MATH 2ZZ3 Lecture Notes - Lecture 7: Isoniazid, Heat Equation
2 Oct 2016
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Pde 2z03 review u x y u x t. All coefficients a,g depend on only x,y (i. e. not u). 2nd order because 2nd derivatives, not 3rd derivatives. A solution, u, of a pde satisfies the pde. We aren"t looking for general solutions to pde"s because they"re really hard. Particular solution means you only find an ode u. This is not going to work in every case for pde and that"s the best we can do. Assume u(x,y) has the form: u = x(x)y(y), then: u x. 2 x u y y e. g. find the product solutions of: x u x y u. Left hand depends on x, not y; right hand depends on y, not x. With respect to both variables, these must both be constant, so they can be called the separation constant: 6 cosh 2 cosh 2 x sinh 2 x. 8 sin 2 x cos 2 x b e.
