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. (POLYMATH file: Example for Using POLYMATH for ODEs)
- Introduction to Nonlinear Regression - Discusses assumption in nonlinear regression (NLR) and uses data for vapor pressure versus temperature to fit to an Antoine equation. Discusses how to evaluate NLR results. (POLYMATH file: Antoine Equation NLR)
- Nonlinear Regression Introduction - uses nonlinear regression to obtain kinetic parameters from kinetic data obtained from an isothermal CSTR. (POLYMATH file: REGRESS)

- Nonlinear Regression using POLYMATH - demonstrates how to use POLYMATH software to carry out nonlinear
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. (POLYMATH file: PFR Adiabatic)
- Isothermal Semibatch Catalytic Reactor - solves mass balances for a semibatch reactor in which a catalyst is continuously fed to the reactor. (POLYMATH file: Isothermal Semibatch Catalyst)
- Adiabatic Semibatch Reactor Part 2 - presents the POLYMATH program used to solve the differential equations generated in part 1. (POLYMATH file: Adiabatic Semibatch Reactor)
- 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. (POLYMATH file: Isothermal Plug Flow Reactor)
- Isothermal Batch Reactor Part 2 - performs the numerical solution using POLYMATH software with the equations generated from part 1. (POLYMATH file: Isothermal Plug Flow Reactor Part 2)
- Membrane Reactor - an example of a membrane reactor that is aimed at improving conversion by removing a specific product from the reactor. (POLYMATH file: Membrane Reactor Example 2)
- Catalytic Packed Bed Reactor - an example where mole balances are solved as a function of catalyst weight in an isothermal packed bed reactor. (POLYMATH file: Packed Bed Example)
- Parallel Reactions in a Batch Reactor - solves mass balances for an isothermal batch reactor with three parallel reactions. (POLYMATH file: Batch Reactor Multiple Rxns)
- Multiple Reactions in a CSTR - solves the mass balance for two reactions (series/parallel) in an isothermal CSTR. (POLYMATH file: Multiple Reactions in CSTR)
- 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. (POLYMATH file:Packed Bed Example)
- Semibatch Reactor with Heat Exchange - solves the mass and energy balances for a semibatch reactor in which two reactions in series take place. (POLYMATH file: Semibatch Heat Exchange and Multiple Reactions)
- Autothermal Reactor - describes the operation and the equations used to model an autothermal reactor. (POLYMATH file: Autothermal PFR in class)
- 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. (POLYMATH file: POLYMATH Linear Regression Kinetic Data)
- Nonlinear 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. (POLYMATH file: NLR Differential Reactor Data Order Rates)
- Nonlinear Regression 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. (POLYMATH file: NLR Michaelis-Menten Kinetics)
- 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. (POLYMATH file: Activation Energy Second Order Reaction POLYMATH NLR)
- Conversion for a Reactor with Segregated Flow - Calculates conversion in a laminar flow reactor for a second-order reaction. Segregated flow is assumed, and the differential equations are solved with POLYMATH. (POLYMATH file: Segregated Flow in Laminar Flow Reactor)

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. (POLYMATH file: Adiabatic Flash)
- 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. (POLYMATH file: Bubble Temperature Raoult's Law)
- 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. (POLYMATH fiile: Bubble Temperature Raoult's Law)
- VLE: Wilson's Equation - models vapor-liquid equilibrium for a binary mixture using Wilson's equation developed in part 1. (POLYMATH file: Wilson Equation VLE)