This is a casebook of math problems from industry. The source code and output are listed. The problems solved range from Algebra thru Differential equations. Problems include Initial-Value, Boundary-Value, Inverse, etc. The equations may be non-linear, any degree, any order, implicit, etc. Codes are very short, normally 30 lines or less PLUS one's equations and sometimes 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. Problem 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 design 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 Methods: A Casebook Approach", http://fortranCalculus.info/textbooks , considers design from the pragmatic concerns of industry. It utilizes casebook studies of math problems with their solutions in real life situations. Because it encourages students to view themselves as part of the design team, this text is the next best thing to an on-the-job training. It shows how setting objectives to problem solving assignments can help students complete work quickly and efficiently, but it also stresses that while every situation is different, the approach remains the same: objective-driven engineers state a math model and an objective function for a given problem while leaving the solving to a calculus-level computer language/compiler.
Our textbook attempts to fill a gap in educational material in the mathematical problem solving arena. Traditional texts leave students in a simulation thinking mode. Simulations require many computer runs causing delays in solution and little gain, if any, in problem understanding. Simulations require a numerical algorithm to be meshed with their math model. In such form, 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 problem at a time, to solving all of their project?s problems at once while tweaking parameters in order to achieve an optimum solution. This requires Calculus-level thinking. An analogy might be thinking in terms of Machine code, one bit at a time. Today, computer simulations have people thinking in terms of Algebraic code, one problem at a time. We are trying to move 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 through TRW called Prose. Prose became available to the public in 1974 through a national computer time-sharing network. Prose ran on large Control Data Corporation (CDC) 6600 computers. Automatic differentiation and operator 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 1980s and thus went Prose. FortranCalculus is the next Calculus language on the 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 distillation 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 while searching for the best refinery(s) to produce products that have pollution by-products. The goal is to minimize pollution by choosing the location 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 deliver is a sound grounding in calculus level thinking for engineering design 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 free the reader from having to attend a class. This would open up the market for the book quickly to practicing engineers."