Polymath For Chemical Engineers
This should give you an idea about how to operate the software. And use it to solve Ordinary Differential Equations. I will be using foggler's book for the examples that have code given with it.
Published on: Mar 4, 2016
Transcripts - Polymath For Chemical Engineers
Polymath Tutorial For Chemical
Hashim Khan (DDP-SP13-BEC-053)
• POLYMATH is a proven computational system which
has been specifically created for educational use by
Mordechai and Michael B. Cut lip.
• 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
• With POLYMATH, the user is able to focus complete
attention to the problem rather that spending
valuable time in learning how to use or reuse the
• 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 & Implicit
• Let us get a few terms clear first…
• In the realm of mathematics, we probably have
little trouble understanding the concept of a
function. A function is an expression that generates
one unique output for each input. Lets say…
• [f(x)=x^2] is a function that for a unique value of x
squares it and gives us the output.
x f(x) x^2
• Explicit Functions
• Explicit functions are such that are explicitly
written. Meaning to say (y=4*x-7) is an explicitly
written function. This function is written in the
terms of a dependent variable y in terms of the
independent variable x.
• It is expressed clearly, and we can easily evaluate
values for the independent variable. If we use
function notation, we can write this explicit
function as f(x) = 4x - 7.
• An explicit function is essentially a rule for
evaluating values of the independent variable. The
rule tells us what is done with the independent
variable so to produce an output. In the example
above, the explicit function tells us to multiply the
independent variable by 4 and then subtract 7
from this product. For instance, let's find the value
of the function when x = 5:
• y = 4(5) - 7 = 20 - 7 = 13
• Implicit Functions
• On the other hand an implicit function is one
defined by an implicit equation. Take for example.
• Basically it is a function or relation in which the
dependent variable is not isolated on one side of
• Differential Equation
• A differential equation is a mathematical equation
that relates some function with its derivatives. In
applications, the functions usually represent
physical quantities, the derivatives represent their
rates of change, and the equation defines a
relationship between the two.
The Algorithm For Reactor Volume
Differential Equations In Polymath
A Brief How To…
y = x^2-3x
Algorithm For A PFR
Problem 1 Reversible Reactions
Problem 2 Membrane Reactors