We make a list of 10 important partial differential equations in two variables. Partial differential equations in general link temporal rate of changes with spacial rate of changes. Here are the 10 PDEs: (note there are two slide typos: f f_x in Burger, x f_x in Black Scholes):
Transport f_t=f_x
Heat f_t=f_xx
Wave f_tt=f_xx
Burgers f+ff_x = f_xx
Laplace f_xx+f_yy=0
Poisson f_xx + f_yy = g
Schroedinger i f_t = -f_xx+V f
Klein-Gordon f_tt = f_xx + f
Eiconal f_x^2+f_y^2=1
Black-Scholes f_t + x f_x = f - x f_xx^2
