POLYMATH

POLYMATH is a proven computational system that has been
specifically created for educational or professional use. The various POLYMATH programs allow
the user to apply effective numerical analysis techniques during interactive
problem solving on personal computers. Results are presented graphically for
easy understanding and for incorporation into papers and reports. Engineers,
mathematicians, scientists, students, or anyone with a need to solve problems
will appreciate the efficiency and speed of problem solution. Developed by: Michael B. Cutlip, University of Connecticut; Mordechai Shacham, Ben-Gurion University of Negev, Israel. For more information on POLYMATH and to download the applications visit the following pages:

**Introductory Videos**

- Solving ODEs using POLYMATH - demonstrates how to solve systems of ordinary differential equations using POLYMATH software. (.POL file)
- Non-Linear Regression Introduction - uses non-linear regression to obtain kinetic parameters from kinetic data obtained from an isothermal CSTR. (.POL file)

- Non-Linear Regression using POLYMATH - demonstrates how to use POLYMATH software to carry out non-linear
regression to determine kinetic parameters from tabulated data.

- POLYMATH Excel Add-in to Solve ODEs - demonstrates how to use POLYMATH to solve ordinary differential equations (ODEs) by transferring the POLYMATH program into Excel.

**Example Problems**

Kinetics/Reactor Design

- Adiabatic PFR - solves the mass and energy balances for an adiabatic plug flow reactor. (.POL file)
- Isothermal Semibatch Catalytic Reactor - solves mass balances for a semibatch reactor in which a catalyst is continuously fed to the reactor. (.POL file)
- Adiabatic Semibatch Reactor Part 2 - presents the POLYMATH program used to solve the differential equations generated in part 1. (.POL file)
- Multiple Reactions in PBR Part 2 - using POLYMATH to solve the differential equations set up in part 1 and inspect the influences of conditions on reactor performance.
- Isothermal Plug Flow Reactor: Part 2 - uses POLYMATH software to solve the ODEs that are mass balances for an isothermal plug flow reactor derived in part 1. (.POL file)
- Isothermal Batch Reactor Part 2 - performs the numerical solution using POLYMATH software with the equations generated from part 1. (.POL file)
- Membrane Reactor - an example of a membrane reactor that is aimed at improving conversion by removing a specific product from the reactor. (.POL file)
- Catalytic Packed Bed Reactor - an example where mole balances are solved as a function of catalyst weight in an isothermal packed bed reactor. (.POL file)
- Parallel Reactions in a Batch Reactor - solves mass balances for an isothermal batch reactor with three parallel reactions. (.POL file)
- Multiple Reactions in a CSTR - solves the mass balance for two reactions (series/parallel) in an isothermal CSTR. (.POL file)
- Determining Rate Constant in a PBR - an example of gas phase reaction in a packed bed reactor where the rate constant of the reaction is unknown. (.POL file)
- Semibatch Reactor with Heat Exchange - solves the mass and energy balances for a semibatch reactor in which two reactions in series take place. (.POL file)
- Autothermal Reactor - describes the operation and the equations used to model an autothermal reactor. (.POL file)
- Linear Regression for Kinetic Data Using POLYMATH - Demonstrates how to use POLYMATH to carry out linear regression to fit kinetic data from a differential plug flow reactor, see part 1. (.POL file)
- Non-linear Regression for Kinetic Data Using POLYMATH - Demonstrates how to use POLYMATH to carry out nonlinear regression to fit kinetic data from a differential plug flow reactor, see part 1. (.POL file)
- Nonlinearregression to determine Michaelis-Menten kinetics parameters using POLYMATH - Demonstrates how to use POLYMATH to carry out nonlinear regression to determine Michaelis-Menten kinetics parameters, see part 1. (.POL file)
- Determine Activation Energy Using Nonlinear Regression using POLYMATH - Demonstrates how to use Polymath to carry out nonlinear regression to determine activation energy and preexponential factor for a chemical reaction from rate constants measured over a temperature range. (.POL file)

Thermodynamics

- Adiabatic Flash of Binary Liquid - presents the POLYMATH solution to the nonlinear algebraic equations that model adiabatic flash of an ideal binary mixture derived in part 1. (.POL file)
- Bubble Temperature (Raoult's Law) - calculates the bubble temperature for a binary system that obeys Raoult's law, using POLYMATH to solve the non-linear equations. (.POL file)
- Bubble Temperature Non-Ideal Liquid - uses POLYMATH software to solve non-linear algebraic equations that arise in vapor-liquid equilibrium calculations developed in part 1. (.POL file)
- VLE: Wilson's Equation - models vapor-liquid equilibrium for a binary mixture using Wilson's equation developed in part 1. (.POL file)