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# What are Math Optimization Problems?

## Finding the optimal objective value for a math model.

Mathematically speaking an Optimization problem consists of one's equations plus an objective function. A solver will tweak all available parameters in a program until the solver finds an optimal objective value. Quick and accurate solutions. Try solving your problem in an Optimization setting. Its great!

## Calculus-level programming solves Optimization Problems

If a solution exists, Calculus programming can find it. Say your math model is y = f(x; a, b, c) and you want to find your parameters a, b, & c that maximize Y at X=3. Calculus programming has a find statement that handles this quite nicely. A few runs should convince you on the solution or that your math model needs improving.

## Calculus programming allows nesting of Optimization problems.

### Optimization Examples:

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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