Polymath Tutorial For Chemical Engineers

Hashim Khan (DDP-SP13-BEC-053)

• POLYMATH is a proven computational system whichhas been specifically created for educational use byMordechai and Michael B. Cut lip.

• The various POLYMATH programs allow the user toapply effective numerical analysis techniques duringinteractive problem solving on personal computers.Results are presented graphically for easyunderstanding and for incorporation into papersand reports.

• With POLYMATH, the user is able to focus completeattention to the problem rather that spendingvaluable time in learning how to use or reuse thesoftware.

• The POLYMATH Numerical Computation Package has four companion programs.

1. SIMULTANEOUS NON-LINEAR EQUATIONS

2. SIMULTANEOUS DIFFERENTIAL EQUATIONS

3. DATA REGRESSION

4. SIMULTANEOUS LINEAR EQUATIONS

Explicit & ImplicitFunctions

• Let us get a few terms clear first…

• Functions

• In the realm of mathematics, we probably havelittle trouble understanding the concept of afunction. A function is an expression that generatesone unique output for each input. Lets say…

• [f(x)=x^2] is a function that for a unique value of xsquares it and gives us the output.

x f(x) x^2

• Explicit Functions

• Explicit functions are such that are explicitlywritten. Meaning to say (y=4*x-7) is an explicitlywritten function. This function is written in theterms of a dependent variable y in terms of theindependent variable x.

• Example

• y=4*x-7

• It is expressed clearly, and we can easily evaluatevalues for the independent variable. If we usefunction notation, we can write this explicitfunction as f(x) = 4x - 7.

• An explicit function is essentially a rule forevaluating values of the independent variable. Therule tells us what is done with the independentvariable so to produce an output. In the exampleabove, the explicit function tells us to multiply theindependent variable by 4 and then subtract 7from this product. For instance, let's find the valueof the function when x = 5:

• y = 4(5) - 7 = 20 - 7 = 13

• Implicit Functions

• On the other hand an implicit function is onedefined by an implicit equation. Take for example.

• x^2-y^2-1=0

• Basically it is a function or relation in which thedependent variable is not isolated on one side ofthe equation.

• Differential Equation

• A differential equation is a mathematical equationthat relates some function with its derivatives. Inapplications, the functions usually representphysical quantities, the derivatives represent theirrates of change, and the equation defines arelationship between the two.

The Algorithm For Reactor VolumeCalculations!!!

DESIGN OF REACTORS

DESIGN OF REACTORS

The Screen!!!

Differential Equations In PolymathA Brief How To…

dx/dy

x

y = x^2-3x

Click

Click

Algorithm For A PFR

Problem 1 Reversible Reactions

Problem 2 Membrane Reactors