Obtain the Fourier sine transform of the function
a>0,0x<∞
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Show that gij is a contravariant tensor of rank 2.
Determine the Fourier transform of the normalized Gaussian distribution
Using the generating function, establish the relation between Hn (x) and Hn (-x).
Show that the vectors are linearly independent.
Obtain the eigenvalues and the corresponding eigenvectors of the matrix:
b) Diagonalized the matrix:
The eigenvalues of A are: λ1 = 2, λ2 =1 and λ3 = -1.
c) Show that gij is a contravariant tensor of rank 2.
d) Show that the vectors are linearly independent.
Using the Laplace transforms, solve the following initial value problem:
where
Consider a triangle P in the z-plane with vertices at i, 1 – i, 1 + i. Determine the triangle P0 which mapped P under the transformation w = 3z + 4 – 2i. What is the relation between P and P0 and also calculate the area magnification.