Preface

This is a tutorial made solely for the purpose of education and it was designed for students taking Applied Math 0330. It is primarily for students who have very little experience or have never used Mathematica before and would like to learn more of the basics for this computer algebra system. As a friendly reminder, don't forget to clear variables in use and/or the kernel.

Finally, the commands in this tutorial are all written in bold black font, while Mathematica output is in normal font. This means that you can copy and paste all commands into Mathematica, change the parameters and run them. You, as the user, are free to use the scripts for your needs to learn the Mathematica program, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately.

Applications

Example 4.9.1: Flow Problems
A 500 liter container initially contains 10 kg of salt. A brine mixture of 100 grams of salt per liter is entering the container at 6 liter per minute. The well-mixed contents
are being discharged from the tank at the rate of 6 liters per minute.

Express the amount of salt in the container as a function of time.

Salt is coming at the rate: 6*(0.1)=0.6 kg/min
d yin /dt =0.6 ; d yout/dt = 6x/500

dx/dt = 0.6 -6x/500 ; x(0)=10

Suppose that the rate of discharge is reduced to 5 liters per minute.