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?

 

[MacGyverS2000]

Why not continue to take classes during the evening/night hours? A single math course per semester will help you not only learn new material, but help you keep the old stuff fresh in your mind.

Unless the subject has a high level of interest for me, I have never found self-taught material to be nearly as effective as having someone teach it to me. But that's personal preference, and others certainly differ in learning abilities.

Dan - Owner

http://www.Hi-TecDesigns.com

 

[FSB1]

just learn in youtube and do exercises that you find online

in youtube you have the advantage of finding someone that explains as it pleases you and also as many times as you wish until you understand. And no fear or pressure of not being a quick learner

 

[handleman]

Khan Academy has courses for most of the subjects you mentioned.

 

[rb1957]

MIT's opencourseware also has a bunch of subjects ... if you're not intimated by "MIT".

Calculus is always good to Know, FEA is more matrix analysis.

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

 

[djhurayt]

What am I missing here?
A) you are still in school
B) you will soon graduate with one degree and going back to begin another degree

soooooooooooooo

Why not just drop back and take a couple of 200/300 level math classes either
a) in your current degree program
b) added to you next degree program class load
c) in between these two programs, aka summer school

after all (and I'm not judging), you do sounds as if your are possibly a career student.

 

[TheTick]

Do what the autodidacts do.

 

[Jboggs]

I've been a practicing machine design engineer for over 40 years. I have designed huge 12-axis robotic systems, highly automated manufacturing systems, very high speed mechanical components, systems for use in and around molten metal, heavy-duty structural support platforms for human occupancy and storage, and a lot more. I don't need one hand to count the number of times I have had to resort to higher level mathematics or even just calculus. In fact, I don't even need one finger to do it. My experience is that by the time you get to building real stuff in most places in the real world, the value of the accuracy and precision that calculus or other higher methods might have contributed to your final design will probably vanish to insignificance.

If my job had been to analyze some unexplored region of the laws of nature in a lab environment and create some formulas or tables for use by others, then I can see how those tools would be indispensable. But usually an engineer is not a scientist, and paying customers are not impressed by mathematical elegance. They want a machine that works, and continues to work despite unexpected abuse, in their world and doesn't cost them an arm and a leg.

Hey, if you want to pursue that stuff and learn everything there is to know about it, go for it. God knows we need smart people! I'm just saying that engineering professors may have a tendency to over-estimate the importance of that stuff in the real world. At least in my experience. Just sayin...

 

[rb1957]

yes, but the OP talked about getting involved in FEA so learning the bedrock is good.

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

 

[SwinnyGG]

You obtained a BS degree in an engineering field and only took a single calculus course???

 

[MacGyverS2000]

Jboggs,

I don't necessarily disagree with your assertion that "by the time you get to building real stuff in most places in the real world, the value of the accuracy and precision that calculus or other higher methods might have contributed to your final design will probably vanish to insignificance". There's no doubt the vast majority of my math (or pick any other random subject) has gone unused (to the point of being forgotten).

However, I think future needs also come into play here, and those are tough to plan for. Had I not continued to learn new math (and at least attempt to keep what I had learned previously somewhat fresh in my mind), I would not have been able to take on several challenges that came across my path later on. Without some chaos theory and wavelet background, I might never have worked on embedded JPEG2000 image/video codecs or fingerprint compression algorithms (that was some slick stuff). Without some differential equations and Kalman filtering, I may never have been able to handle the backup flight controller design (challenging!).

It never hurts to learn, because you simply never know...

Dan - Owner

http://www.Hi-TecDesigns.com

 

[GregLocock]

Some of us do actually use Fourier and differentials in our day jobs. Kreyzsig is pretty good in my opinion. It's not really advanced. My /copies/ are annotated and broken backed.

I've got a bit of a terminology problem

- linear algebra -what do you mean by this?
- vector calculus - how advanced? Div grad curl? I never found a good textbook on that.
- differential equations (focus on ordinary differential equations primarily) - how advanced?
- fourier analysis - can't really help you there, it is (and always was) so intuitive to me that i just read up on some new detail and implement it.

having said that I agree Khan is a great place to start, I should take that advice and look at the vector calculus stuff, I feel embarrassed that I winged it at uni.

Cheers

Greg Locock


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

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[rb1957]

linear algebra = simultaneous equations = matrix methods

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

 

[isok89]

Thank you for the kind feedback. I think I'm going to take the following approach:

The book advanced engineering mathematics as a basis and every topic I don't understand
I will look up elsewhere (like youtube).

To give you some more background; I have been working for almost 2 years as a graduate seismic structural engineer
and doing my MSc part-time. However I have the idea that I will get bored with the regular codes and stuff.
These days I do a lot of FEA stuff in Abaqus but I can't stand it that I don't know what happens under the hood of these programs.

I want to specialise in structural dynamics and really understand it analytically. Some day I hope to write my own fea program in
Python for example.

 

[MacGyverS2000]

It's funny... I find linear algebra (matrices) to be very easy to work with... and somehow it's the first thing I forget. Every time I need to work with a matrix I need to go back to the books and figure out how to break it down for a particular format.

Dan - Owner

http://www.Hi-TecDesigns.com

 

[rb1957]

if you're returning (continuing) with university you should have lots of help available (better than youtube).

there should also be like minded students around ... interested in getting a solid grasp of the bedrock knowledge.
there should be many profs/TAs interested in teaching interested students.

good luck !

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

 

[3DDave]

There are online university courses on how FEA works. I think MIT has posted the class videos.

https://ocw.mit.edu/resources/res-2...for-solids-and-structures-spring-2010/linear/

 

[PNachtwey]

Get a CAS. Computer Algebra System like Mathematic or Maple. They take the drudgery out of doing the math. You can focus more on solving problems.
Learn how to numerical analysis. ODEs acan be interated by computer easily.

Ditto the suggestions about learning on-line. Khan Academy didn't go very deep the last time I looked.


Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

 

[jrs87]

Taking the drudgery out with MapleSoft is a good idea. I have seen some youtube videos that espouse mathematics is not real. 12 years of college for nothing.

 

[Ron]

How did you get an engineering degree with only a single calculus course?