Dean's Mathematics Page

Dean's Mathematics Page

Last Updated January 6, 2022

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From Continuous to Discrete From Continuous to Discrete

This mathematics book relates integer (diphontane) equations to algebraic equations, difference equations to differential equations, and analog elecronics to digital electronics. It is currently being republished and will hopefully be available in 2022.

New General Analytic and Numerical Methods in Constrained Optimization with Applications to Optimal Consumption
Utilitas Mathematica 52 ( 1997 ), pp 123 - 128
This concerns mathematical methods involving the calculus of variations on how to expend a resource over time.
PDF Document
Supplement to Above Paper
This is a supplement to the above paper on optimal consumption. It also gives a worked example done with the simulation program below.
PDF Document
Optimal Spending Model
Concerns how to spend a fixed amount of resources for optimal utility over a fixed amount of time and known interest rate. Based on the above paper.
Excel Worksheet
Application of Pseudo-Wavelets to Optimal Control ( Thesis )
Wavelets are powerful approximating functions. Here they are applied to the MEI ( Measured Equation of Invariance ) method and some various optimal control problems for improved computational speed and quicker convergence to a solution.
PDF Document

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