- #1
-Dragoon-
- 308
- 7
Such as topics in topology, complex analysis, etc.?
Do engineering researchers often use advanced math as tools?
- Thread starter -Dragoon-
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Discussion Overview
The discussion explores the use of advanced mathematics in engineering research, specifically examining topics such as topology, complex analysis, and various signal analysis techniques. Participants share their experiences and perspectives on the relevance and application of these mathematical concepts in different engineering fields.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants mention the use of topology and complex analysis in engineering, particularly in aerodynamics and nonlinear dynamical systems.
- Others argue that while complex analysis is important, topology has limited applications in engineering, with some participants stating they have never used it.
- One participant highlights the use of various signal analysis techniques, including Fourier analyses and wavelet decompositions, in engineering contexts.
- There is a suggestion that advanced mathematics is critical to engineering research, though its applicability may vary by field.
- Some participants express skepticism about the practical applications of other mathematical topics, such as set and number theory, in engineering.
- A participant shares their extensive use of vector and tensor analysis, curvature tensors, and calculus of variations in their engineering work.
- In response to a question about which mathematical topics to focus on for signal processing and control systems, Fourier analysis is recommended as a primary area of study.
Areas of Agreement / Disagreement
Participants express a mix of opinions regarding the relevance of advanced mathematics in engineering, with some asserting its critical importance while others note its limited practical application in certain areas. No consensus is reached on the overall utility of specific mathematical topics.
Contextual Notes
The discussion reflects varying experiences and perspectives on the applicability of different mathematical concepts in engineering, highlighting the field-dependent nature of these applications.
- #2
Topher925
- 1,563
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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
- 3,482
- 1,293
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
Homework Helper
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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-
- 308
- 7
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-
- 308
- 7
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
- 3,482
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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
- 67
- 0
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-
- 308
- 7
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
- 3,482
- 1,293
Fourier analysis would be your number one target to start with. Then maybe things like statistics, proper orthogonal decomposition, Hilbert transforms, etc.
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