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## Root/Fundamental Modeling and Simulation Level

### Have a math problem that needs some tweaking?

FortranCalculus can tweak parameters in the following types of math problems ...

 Differential Equations (ODEs & PDEs) Integral equations Nonlinear equations Implicit equations Constrained equations

We are attempting to explain how a company can execute an optimization of other optimization problems in order to truly optimize the company's objective. The FortranCalculus compiler provides this ability to nest optimization problems. Root modeling and simulation problems need to plan on other company members executing their root programs from within their member's own programs.

### Oil Refinery Example Problem

Building Science and Engineering Math Models is the key work at this level. Each process must have a model that describes the break down of molecules coming in as input to each process (eg. distillation or cracking units) and how they bind to other particles to form a desired end product. This modeling is for the fundamental chemistry that incurrs in a given processing unit. Each model may consist of algebraic equations, ordinary differential equations, and/or partial differential equations. For example, movement of oil may involve heat transfer and thus requires some partial differential equations that would be part of ones model for each processing unit that causes heat transfer.

Next building Control Valve Math Models for each control valve type used in any processor on given site. These models must simulate real time events and responses. For example, a pressure guage when increased would force the processor to reduce input while decreasing the pressure guage would increase input or whatever. These models must be very exact.

Simulations: Once models are built start simulating each different processing unit type. Does the simulation respond as a unit in the real world? Keep working on models until you can answer this question with a yes. Then pass this processing unit's math model on to ones individual simulations group

Productivity History: In the 1970s a gold, silver, and red star experimental program was created at Chevron's Richmond, California Refinery with a goal to improve productivity by motivating the control room operators. Before this star program was created the experienced operators often started their shifts by setting their controls into 'safe' regions and then sit back and relax for the rest of their shift. This star program got operators competing against each other to see who had the most and highest stars. The stars were handled out to the operators that showed the most improvement in productivity for the week. The program had computers watching each movement an operator made. If he/she went into a danger region with a control valve the computer would warn the operator and get him/her back into the proper region. But it would not tell him/her where it was optimal. He/she had to figure that out on their own. The increased productivity from this experimental program quickly paid off the cost of creating the software to monitor each control room and all associated hardware. Just a simple star got things running nicely. :)

Read our textbook (see below) and learn more on how the operators increased Black Gold production that paid for this computer experiment.

### Book for CEOs

See following list of example Fundamental Level Simulations/Optimizations problems solved with Calculus-level programming:

Root Level (Modeling, Simulations, & Optimizations) Examples:

Magnetic Recording

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## Problem-Solving Applications include:

 CurvFit: a curve fitting program with Lorentzian, Sine, Exponential and Power series are available models to match your data. Match-n-Freq: a Matched Filter program used to filter signals and slim pulses.

## Industry Problem-Solving Descriptions include:

 Business Strategies & War Gaming: Buy, Sell, Hold options may be tested for an entire company, individual plant(s), or whole product lines. Imagine an increase in control settings from a 1 or 2 digits (i.e., a guess value) to an 8+ digit accuracy resulting from a Calculus programming calculation! Pulse Slimming to minimize InterSymbol Interference: via Arbitrary Equalization with Simple LC Structures to reduce errors. Voice Coil Motor: basically an electromagnetic transducer in which a coil placed in a magnetic pole gap experiences a force proportional to the current passing through the coil. Electrical Filter Design: find the transfer function's poles & zeros; H(s) = Yout(s) / Yin(s). Digitized Signal from Magnetic Recording: Magnetic recording of transitions written onto a computer disc drive may produce an isolated pulse as shown. AC Motor Design: a simulation program for A.C. motor design that was reapplied as a constrained optimization problem with 12 unknown parameters and 7 constraints. PharmacoKinetics: an open-two- compartment model with first order absorption into elimination from central compartment is presented here.

 Calculus (level) Problem-Solving for Engineers & Scientists

Textbooks - Parameter Estimation 4 ODE/PDE - Signal Analysis / Spectral Estimation - Body Plasma - Solar Cell
Increasing Productivity Examples: AC Motor Design - Matched Filters - Pulse Slimming / InterSymbol Interference - Pilot (safe) Ejection - PharmacoKinetics Simulation - Business Strategies & War Gaming - BVP - Implicit Equations