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# 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
Published in: Engineering

#### Transcripts - Polymath For Chemical Engineers

• 1. Polymath Tutorial For Chemical Engineers Hashim Khan (DDP-SP13-BEC-053)
• 2. • 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 and reports. • 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 software.
• 3. • 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
• 4. Explicit & Implicit Functions
• 5. • Let us get a few terms clear first… • Functions • 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
• 6. • 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. • Example • y=4*x-7 • 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.
• 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
• 8. • Implicit Functions • On the other hand an implicit function is one defined by an implicit equation. Take for example. • x^2-y^2-1=0 • Basically it is a function or relation in which the dependent variable is not isolated on one side of the equation.
• 9. • 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.
• 10. The Algorithm For Reactor Volume Calculations!!!
• 11. DESIGNOFREACTORS
• 12. DESIGNOFREACTORS
• 13. The Screen!!!
• 14. Differential Equations In Polymath A Brief How To…
• 15. dx/dy x y = x^2-3x
• 16. Click
• 17. Click
• 18. Algorithm For A PFR
• 19. Problem 1 Reversible Reactions
• 20. Problem 2 Membrane Reactors