This worksheet introduces you to the use

**Getting Started**

To access mathematica in your PC follow these steps:

1. Click on the ``start'' button in the lower left corner of the screen.

2. Move the cursor ``Programs Mathematica Mathematica ''

3. Click on Mathematica.

4. Under the format menu click on ``Show Toolbar''

5. Again, go the format menu and click on ``Screen Style Condensed''

You will now get a screen where you can carry out the following simple exercises to get an idea of how to use Mathematica.

i) Type ``2+4'' and hold down the ``shift'' button in the key board and push ``enter'' (each time you want to get the result for what you have typed, you have to type ``shift+enter''). In the output the screen will give you back the result.

ii) Type ``10/2'' to check that you'll get 5 in the output.

iii) To find the roots of an equation (e.g. *x*^{2}-1),
type ``Solve[x2-1 == 0,x]''. In the output
you'll get +1 and -1 as the two roots.

iv) You can do much more! You can factorize the expression *x*^{2}-1 as we
usually do to get the roots. In order to do that
type ``Factor[x2-1]'', and check if you get (x+1)(x-1).

v) Mathematica has extensive plotting tools. For example plot the function sin(x). To do this type ``Plot[Sin[x],{x,0,6.28}]''.

vi) Help??? Mathematica has an extensive online help library. Try looking up the sin(x) function to make sure you have the right format.

vi) Here is an example how you can perform differentiation using
mathematica: suppose
*f*(*x*) = *x*^{n}; then
.
To check it type ``D[xn, x]'' and see the output.

vii) Likewise, you can perform integration on
*f*(*x*) = *x*^{n}.
Type ``Integrate [xn, x]'' and assure yourself that you
indeed get back
.

**Assignment 1. - Hand in by Thursday Jan. 20th**

**Examples**. Hand in the results of 10 mathematica
operations you experimented with.

**Problem 1**. The displacement
of a particle undergoing one dimensional motion under
constant acceleration is given by the equation
. Choose values of *u* and *a* that
you think are physically reasonable.
Find and plot *x*(*t*) and *v*(*t*) over a reasonable range of time
(this depends on your choice of *u* and *a*).
Note: In plotting, use ``Plot[Evaluate[x[t]],{t,0,5}]'' after
defining x[t].

**Problem 2** The velocity
of a particle is given by
*v*(*t*) = 0.10 *t* - *cos*(2*t*) in the
positive *x* direction. At
t=0, it was located at *x*(0)=0. Find and plot *x*(*t*) for
*t* up to 10*s*.