equation (Pugh) Silvestre's solver 2/13(T) 2.3, 2.4 Lecture 8 Homework 4: (due Feb 16) random walk  Brownian motion binomial distribution    Normal Distribution error function random walk  random walk 2d random walk 3d Brownian motion Binomial dis Normal dis heat eq 1 heat eq 2 2/15(R) 2.4, 2.5 gravitational waves: Einstein field equation, linearized equation another one 2/20(T) 4.1 Lecture 9 Homework 5: (due Feb 23) Matlab: eigenfunction 1, 2, 3, Robin Eigenvalue 2/22(R) 4.2-4.3 Lecture 10 Joseph Fourier pi Leibniz formula for π  Euler's formula for pi trig formulas 14 proofs of Euler's formula 2/27(T) 5.1 Lecture 11 reference Legendre Polynomial wavelet 3/1(R) Midterm Exam Turing pattern talk quantum graph talk 3/3-11 Spring Break

 Date Sections Lecture Homework Other readings Programs 3/12(T) 5.2 Lecture 12 Homework 6: (due March 15) Matlab Fourier series fitting Matlab: fourier 1, 2, 3, 4 wave with boundary 1, 2 3/14(R) 5.3-5.4 Lecture 13 trig formula Gibbs Phenomenon Matlab: Dirichlet, Gibbs 3/19(T) 5.5 Lecture 14 Homework 7: (due March 26) Possion's equation Laplace equation Matlab pdetool 3/21(R) 6.1-6.2 Lecture 15 Laplace in 3D   spherical harmonics 3/26(T) 6.3 Lecture 16 Homework 8: (due April 2) 3/28(R) 6.4 Lecture 17 force gravitational force electrostatic force 4/3(T) 8.1, 8.2 Lecture 18 Homework 9: (due April 9) Green's identities, Green's function, Newton potential Matlab PDE 4/5(R) 8.2 Lecture 19 Kelvin tranform eigenfunction of disk spherical harmonics Legendre polynomials 4/10(T) 7.1-7.2 Lecture 20 Homework 10: (due April 16) Can One Hear the Shape of a Drum? (Amer. Math. Monthly, 1966)  (Wiki: Hearing the shape of a drum)Drums That Sound the Same (Amer. Math Monthly, 1995) Rayleigh–Faber–Krahn inequality isoperimetric inequality Matlab: Forward Neumann Forward Dirichlet 4/12(R) 10.1,10.4 Lecture 21 4/17(T) 12.1-12.2 Lecture 22 Homework 11: (due April 25) Papers on Morphogen Gradient bacteria growth pattern 4/19(R) 12.3 Lecture 23 NIST Fourier transform 4/24(T) 12.4-12.5 Fisher's equation  Schrodinger's equation KdV equation Soliton  Peregrine soliton Sine-Gordon equation breather 4/26(R) research topics Lecture 24 Quantum graph  Turing instability Turing 1952 Kondo-Miura 2010 5/7(M) Final Exam

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