PARTIAL DIFFERENTIAL EQUATIONS
web.math.ucsb.edu › ~grigoryan › 124AIn contrast to ODEs, a partial di erential equation (PDE) contains partial derivatives of the depen-dent variable, which is an unknown function in more than one variable x;y;:::. Denoting the partial derivative of @u @x = u x, and @u @y = u y, we can write the general rst order PDE for u(x;y) as F(x;y;u(x;y);u x(x;y);u y(x;y)) = F(x;y;u;u x;u y) = 0: (1.1)
Partial Differential Equations
www.math.toronto.edu › ivrii › PDE-textbookA partial di erential equation is an equation for a function which depends on more than one independent variable which involves the independent variables, the function, and partial derivatives of the function: F(x;y;u(x;y);u x(x;y);u y(x;y);u xx(x;y);u xy(x;y);u yx(x;y);u yy(x;y)) = 0: This is an example of a PDE of order 2. Solving an equation like this