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02-2 Applications of systems of linear equations: electrical networks (part 1/2)

Our second example will deal with Nutrition. By creating a system of equations we will be able to determine the precise balance of protein, carbohydrates and fats for a particular diet.

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Next, we will look at Network Flow, which is the study of the flow of some quantity through a network such as monitoring the patten of traffic flow in a city grid. Then we will look at two examples of Electrical Network Flow. An electrical circuit consists of a set of points called junctions, or nodes, with lines or arcs called branches connecting some or all of the junctions. Lastly, we will look at the Linear Difference Equation or Recurrence Relation, and how it applies to population movement or migration patterns.

SIAM Journal on Scientific Computing

This type of linear system allows us to mathematically model a dynamic system that changes over time. This type of study will allow us to track the movements of commodities and people groups and is even helping law enforcement track criminals. Options: if system is perturbed —Stable- system goes to a steady-state —Unstable: system leaves steady-state —Metastable: system is indifferent.

Can solve it, analytically and via computer Gaussian Elimination at steady state Properties are well-known BUT: world is nonlinear, see systems of equations from simple systems that we have already looked at. It is good in a range around that point, not everywhere.

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Some useful linear algebra. Linearly independent vectors span V : span of vector space V is all linear combinations of vectors v i, i. Similar presentations.

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