1. Mathematics
2. Fourier Analysis
3. 581963

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Using the chain rule of partial differentiation, to show that the differential equation              
       Au_xx + Bu_xy +  Cu_yy + Du_x + Eu_y + Fu = G        
  transforms into the differential equation             
       A' u_,aa + B'u_bb + C'u_cc + Du_a + Eu_b + Fu = G                    

   The complete problem is in the attached file.