Physics 350:
Computational Methods
for the Physical Sciences

Spring Semester 2009

Solutions for Physics 350 Lab 1: Maple Basics

It's always a good idea to first restart your Maple spreadsheet.

>	restart;

The first question you are asked is for the indefinite integral of x^5*exp(-7x), so we can try:

>	*s := int(x^5exp(-7x),x);*

(1.1)

Next we are asked for the definite integral of exp(-q*x) from 0 to infinity. You are told this only converges for q>0, therefore I use:

>	assume(q>0);

>	*int(exp(-qx),x=0..infinity);**

(2.1)

We are also asked to evaluate the definite integral of ([sin(x)]^2)/(x^2+a^2) from -infinity to infinity, assuming a>0, which is just:

>	assume(a>0);

>	f := (sin(x)^2)/(x^2+a^2);

(3.1)

>	g := int(f,x=-infinity..infinity);

(3.2)

Then we are asked to plot the integral from a=0 to infinity and to determine the limit as a --> 0, I do that next:

>	plot(g,a=0..10);

>	limit(g,a=0);

(3.3)

Finally, I am asked to compute the value of molecular velocity which maximizes the distribution of molecular speeds of a gas, so I solve for when the first derivative is zero (either a minima or maxima), then plot up the function to see which it is:

>	*f := N(v^2)exp((-mv^2)/(2kT));**

(4.1)

>	g := diff(f,v);

(4.2)

>	solve(g = 0, v);

(4.3)

>	*subs(v=0,f);subs(v=(2^(1/2)(mkT)^(1/2)/m),f);subs(v=-(2^(1/2)(mkT)^(1/2)/m),f);*

(4.4)

Physics 350: Computational Methods for the Physical Sciences

Spring Semester 2009

Physics 350:
Computational Methods
for the Physical Sciences