##### SAGE Server
Jason Hill has been kind enough to maintain a SAGE server: http://sage.colorado.edu.
If you are on campus, you can create an account and view public worksheets.
##### Riemann sum Mathematica notebook
I created a little notebook to run in Mathematica that hopefully will help visualize Riemann sums. Simply put in the function you'd like to examine, and make sure [a,b] is in the domain of the function.
A debt of $105,000 accrues 8% interest annually. If the payment at the end of every year is$10,500 plus the interest from the past year, find a formula for the yearly payment.
\begin{align*} B_1 &= 105000\cdot 1.08,\\ P_1 &= 10500+.08\cdot 105000 = (.18)105000. \end{align*} Year 2:
\begin{align*} B_2 &= (B_1-P_1)\cdot 1.08 = (.9B_0)1.08,\\ P_2 &= .1B_0+(.9\cdot .08)B_0=(.172)B_0. \end{align*} Year 3:
\begin{align*} B_3 &= (B_2-P_2)\cdot 1.08 = (.8B_0)1.08,\\ P_3 &= .1B_0+(.8\cdot .08)B_0=(.164)B_0. \end{align*}