AMATH350 Lecture 12: Formula Sheet

• School: University of Waterloo
• Department: Applied Mathematics
• Course: AMATH350
• Professor: Mohamad Alwan

Document Summary

Euler"s formula: ei = cos( ) + i sin( ) Pdes: when the transformation = (x, y), = (x, y) is applied to a(x, y)uxx + b(x, y)uxy + c(x, y)uyy + d(x, y)ux + e(x, y)uy + f (x, y)u = g(x, y), it becomes. A u + b u + c u + d u + e u + f ( , ) u = g( , ), where u( , ) = u(x( , ), y( , )) and x + b(x, y) x y + c(x, y) 2 y , B = 2a(x, y) x x + b(x, y)( x y + y x) + 2c(x, y) y y, D = a(x, y) xx + b(x, y) xy + c(x, y) yy + d(x, y) x + e(x, y) y,