A nested structure
However, in my understanding most of the quant theories suggest functional decomposition. So I look at functions as the smallest units. They create tasks that create workflows that create subsystems that create the system.
What's important to remember is that these units are usually nested.
The most important unit is the task...Value a financial instrument, a portfolio…pick a part in the box and load it into the machine…make an operational plan for certain bending operations…
They're built of (nested) functions.
Special functions
In mathematics we have special functions, symbols we know by name, meet quite often, know their form, shape and behaviour. From the simple Sin, Cos, Exp, .. to the Meijer G-Function, which is very general.
Some of them are good friends, we can artistically create derivatives, integrals...when they dominate in expressions, equations we use them as Ansatz for, say, solving differential equations.
They're so well known that we don't need to think much about the building blocks…constructor - progressive problems - solution. But they may need some preprocessing and postprocessing.
New special functions expand the domain of closed form solutions. Closed form solutions are elegant, but usually they do approximate only small worlds.
Some of them are good friends, we can artistically create derivatives, integrals...when they dominate in expressions, equations we use them as Ansatz for, say, solving differential equations.
They're so well known that we don't need to think much about the building blocks…constructor - progressive problems - solution. But they may need some preprocessing and postprocessing.
New special functions expand the domain of closed form solutions. Closed form solutions are elegant, but usually they do approximate only small worlds.
Higher functions
In the vast majority of the cases you need numerical schemes to make the predictions and simulate your models. To model, say, the material flows, chemical reactions, and conservation of energy in, say, a blast furnace you need to solve systems of dozens of coupled nonlinear Partial Differential Equations.
To solve them it is required to decompose the domain (space and time)…especially if you use Finite Element techniques…They're often used many times and it's really important to understand their buildings blocks…If say, the convection part of a reaction-convection-diffusions PDE becomes dominant, you need to introduce some stabilization techniques (upwinding) to avoid the risky horror of spurious accuracy…
There are many of such traps in mathematical problem solving
In one of the coming posts, I will look into tasks…they are usually represented in languages and need various data with a wide range of types...
