Date Chapter.Section/Topics or Page/Problems M Jan 6 Lecture 1: Introduction: ordinary derivatives Assignment 1 Due Friday January 24 W 8 Lecture 2: convexity M 13 Lecture 3: partial derivatives Assignment 2 Due Friday January 31 W 15 Lecture 4: partial derivatives and the structure of ordinary differential equations M 20 Holiday Assignment 3 Due Friday Febuary 7 W 22 cold/snow day M 27 Lecture 5: ordinary differential equations and partial differential equations Assignment 4 Due Friday Febuary 21 W 29 Lecture 6: clean up day... higher order ODE and systems axially symmetric solutions of Laplace's equation questions---asking your own questions M Feb 3 Lecture 7: Green's function(s) and integration Assignment 5 Due Friday Febuary 28 W 5 Lecture 8: Convolution with a fundamental solution M 10 Lecture 9: Regularity for convolution integrals W 12 Lecture 10: Laplacian of convolution with the fundamental solution Assignment 6 Due Friday March 14 M 17 Lecture 11: Laplacian of convolution with the fundamental solution (continued) W 19 Lecture 12: The boundary value problem (intro) M 24 Lecture 13: Green's function: The boundary value problem (overview of Cauchy-Kowalevski theorem) Assignment 7 Due Friday March 28 W 26 Lecture 14: Green's corrector function symmetry and Green's solution M Mar 3 Lecture 15: Green's solution of Poisson's equation (continued) Green's function for the ball (n > 2) (intro) W 5 Lecture 16: Green's function for the ball (n > 2) (continued) average values of harmonic functions (mean value property) M 10 Lecture 17: avarage values and maximum principle(s) W 12 Lecture 18: strong maximum principle Assignment 8 Due Friday April 4 M March 17 Holiday W March 19 Holiday M 24 Lecture 19: derivation of the heat equation W 26 Lecture 20: 1-D heat equation, some solutions Assignment 9 Due Friday April 11 M 31 Lecture 21: 1-D heat equation, separation of variables (pinned zero boundary values) W April 2 Lecture 22: Fourier expansions in L^2 M 7 Lecture 23: Laplace's equation on a disk by separation of variables W 9 Lecture 24: Laplace's equation on a cylinder and Bessel's ODE M 14 Lecture 25: Assignment 7 Problem 2 part (a) (weak maximum principle) Many thanks to Shahab for the question which was crucial to the occurrence of what was in my opinion probably the best and most useful meeting of the semester. W 16 Lecture 26: Laplace's equation on a cylinder (continued---perhaps) M 21 Lecture 27 (last lecture): =============================================================================== =============================================================================== F April 25 Final Exam 11:20-2:10 Final Assignment Due Friday April 25 =============================================================================== =============================================================================== =============================================================================== =============================================================================== =============================================================================== =============================================================================== =============================================================================== =============================================================================== =====================Old Schedule Spring 2023====================== Assignment 2 Due Wednesday February 1 Assignment 3 = Exam 1 Due Wednesday February 8 W 18 Lecture 3: differentiability and continuity M 23 Lecture 4: multivariable power series Assignment 4 Due Wednesday February 15 W 25 Lecture 5: Assignment 5 Due Wednesday February 22 M 30 Lecture 6: continuous (partial) differentiability (C^1) implies continuity Assignment 6 = Exam 2 Due Wednesday March 1 W Feb 1 Lecture 7: Full differentiability for functions of several variables modeling the slinky (preliminaries---step zero) M 6 Lecture 8: What we didn't do: continuous (partial) differentiability implies full differentiability modeling the slinky (preliminaries) What we actually did: Directional derivatives, parameterized curves, and first order PDE (also a review of ODE) W 8 Lecture 9: What we didn't do: First Order Quasilinear PDE Method of Characteristics What we actually did: Started talking about integration...along with weak derivatives and compactly supported functions M 13 Lecture 10: smooth compactly supported functions and hopefully some PDE Assignment 7 Due Wednesday March 8 W 15 Lecture 11: Lagrange multipliers (graphs, level sets, parameterized curves, etc.) Slinky data (coil measurements) taken so far (Mathematica notebook) Slinky data (coil measurements) taken so far (pdf format) M 20 Lecture 12: no lecture Assignment 8 Due Wednesday March 15 W 22 Lecture 13: d'Alembert's solution via the method of characteristics Assignment 9 Due Wednesday March 29 M 27 Lecture 14: Integration (definition) W Mar 1 Lecture 15: Integration (Fubini's theorem and change of variables) Assignment 10 Due Wednesday April 5 M 6 Lecture 16: Special integrands The divergence and the divergence theorem Assignment 11 Due Wednesday April 12 W 8 Lecture 17: Derivation of the heat equation(s) M 13 Lecture 18: Philosophy and integration Assignment 12 Due Wednesday April 17 W 15 Lecture 19: canceled (?) M 20 Spring Break W 22 Spring Break M 27 Lecture 19: Laplace's equation Derivation via calculus of variations Assignment 13 Due Wednesday April 22 W 29 Lecture 20: M Apr 3 Lecture 21: Calculus of variations W 5 Lecture 23: M 10 Lecture 24: W 12 Lecture 25: Final Assignment Due Wednesday May 3 M 17 Lecture 26: W 19 Lecture 27: M 24 Lecture 28 (last lecture): F Apr 28 Final Exam 11:20-2:10 Th May 4 Game Over