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https://authors.library.caltech.edu/63245/1/00683365.pdf

BTW, this site has some really good papers, most of which you can read for free.

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- Thread starter DaveE
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In summary, the conversation discusses a paper from a former EE instructor that highlights the difference between memorizing a mathematical result and truly understanding it. The instructor emphasizes the importance of simplifying solutions in engineering for practical use and the value of approximation in design. The conversation also mentions the availability of free papers on the website and the instructor's approach to teaching at CalTech.

- #1

- 3,960

- 3,605

https://authors.library.caltech.edu/63245/1/00683365.pdf

BTW, this site has some really good papers, most of which you can read for free.

Engineering news on Phys.org

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Nik_2213

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Also, yes, it was expected you'd hand-calculate it, possibly with aid of slide-rule, four-figure logs, six if fussy.

"TEN significant figures ? You doing orbits, tide-charts or something ??"

Akin to way the generic 'Standard Deviation' formula does not suit use in a computer algorithm, requiring loops through stored data. Collecting the 'needful' as data entered is much faster and more accurate...

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Yes, it's easy to remember a solution by 'completing the square'. His point is, both here and more generally in engineering, that you aren't done with your derivation until you get the result into a simple, practical, form. Simple forms increase understanding and allow you to make good decisions in design efforts. Things like simplification with good approximations for example. This isn't often taught to university level students they're stuck with their high school "hapless students' brain version".Nik_2213 said:Possibly because that 'original' version could be derived / solved without melting us hapless students' brains ?

He used to say "Engineering is the art of approximation", which I think is true. It should be explicitly taught, as he did at CalTech. He has several more complex versions like this in Analog EE analysis. I like this one because everyone uses the quadratic formula and everyone thinks they know all about it from high school.

An engineer's approach to the quadratic formula often emphasizes practical application and approximation rather than purely theoretical derivation. Engineers might focus on numerical methods, simplifications, and real-world applicability when solving quadratic equations.

Engineers may use approximations or iterative methods to simplify the quadratic formula. For example, they might employ numerical algorithms like the Newton-Raphson method or use simplified forms of the formula when certain terms are negligible in practical scenarios.

Engineers often deal with real-world problems where exact solutions are either unnecessary or impractical due to measurement errors or complex models. Numerical methods provide sufficiently accurate solutions more efficiently, especially when dealing with large systems or real-time applications.

One common application is in the analysis of projectile motion. Engineers use the quadratic formula to determine the time of flight, range, and maximum height of a projectile by solving the equations of motion under the influence of gravity.

Engineers often use software tools such as MATLAB, Python (with libraries like NumPy), or specialized engineering calculators to solve quadratic equations. These tools allow for quick and accurate computations, including handling complex or large systems of equations.

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