Math 316/257
Partial Differential Equations/Ordinary Differential Equations II
Provisional Schedule

 # Date Topic/Notes Reading Homework 1 Wed Sep 07 Some famous pde, ode from pde, linearity, series solutions (power, Fourier, special fns) Lecture Notes assignment 1 2 Fri Sep 09 Taylor thm, power series, convergence, differentiating under the sum A4 3 Mon Sep 12 Solution of ode by power series A4,A5 4 Wed Sep 14 Solution of ode by power series A6 assignment 1 due  assignment 2 5 Fri Sep 16 Bessel Equation, series solution, Gamma fn 4.7 6 Mon Sep 19 Some identities. 4.7, 4.8 7 Wed Sep 21 Periodic funs: Fourier series versus power series, piecewise smooth functions, orthogonality from y''=-y 2.1 assignment 2 due assignment 3 8 Fri Sep 23 Euler formulas, series for sawtooth, manipulations 2.2 9 Mon Sep 26 Other periods, even/odd fns, 2.3 10 Wed Sep 28 Half range expansions, extension by symmetry 2.4 assignment 3 due assignment 4 11 Fri Sep 30 Mean square approximation 2.5 12 Mon Oct 03 Modeling, vibrating string 3.1, 3.2 13 Wed Oct 05 separation of variables 3.3 assignment 4 due Prepare for midterm 14 Fri Oct 07 3.3 Mon Oct 10 Thanksgiving 15 Wed Oct 12 Midterm test on assignments 1-4 assignment 5 16 Fri Oct 14 D'Alembert solution, characteristics 3.4 17 Mon Oct 17 1d heat equation 3.5 18 Wed Oct 19 Different boundary conditions (omit 3.6 until Sturm Liouville) 3.5 assignment 5 due assignment 6 19 Fri Oct 21 2d wave, heat eqns (Brydges is away from Oct 18 - 22) 3.7 20 Mon Oct 24 Laplace Eqn on rectangular domain 3.8 21 Wed Oct 26 assignment 6 due assignment 7 22 Fri Oct 28 Poisson eqn, eigenfn expansion, remarks on linear algebra and orthogonality 3.9 23 Mon Oct 31 Orthogonality in Sturm Liouville problems 6.2 24 Wed Nov 02 Different boundary conditions 6.2, 3.6 assignment 7 due assignment 8 25 Fri Nov 04 Orthogonality of Bessel fns and expansions in Bessel fns 4.8 26 Mon Nov 07 Laplacian in Polar and cylindrical coordinates 4.1 27 Wed Nov 09 assignment 8 due Prepare for test Fri Nov 11 Remembrance Day (Fields meeting Nov 12) 28 Mon Nov 14 Circular membrane, symmetric case 4.2 29 Wed Nov 16 4.2 Midterm test [On assignments 5,6,7,8] assignment 9 30 Fri  Nov 18 Circular membrane, general case 4.3 31 Mon Nov 21 4.3 32 Wed Nov 23 Laplace eqn in circular region 4.4 assignment 9 due assignment 10 33 Fri Nov 25 4.4 34 Mon Nov 28 Cylindrical regions 4.5 35 Wed Nov 30 4.5 assignment 10 will not be collected 36 Fri Dec 02 Last day of classes TBA Final , information practice final