Lecture 2.9: First order Partial Differential Equations - Tutorial of Quasilinear equations
Channel: IIT Bombay July 2018
Date: 2021-07-29

Welcome to the tutorial on quasilinear equations. We will work out examples of the method of characteristics applied to first order quasilinear equations. We will also mention the local nature of solutions in some of the examples.

Erratum: 
(1) Please note the following corrections to Slide 22:
(a) "z=Z(t,s)=1/(s-t)" is to be replaced with "z=Z(t,s)=s/(1-st)"
(b) "u(x,y)=Z(T(x,y),S(x,y))=1/(x-2y)" with "u(x,y)=Z(T(x,y),S(x,y))=(x-y)/(1-xy+y^2)"
(c) The last two lines on the Slide is to be replaced with "which is defined on any domain in R^2 which does not intersect the set {(x,y)\in R^2 : 1-xy+y^2=0}. For example {(x,y)\in R^2 : x in (-2,2), y\in R}"

(2) The first bullet point on Slide 23 must be read with the modifications in (1) above.

(3) On Slide 26, "R^2\{x-axis}" should be replaced with "R^2\{y-axis}"