Mathematical Modeling and Optimization: An Essay for the by Tony Hürlimann

By Tony Hürlimann

Computer-based mathematical modeling - the means of representing and coping with versions in machine-readable shape - continues to be in its infancy regardless of the various strong mathematical software program programs already to be had which may remedy astonishingly complicated and big versions. at the one hand, utilizing mathematical and logical notation, we will formulate versions which can't be solved by means of any desktop in moderate time - or which can't also be solved via any process. nonetheless, we will be able to clear up sure periods of a lot higher types than we will be able to virtually deal with and control with out heavy programming. this can be very true in operations study the place it's common to unravel types with many millions of variables. Even at the present time, there are not any basic modeling instruments that accompany the complete modeling technique from begin to end, that's to assert, from version production to record writing. This ebook proposes a framework for computer-based modeling. extra accurately, it places ahead a modeling language as a kernel illustration for mathematical types. It offers a basic specification for modeling instruments. The booklet doesn't divulge any answer equipment or algorithms that may be necessary in fixing versions, nor is it a treatise on the way to construct them. No assistance is meant right here for the modeler by means of giving functional modeling workouts, even supposing numerous types might be awarded that allows you to illustrate the framework. however, a brief advent to the modeling method is given with a view to expound the required historical past for the proposed modeling framework.

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Chapter 2 20 Figure 2-3: Topological Deformation Now the problem is easily solvable. Connect the squares as prescribed. After this, return the rubber to the initial state again (see Figure 2-4). A Figure 2-4: Solution to the Intersection Problem The solution is now so obvious that we can immediately "see" it. By the way, u the problem is a nice exercise in topology. Simplicity and conciseness also playa key role in all sciences and particularly in mathematics. Einstein put it this way: "Make it as simple as possible, but not simpler".

The overview will begin with general, unspecified notions, and then proceed to more formal concepts. Finally, a short historical digression will be presented to suggest further arguments for the importance of mathematical modeling. 1. Model: a Definition The term model has a variety of meanings and is used for many different purposes. We use modeling clay to form small replica of physical objects; children - and sometimes also adults - play with a model railway or model aeroplane; architects build (scale) model houses or (real-size) model apartments in order to show them to new clients; some people work as photo models, others take someone for a model, many would like to have a model friend.

The first is hurriedly collecting too much inadequate or incomplete data and irrelevant relationships, and the other is deciding prematurely on the methods to be used to solve the problem. The first mistake comes from an erroneous idea that the final and formalized model and its solution are more important than this "preliminary" stage, although a careful and accurate study of the problem is essential. The second mistake often arises because many modelers think that using some formalism is more important than using an appropriate notation that reflects the problem.

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