- #1
-Dragoon-
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Such as topics in topology, complex analysis, etc.?
Do engineering researchers often use advanced math as tools?
- Thread starter -Dragoon-
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In summary, the conversation discusses the use of topology and complex analysis in various fields of engineering and their practical applications. It is mentioned that topology is particularly useful in analyzing nonlinear dynamical systems, while complex analysis is important in areas such as aerodynamics and electrodynamics. Other mathematical topics such as set theory and number theory are not as commonly used in engineering, but areas like signal processing and control systems do require knowledge of advanced math, particularly Fourier analysis.
- #2
Topher925
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I've never used topology for anything. Complex analysis is rather important in many subjects. It used to be the most widely used method for analyzing airfoils.
- #3
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Topology finds a bit of use in any field concerning nonlinear dynamical systems. Working in phase space in these situations lends itself nicely to topological analysis in some cases.
Complex analysis is used at the very least a little bit in aerodynamics and electrodynamics or any field that uses potential theory.
There are also a whole heck of a lot of signals analysis techniques in use such as various Fourier analyses, wavelet decompositions, Hilbert transforms and the like.
Complex analysis is used at the very least a little bit in aerodynamics and electrodynamics or any field that uses potential theory.
There are also a whole heck of a lot of signals analysis techniques in use such as various Fourier analyses, wavelet decompositions, Hilbert transforms and the like.
- #4
AlephZero
Science Advisor
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It might be a coincidence that one of the guys we have working on superplastic forging technology has a PhD in topology. Or it might not be... 
- #5
-Dragoon-
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AlephZero said:It might be a coincidence that one of the guys we have working on superplastic forging technology has a PhD in topology. Or it might not be...
Very interesting. What area do you specialize in?
- #6
-Dragoon-
- 309
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I have yet to see applications of other topics in math to engineering such as set and number theory. Are they just not practical for applications in engineering? I have seen quite a few applications of these topics in computer science, though.
- #7
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They aren't that practical. There are niche areas where you will run across a little bit of that sort of stuff, but on the whole it isn't all that common, at least as far as I have experienced.
- #8
FeX32
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It's all field dependent. Advanced math is critical to engineering research.
- #9
OldEngr63
Gold Member
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I have made a good bit of use of vector and tensor analysis, curvature tensors, calculus of variations, and Fourier analysis, both finite and infinite.
- #10
-Dragoon-
- 309
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Thanks for all your input, very interesting to hear of applications of advanced math in engineering.
What I'm mostly interested in at the moment is signal processing and control systems. It seems applied math departments also do research in these topics of engineering, which I find to be odd. For someone interested in eventually doing research in these fields, which topic in mathematics would be best to get well acquainted with?
What I'm mostly interested in at the moment is signal processing and control systems. It seems applied math departments also do research in these topics of engineering, which I find to be odd. For someone interested in eventually doing research in these fields, which topic in mathematics would be best to get well acquainted with?
- #11
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Fourier analysis would be your number one target to start with. Then maybe things like statistics, proper orthogonal decomposition, Hilbert transforms, etc.
1. What type of advanced math do engineering researchers typically use?
Engineering researchers often use advanced math concepts such as calculus, linear algebra, differential equations, statistics, and probability theory to solve complex problems and analyze data in their research.
2. How do engineering researchers use advanced math in their research?
Engineering researchers use advanced math as tools to develop models, simulate real-world systems, and analyze data. They also use it to optimize designs, make predictions, and test hypotheses.
3. Can engineering researchers conduct their research without using advanced math?
While it is possible for engineering researchers to conduct their research without using advanced math, it is often necessary to use these tools to solve complex problems and draw meaningful conclusions from their data.
4. Do all engineering researchers have a strong background in advanced math?
No, not all engineering researchers have a strong background in advanced math. However, they are typically trained to use these tools in their research and may collaborate with mathematicians or statisticians for more complex analyses.
5. How does using advanced math benefit engineering research?
The use of advanced math in engineering research allows for more accurate predictions, efficient problem-solving, and a deeper understanding of complex systems. It also allows for the development of new technologies and innovations in engineering fields.
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