## The truth about differential equations

## The truth about differential equations

2

GregLocock (Automotive)
(OP)

https://web.williams.edu/Mathematics/lg5/Rota.pdf

Engineering degrees should be far more focused on numerical methods than solving the few solvable equations.

Engineering degrees should be far more focused on numerical methods than solving the few solvable equations.

Cheers

Greg Locock

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## RE: The truth about differential equations

Not because I used Mathcad or some software to do it for me, but because the need literally never presented itself.

If I had to solve a differential equation today, I think I'd have to study for a week and re-learn it.

## RE: The truth about differential equations

## RE: The truth about differential equations

I'm kinda 'old school', archaic maybe, the advantage of having a formula as opposed to using a linear method is that it gives you an idea of what the variables are and how they act.

My $.02... other than helping a student with Grade 12 Calculus

a couple of years back, I haven't used it often, but it still pops up.So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: The truth about differential equations

really, reallyfluent in calculus and math in general. Needless to say, I wasn't one of them.I had a lecture in an upper level engineering course where the subject (don't recall) needed solution of a differential equation. The professor, working on the white board said "We are going to solve this by the graduate student method. We're going to just write down the answer." Both illustrative of how certain problems are well known and funny too I thought.

This same profesor in a lecture would ask "Why do we study mechanical engieering? (pause for effect) Electricity and chemistry." I loved his classes.

The problem with sloppy work is that the supply FAR EXCEEDS the demand

## RE: The truth about differential equations

## RE: The truth about differential equations

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: The truth about differential equations

I said It could be done with calculus. This was before computers, etc., so another engineer and I did the math and solved the problem.

My recollection is that our general arrangement group had already developed the sizes (diameters, height, and hopper angles), so our efforts weren’t implemented.

gjc

## RE: The truth about differential equations

Several years ago, a complex problem came to me that I could have solved with a system of differential equations, but the computation and setup would be equivalent to doing it numerically. The iterative solution had the advantage of delivering mountains of step-by-step data that would describe the process in detail, not just the final result at the end.

## RE: The truth about differential equations

notfondly remember taking differential equations in college. At work, I have used double integration method to solve beams. When I am asked about vibration deflection and acceleration, I differentiate the basic motion equation.At home, I was playing around with beam analysis, and I set up a spreadsheet to do basic beam theory and interation to find an accurate solution. Double integration actually is not correct. I also played with the basic vibration free body equation.

mx''+cx'+kx......where

cis the damping factor assuming a fluid damper. The force for fluid friction really ought to be Cx'^{2}. I assume the resulting differential equation is not solvable by algebra, although the numerical solution is easy, even with a spreadsheet.--

JHG

## RE: The truth about differential equations

But yeah, solving diff. equations numerically (FEA, controls theory, CFD) is incredibly useful.

## RE: The truth about differential equations

^{2}, the whole mess is no longer analytically solvable for acceleration, so far as I know.Cheers

Greg Locock

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## RE: The truth about differential equations

But potentially it was all that intense maths i did in university that make these daily maths i do, that most people couldnt do, seem "easy"

## RE: The truth about differential equations

Rota has some very valid points but I would argue that "Calc II" (integral) as taught stateside is the most difficult due to the volume of material, ordinary diff eq was easy by comparison. I'd also argue that word problems are essential to show the usefulness of the material and their subjects should vary to force students to engage the brain a bit. The bigger issue with textbooks today IMO is that they're written by academics with little-no real-world experience, if word or other problems stink its bc the author stinks at writing them. I started collecting obscure/niche textbooks while still working in the trades bc I found they were great reference material for machine/tool setups in the shop. In college I started picking up engineering/other texts and one thing I have found is that even among math/calc books, older texts were written in more plain/simple language and thus more understandable. Half of the books today make me wonder if they weren't ghost-written by an algorithm at IBM.

## RE: The truth about differential equations

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: The truth about differential equations

When I was a professor, I taught students to perform system modeling using first principles with ODEs and block diagram editors, and also to develop diff eq models using system identification methods fed with experimental data obtained from existing systems. Did this for a buck converter in my power electronics class, a water flow control system in my controls class, and a few other lab projects. Once the model had been developed and validated, then the students would design a control algorithm for the system model, implement the algorithm in a controller (e.g., analog circuit made from op-amps for the buck circuit, tuned PID or discrete-time filter in PLC/microcontroller), and test it on the real system. All these projects started with obtaining the diff eq's through analysis or experimentation. The students really enjoyed the theory-to-practice side of things, as did I.

xnuke

"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand,

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