Snippets of Purified Applied Mathematics (SPAM)

- "If Nature can solve its Equations, so can We" (D.Brian Spalding)

The new discipline preferrably shall be called 'Pure Applicable Mathematics'. ('Purified Applied Mathematics' would also be an good calling sequence.) Snippets of Pure Applicable Mathematics (called SPAM ;-) are characterized by the following properties:

- All mathematical entities shall have their origin in the Real World. We are
definitely
**not**interested in entities which will turn out to be just a brain wave of some mathematical genious, and which cannot possibly have a counterpart in the physical reality around us. Thus Mathematics should be**applicable**. Read my lips: applicable. Applicable is not the same as Applied. - On the other hand, Snippets of Pure Applicable Mathematics shall exhibit
a sufficient level of abstraction. Nobody could have
foreseen the enormous
*practical*consequences of a formula like

e^{ix}= cos(x) + i.sin(x)

Remember that complex numbers were just a curiosity at that time. They were not Applied. But they have been Applicable ever since they were invented or discovered. - Let's not give up our rights of being born First, for a mess of pottage!
Example. Mr. Lodewijk has said that pressure drops in a helically
coiled evaporator can be calculated within 50 percent accuracy. Now it's
up to you to prove it. Because otherwise we must do costly experiments.
**Don't!** . How bout the computerized*Absolute rigour is a phantom**proof*of the Jordan Curve Theorem? How about the Andrew Wiles' courtroom style proof of Fermat's Last Theorem? Who is going to check and debug all this?- Attention shall be paid to issues, which were touched by some researchers, but have been worked out insufficiently: because of their supposedly low impact in an Industrial environment. It is emphasized that such issues were discarded only because of the rat-race for cheap "results", which is declared here to be irreconcilable with the spirit of Pure Applicable Mathematics.
- Especially with "demanding applications", details which are interesting
from a pure theoretical point of view (at first sight) tend to be drowned.
Have we forgotten that theoretical results
**very often**have the potential to become important in practice? Do not overlook any such "insignificant" details, because any chain is as weak as its weakest part. And the hand of God is in tiny details, Not in Generality ;-)

- MultiGrid Calculus (1-D)

Related: Fibonacci Iterations

Extension: TripleGrid Calculus - Elementary Substructures (2-D)

With a lucid explanation by Gerard Westendorp

together with sources & executable code

and some extensions to 3-D - Quadratic Splines
- Lie Groups (1-D & 2-D)

with exe and source - Graph Theory
- Cosine Powers
- Collatz Problem
- Fuzzy Frenet and Lissajous Analysis
- The Least Squares Finite Element Method

and accompanying L.S.FEM software - About the infamous Inside / Outside Problem

and accompanying documentation / software - Inverse Perfect Hashing &
software

Preliminary theory may be found with Google.

Theory as well as practice have been upgraded. -
Chebyshev and stuff (
PDF )

together with software & source

Very much related subject: Cosine Powers

Important fact is the one-to-one mapping between

Polynomial Space and Cosine Space -
Is the Euler-Mascheroni constant rational or irrational ?

Really don't know, but anyway, here comes

some research with software & source