advice on mathematics

[isok89]

Dear all,


I am seeking your advice on the following issue:

I am a soon to be graduate with a MSc in structural engineering.
Soon I'll start with an MSc degree in geotechnical engineering.

However I am not satisfied with my level of understanding of finite element method, continuum mechanics
and structural dynamics. The reason for this is that I struggle with mathematics, during my bachelor I had a calculus course but
that was about it. As I was younger back then, passing the exam was more important than understanding it...

I would like to gain a good understanding of the following topics:

- linear algebra
- vector calculus
- differential equations (focus on ordinary differential equations primarily)
- fourier analysis

I've looked at books like:

- Ordinary Differential Equations by Tenenbaum (very good book but it's 850 pages just about ODE)
- Advanced Engineering Mathematics by Kreyszig (explains everything fundamentally but according to reviews it's is sometimes unclear)


Do you have any suggestions on how to approach this?

 

[GregLocock]

Of the various mathematical notebook type applications I recommend you also consider MathCad (sadly not a patch on the older versions) or SMathStudio, which is a free and useful alternative with a similar language. The advantage of those two is that they are human readable and the notation resembles a handwritten analysis to a much greater extent than Mathematica. In comparison to these two Mathematica doesn't have a learning curve, it has a staircase with 10m tall steps. The first step is 20m tall.

You might consider Matlab or it's free and remarkably complete equivalent Octave, or even Python, in particular PyLab. They are programming languages, not ideally suited for pretty output, and debugging other people's Matlab code is um, nobody's favorite job. In practice I use all the above except Mathematica, and I wish that Mathcad had been around when I was at uni.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[rb1957]

"Taking the drudgery out with MapleSoft is a good idea." ... it may be a good idea for doing the calcs in practice, but isn't a good way to learn basic theory.

another day in paradise, or is paradise one day closer ?

 

[lilliput1]

Be careful of mathematical analysis which are often based on theoretical ideal situations - plane sections remain plane etc. Follow structural design codes to insure adequate safety factor is provided. Remember you could be liable for your structural design if it fails and cause property damage, injury or loss f life!

 

[jrs87]

lilliput1 27 Mar 18 04:37. Good point. It there a good source that explains what safety factor is? What separates safe from unsafe? For example, cars are considered safe if roof is strong. Where does that leave convertibles? Convertibles are not as safe as hardtops, but they are not banned either. Is absolute safety tempered by expected safety?

 

[MacGyverS2000]

quote jrs87]For example, cars are considered safe if roof is strong. Where does that leave convertibles? Convertibles are not as safe as hardtops, but they are not banned either.[/quote]
Convertibles have beefed-up A-pillars, as well as increased rigidity in the lower door frames. "Safe" is not the proper word to use here as both hardtops and convertibles are just as safe as the other when properly used (safety belts, child seats, etc.).

Dan - Owner

http://www.Hi-TecDesigns.com

 

[rb1957]

The OP isn't looking to replace code-based analysis with his own math ... he's looking to develop his foundation in math so he has a better understanding of the math involved in FEA and other math based analyses. "he" used in it's non-gender-specific sense.

another day in paradise, or is paradise one day closer ?

 

[enginesrus]

This all makes me wonder how many younger folks and maybe even older folks need or use math in any job description these
days, since there are some many computer programs that do all that work for you.

 

[rb1957]

sorry but that scares the cr@p out of me ... IMHO people need to understand the tools they use, that means lifting the figurative bonnet/hood and see how it ticks.

another day in paradise, or is paradise one day closer ?

 

[CWB1]

Not to be negative toward higher level math but IMHO its a bit over-hyped. As an undergrad both FEA and CFD classes were roughly half pen and paper math, half software based solving. I'm more than capable of solving complex problems mathematically if need be but honestly haven't had much need for Fourier and Laplace since college, and I'd wager I've done heavier analysis than most. JME but most engineers never use the math they know, and strangely enough advanced degrees require ever more math as if its the key to being a good engineer...its not.

 

[SwinnyGG]

I use Fourier quite a bit. Not everyone has the luxury of closing the books on graduation day.

I would assume that my experience is atypical of course.

 

[Nescius]

One perspective...and a little advocacy for the devil...

Of course, an "engineer" (whatever that term means) should have a strong mathematics foundation, strong relative to most occupations, at least.

However, math is a tool for us, nothing more. At some point, increased time spent on math is a distraction. Math is not unique in this way; anything can similarly become a distraction.

The nature of modern engineering doesn't fit a romantic notion. Did it ever? The overwhelming majority of us aren't PE's. We don't use higher-level math regularly. We'll switch jobs every few years, often not by choice. Most of us design and manufacture mundane, everyday stuff or unidentifiable pieces of much larger wholes.

Depressing, no?

Here's the good news: Designs are more sophisticated than ever. Engineers actually know more than ever. The breadth and depth of available tools, materials, and free knowledge is unprecedented. Possibilty is in abundance.

Not only is it not advantageous to know how every "thing" in your engineering life functions, I submit that it is impossible.

I gave up trying to be "pure" and know everything about everything some time ago. I think the true essence of being an engineer is attacking a problem with all available weapons, with no mental snags; use what you need and damn the rest. Sometimes that's higher-level math, sometimes it's not.

 

[SreeSiv]

Additional to Kreysig, I would also recommend 'Numerical Methods for Engineers'- By Steven C. Chapra/ Raymond P Canale

A lot of engineers reach your situation. Its better to get that basic understanding of mathematics (atleast a feel for the concepts), when you use tools like Abaqus. Will help you understand limitations of the results you get from FEA as well.

Agreed that coding a program is the best way to understand other FEA programs.
Here is example of such an effort.

https://www.ijraset.com/fileserve.php?FID=2770

 

[MacGyverS2000]

I'm more than capable of solving complex problems mathematically if need be but honestly haven't had much need for Fourier and Laplace since college, and I'd wager I've done heavier analysis than most.

I don't use it every day, but every time a signal processing project comes up, out come the Fourier/Laplace transforms.

Dan - Owner

http://www.Hi-TecDesigns.com