I attended Oregon State U. and majored 3 years in Electrical Engineering. Then I switched to a Math major for my final years and graduated with a B.S. in Math.
My first job was with Lockheed Aircraft Co. building the SR-71 (Black Bird). One assignment had me designing the pilot's suit. It was to be 1/4" thick consisting of 5 materials and required to drop the outside temperature from its high to 98 degrees next to the pilot's body temperature. A great math problem!
Another job was at Memorex Corp. designing a "Matched Filter" for a 14" disc drive. This electrical filter was to make a pulse more symmetric and thinner. The more symmetric and thinner a pulse, would help minimize the "Pattern-Induced-BitShift" (PIB). Heavy math problem! (Main LaPlace transform equation took me 22 pages of hand written notes to derive the necessary equations. Oh, those little minus signs kept giving me trouble!)
Next job was at Lockheed Missiles & Space Co. Here I had different assignments. One assignment had me analyzing, what is called Digital Signal Processing (DSP), a plume from a space craft to try and label it as a "Friend or Foe". If its a Friend no problem, but a Foe may require action to be taken for it may shoot you down. This job required understanding the Fourier Transform. (FFT algorithm was being used. That was a BIG math mistake. I switched to 10 other algorithms and partially solved the problem.) For more, see my SpectrumSolvers v. 6 app... fortranCalculus.info .
After a lay-off in 1991, I started writing my math textbook / casebook. 26 years later the book is done plus a website, 4 apps developed, & front-end for a compiler I developed in order to show a new computer language that makes solving math problems very easy. This 'new' language takes a 'automobile' level computer to a 'airplane' level computer. Design solution times drop by (around) 95%; i.e. what took 20 months is now done in less than 1 month and the solution is optimal.
Our Compiler improves Math Modeling, Simulation & Optimization efforts for Engineers & Scientists by improving their productivity by 20 times! Solving differential equation math problems with today’s compilers often take more than 1 man year but our compiler can do it in hours with improved accuracy in the results. Our compiler also allows one to tweak their parameters for an optimal solution. Solutions are Faster, Improved Accuracy, & Cheaper.
Get future engineers and scientists thinking optimal solutions. What’s the different between simulation and optimization? Picture a saw horse construction project. A Simulation would yield A saw horse where Optimization would yield an Optimal saw horse. If the objective (function) was good and proper then the Optimal saw horse would be the best solution, right? For example, the objective might be lightest & strongest saw horse. A wrong objective might be just the strongest saw horse. This might yield a strong horse but a very heavy one.If you were a manager or CEO and had the choice of a simulation design versus an optimization design, which would you pick?
Teach Educators: Modeling & Simulation’s next step is (Mathematical) Optimizations. Optimizations require an Objective (function). Today's Engineers & Scientists solve problems with a “Find X” mind-set. With some Operational Research training they could expand their thinking to a “Find X to Optimize Y” mind-set. Then they would be ready for Optimizations, Calculus-level programming and software. (This would drop today’s design times that require months even man years to one or two days! Manufacturing processes could be optimized to the days demand and thus maximize their profits.)
“Find X to Optimize Y” thinking among professors will cause most engineering & science textbooks to be rewritten with optimization examples and discussions. This will be great stuff for industries and government; applied engineering and/or science not just theories.
Objective required for Optimization
• Engineers & Scientists need to move from a “Find X” mind-set to a “Find X to Optimize Y” mind-set teaching in schools.
• Industry/Company Leaders need to state their company objectives so ALL employees know it; Leadership by objectives.