4C: Derivatives





sum must satisfy the limiting values defined by (4.17). We should recognize that the changes happen only because of actions and not because of passage of time. Thus a careful evaluation will always show that the derivative is an action reaction law and therefore is a sigma law.

In modern days we analyze our systems using differential equations. Since the derivative obeys the laws of conservation, the differential equations will also obey them. Thus our system models can be designed using the sigma law (4.17). It appears also that there is only one law in nature, and that is the sigma law. It is very unlikely then, that our modeling effort will violate any unknown law of nature. The ideal model will automatically satisfy the sigma law, and therefore will represent the true nature of all systems.

The algorithm to create such a model is based on the concept of system theory, which is briefly outlined in the following section. Our objective is to show the existence of a systematic algorithm for such a model and our emphasis is on the development of a thought process based on the laws of conservation. The existence of such a model will prove that all systems obey the sigma law.



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