This is a casebook of math problems from industry. The source code and out put are listed. The problems solved range from Algebra thru Differential e quations. Problems include Initial-Value, Boundary-Value, Inverse, etc. T he equations may be non-linear, any degree, any order, implicit, etc. Code s are very short, normally 30 lines or less PLUS one's equations and someti mes plot code. Number of equations may be from 1 to 1,000 or more.
Teaching engineering, science and/or operations research student?s problem solving techniques that will work in the future is not easy. Probl em solving requires a broad based knowledge in math and science as well as discernment and flexibility to challenge the way it has always been done in the past. Generally, an objective driven design will yield the best desig n in the least amount of time. Companies need engineers trained in setting objectives before they begin the time-consuming process of formulating and testing new concepts and designs.
Our textbook titled "Engineering Design Optimization using Calculus Level M ethods: A Casebook Approach",
Our textbook attempts to fill a gap in educational material in the mathemat ical problem solving arena. Traditional texts leave students in a simulati on thinking mode. Simulations require many computer runs causing delays in solution and little gain, if any, in problem understanding. Simulations r equire a numerical algorithm to be meshed with their math model. In such f orm, math models are hard to recognize and discuss. Besides slowing their understanding, users lose confidence in program solutions.
This textbook tries to move today?s thinking from solving one probl em at a time, to solving all of their project?s problems at once wh ile tweaking parameters in order to achieve an optimum solution. This requ ires Calculus-level thinking. An analogy might be thinking in terms of Mac hine code, one bit at a time. Today, computer simulations have people thin king in terms of Algebraic code, one problem at a time. We are trying to m ove people to Calculus-level code, solving entire projects at a time. This will reduce development time and improve accuracy of their math models.
History: NASA funded the development of the first Calculus-level language t hrough TRW called Prose. Prose became available to the public in 1974 thro ugh a national computer time-sharing network. Prose ran on large Control D ata Corporation (CDC) 6600 computers. Automatic differentiation and operat or overloading were key technologies for this project. I taught the Prose language to Engineers & Scientists in the San Francisco Bay Area from 1975 through 1979. Most national time-sharing computer networks died in the 198
0s and thus went Prose. FortranCalculus is the next Calculus language on t he horizon. It is in testing mode now and will soon be released on the web .Book goal: get users thinking outside their box. For example, the Oil Refinery problem shows how one could solve oil production for one distillat ion unit, or one plant, or an entire corporation (i.e. many refineries) all at once! This may consist of one, 100, or 10,000 differential equations w hile searching for the best refinery(s) to produce products that have pollu tion by-products. The goal is to minimize pollution by choosing the locati on where each product is produced. Solve the whole problem in one run not just part of problem.
One reviewer wrote: "The most important pedagogical value the book could de liver is a sound grounding in calculus level thinking for engineering desig n optimization. This approach is as significant for engineering/science as object oriented programming has been for computer science. Independent access to a computer system running the calculus tools would fr ee the reader from having to attend a class. This would open up the market for the book quickly to practicing engineers."
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