Solutions 7

• cours magistral - matière potentielle : notes
• cours magistral

ITET Analysis III HS 2011 A. Cannas da Silva Solutions 7 1. 1. We change variable and obtain ∫ 5 1 δ(x)(x+ 3)2dx, then the definition can be applied and gives zero, since the point x = 0 is not in the interval ]1, 5[. 2. We use the definition of the distributional derivative and obtain − ∫∞ −∞ δ(x − pi) cosxdx = 1.

• direction perpendi- cular to the boundary line
• green function of the upper half plane
• start with the wanted equation for distribu- tions
• function