Math 442 Schedule

 Date Sections Lecture Notes Homework Other readings Videos/software 1/17(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 1/22(T) 1.2 Lecture 2 Homework 1 (due Jan 25) Matlab: plotting a solution of 1st order PDE Diffusion (intuition) Diffusion 1/24(R) 1.3 Lecture 3 Laplace operator in polar/spherical coordinate spherical coordinates  Divergence 1/29(T) 1.3 Lecture 4 Homework 2: (due Feb 1) Diffusion Molecular diffusion  diffusion coefficient Fick's law Fourier's law heat equation Laplace operator Matlab(transport equation): pulse 1/31(R) 1.4,1.5,1.6 Lecture 5 Wave equation  vibrating string vibration of drum Jean le Rond d'Alembert  continuity equation Vibration of strings 2/5(T) 2.1 Lecture 6 Homework 3: (due Feb 11) 1st order linear ODE 2nd order linear ODE Matlab(wave equation): plucked string  hammer 2/7(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 2/12(T) 2.3, 2.4 Lecture 8 Homework 4: (due Feb 15) 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 2/14(R) 2.4, 2.5 Lecture 9 gravitational waves: Einstein field equation, linearized equation another one 2/19(T) 4.1-4.3 Lecture 10 Homework 5: (due Feb 22) Matlab: eigenfunction 1, 2, 3, Robin Eigenvalue 2/21(R) 5.3 Lecture 11 Joseph Fourier trig formulas 14 proofs of Euler's formula 2/26(T) 5.1 Lecture 12 reference Legendre Polynomial wavelet 2/28(R) Midterm Exam Turing pattern talk quantum graph talk 3/2-10 Spring Break

 Date Sections Lecture Homework Other readings Programs 3/12(T) 5.2 Lecture 13 Homework 6: (due March 15) Matlab Fourier series fitting Matlab: fourier 1, 2, 3, 4 wave with boundary 1, 2 3/14(R) 5.4 Lecture 14 pi Leibniz formula for π  Euler's formula for pi Matlab: Dirichlet, Gibbs 3/19(T) 5.5 Lecture 15 Homework 7: (due March 22) trig formula Gibbs Phenomenon Matlab pdetool 3/21(R) 6.1 Lecture 16 Possion's equation Laplace equation Laplace in 3D   spherical harmonics 3/26(T) 6.2-6.3 Lecture 17 Homework 8: (due March 29) 3/28(R) 6.3-6.4, 7.1 Lecture 18 force gravitational force electrostatic force 4/2(T) 8.1, 8.2 Lecture 19 Homework 9: (due April 8) Green's identities, Green's function, Newton potential Matlab PDE 4/4(R) 8.2 Kelvin tranform eigenfunction of disk spherical harmonics Legendre polynomials Matlab: Forward Neumann Forward Dirichlet 4/9(T) 12.1-12.3 Lecture 20 Homework 10: (due April 15) 4/11(R) 12.3-12.4 NIST Fourier transform  FFT convolution Convolution and machine learning  kernel 4/16(T) 10.1, 10.4 Lecture 21 Fermat two-square Legendre three-square Lagrange four-square 4/18(R) research topics Lecture 22 Quantum graph  Turing instability Turing 1952 Kondo-Miura 2010 Papers on Morphogen Gradient bacteria growth pattern Turing system Turing patterns 4/23(T) 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 4/25(R) Fisher's equation  Schrodinger's equation KdV equation Soliton  Peregrine soliton Sine-Gordon equation breather 4/30(T) Final Exam

Possible Math 300 topics
Other courses using the same textbook

Peter Olver's course