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# Calculus Solvable Math Models include:

• Differential Equations (ODEs & PDEs)
• Nonlinear equations
• Implicit equations
• Constrained equations
Calculus programming is a Proven Approach ...
• Allows Rapid Prototyping
• Decouples Math Models from Algorithms
• Accelerates Problem "Understanding"
• Enabled by Automatic Differentiation

Most problems are solved in hours! A PDE make require a day or two. Code consists of ones equations and a dozen or so other lines. Try it you'll like it!

Math Modeling 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:

 Electrical Filter Design: find the transfer function's poles & zeros; H(s) = Yout(s) / Yin(s). 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. 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. Digitized Signal from Magnetic Recording: Magnetic recording of transitions written onto a computer disc drive may produce an isolated pulse as shown. 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 - BVP 4 PDE Equations - Implicit (Differential) Equations