MTH 621 : Partial Differential Equations - Fall 2021
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General information
General information
Instructor: Malgorzata Peszynska, Professor of Mathematics (Contact information including office hours on instructor's department website)
Class: Lecture: MWF 13:00-13:50pm, STAG 162.
Course information: see CANVAS.
Schedule: [textbook] {assignments}
  • 9/22: Introductions. Classification of ODEs and PDEs. [Chap.1 plus Appendices].
  • 9/24: Picard-Lindel\"of theorem. Examples.
  • 9/27: Proof of Picard thm (E by iteration, U and dependence on IC with Gronwall lemma. Regularity by bootstrap). {Extra 00: first day survey}
  • 9/29: First order PDEs [Chap.3]. Solution "algorithm".
  • 10/1: First order PDEs: justification of formal steps; how to recognize characteristic data. {Extra 1}{HW1 due}
  • 10/4: Where do the first order PDEs come from: transport problem. Non-smooth solutions: do they make sense?
  • 10/6: Generalize the transport equation. Burgers equation. Can the characteristics cross?
  • 10/8: Calculation of shock speed in Burgers eqn and beyond (Rankine-Hugoniot condition) {HW2 due}
  • 10/11: Second order PDEs in $\R^2$; classificaiton and change of variables to the canonical form. [Chap 2.1-2.3 and Chap 4]
  • 10/13: Solving wave equation.
  • 10/15:
  • 10/18: {HW3 due}
  • 10/20:
  • 10/22:
  • 10/25:
  • 10/27:
  • 10/29: Midterm, in class.