the 1d heat conduction problem has the strong form: 2 2 0 governing equation: for 0 , where boundary conditions: 0 ; ; initial conditions: 0 ( , ) ( , ) [ , ] ( , ) ( , ) ( , ) ( ). l d t t x t ct k s x t x l t dx t t t t t l t t t x t x the heat capacity c and thermal conductivity k are known constants. the heat source function s x t ( , ) and the initial temperature distribution t x( ) are given. (a) (5%) to derive the weak form, we must postulate the test function ( , ) x t . what conditions must the test function satisfy?