Types: 0.3 Applied Math Modeling in Multivariable Calculus
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Find and solve real-world problems using the applied math modeling process. In linear algebra, we focus on transforming our real-world problem into an ideal mathematical model that is stated in terms of vectors and matrices. Then, we attempt to represent the most pertinent aspects of our problem using at least one of the linear-algebraic problems stated below.
What would be cheaper, spending billions to build and test individual airplanes to find out if they fly or not or spending millions to ensure the airplanes fly before building them? The latter, obviously. This is the principle behind the Applied Math Modeling Problem. Companies like Boeing hire thousands mathematicians to save themselves money, and this also means you could be getting a fat paycheck (if you're good at applied math)!
A set of questions used to illicit information that can be stated using quantitative data observable by human beings.
The first phase of the applied math modeling problem is identifying a real world problem through data analysis. From this data, we can mathematize the results into a collection of relevant math ideas. Some examples could be introducing mathematical notation, defining variables, and imposing assumptions. Once we've decided on a mathematical model, we need to mathematically analyze it. A good motto for this stage is “error and error and error, but less and less and less. The dream of applied mathematics is that we might analyze our ideal model using a suite of technical mathematical results and produce an ideal solution to this problem. The fantasy of applied mathematics is that the ideal solution we produce via mathematical analysis leads to valuable progress in discovering aspects of the meaningful real-world solution that we so desire.