These exercises should be performed using Mathematica. Output can be in printed Mathematica notebook form. Both input and output should be displayed.
Q1. Find the integral of
. Differentiate the result to compare with the original form.
Q2. Find the integral of
.
Q3. Expand 
.
Q4. Obtain the eigenvalues and eigenvectors of a 10 by 10 random symmetric matrix. (Hint: generate a random 10 by 10 random general (possibly asymmetric) matrix and symmetrise it by a number of approaches e.g. add it to its transpose and divide by 2). Check the eigenvectors for orthonormality.
Q5. Find the Laplace Transforms of sin(x), 
, 
and 
.