PHYS 607 Assignment 1

Problem 1

Evaluate the integral

In[3]:=

∫_0^3∫_0^4∫_ (y/2)^(y/2 + 1) ((2x - y)/2 + z/3) xyz

Out[3]=

12

Problem 2

Solve the differential eqution:

In[4]:=

DSolve[y''[x] + y[x] == 3/Sin[x], y[x], x]

Out[4]=

{{y(x) c_1 cos(x) + c_2 sin(x) - 3 (x cos(x) - log(sin(x)) sin(x))}}

Problem 3

Find eigenvalues and eigenvectors of the martix

In[5]:=

A = {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}

Out[5]=

( 0   1   0 )            1   0   0            0   0   0

In[6]:=

Eigenvalues[A]

Out[6]=

{-1, 1, 0}

In[7]:=

Eigenvectors[A]

Out[7]=

( -1   1    0  )            1    1    0            0    0    1


Created by Mathematica  (September 23, 2003)