Mathematics involved in Aerodynamics

[woleka]

I'm just beginning to study aerodynamics, and i was wondering if anyone could list the topics, fields, and types of math that are used in textbooks, research papers, journals etc. that one would read when studying aerodynamics?

 

[FredGarvin]

In regards to math, you can see the whole spectrum of math subjects:
- Algebra
- Calculus
- Differential Equations
- Partial Differential Equations
- Vector Calculus

Research papers are kind of fun in a way. They are usually extremely dry and boring, but the topics are so varied and widespread. I often find myself wondering "how the heck did they come up with that topic?"

 

[woleka]

So i will never come across:
topology, number theory, abstract algebra, group theory, order theory, topology, fractals, chaos, logic, set theory, category theory, graph theory, combinatronics or any others beyond the above mention?
Also, specifically what type of algebra?

 

[FredGarvin]

Never is a dangerous word to use. Chaos theory is a stretch. I can't think of any papers or topics off the top of my head that would deal with aerospace and chaos theory. I know there is a decent amount of interest in it in control systems and the like. Topology may be run across. I wasn't quite thinking about that level of detail in response to your question.

You may run into those fields. Who knows? The area of aerospace is so broad. If you are looking for those things, I would think you need to push for research positions.

 

[NateTG]

So i will never come across:
topology, number theory, abstract algebra, group theory, order theory, topology, fractals, chaos, logic, set theory, category theory, graph theory, combinatronics or any others beyond the above mention?

The bulk of physics-associated math, including fluid dynamics, is primarily covered by various 'linear' and 'differential' topics - linear algebra, differential equations, differential geometry, and so on. Chaos and fractals are both strongly associated with differential equations, and do show up in physics and fluid dynamics.

Probability and statistics are important for testing and experimenting, but the rest of the pure mathematics suite - logic, set theory, abstract algebra, graph theory, point set topology and so on tend to find fewer physics applications beyond the fundamental connections to the more directly applicable topics.

 

[D H]

So i will never come across:
topology, number theory, abstract algebra, group theory, order theory, topology, fractals, chaos, logic, set theory, category theory, graph theory, combinatronics or any others beyond the above mention?
Also, specifically what type of algebra?

Fred gave a list of mathematical topics with which he has some familiarity. He did not say hist list was exhaustive.

Abstract algebra. I have a massive tensor-induced headache right now. Many aerospace engineers use quaternions on a daily basis.

Topology, logic, set theory, graph theory, combinatorics. Building and operating flying vehicles is fraught with hazards. The systems we build have to be extremely reliable. The science/engineering behind building reliable systems and proving that the systems are reliable involve all of these fields of math.

 

[Sojourner01]

It's possible that you might use some elements of chaos theory in turbulent flow - over airfoils and such like, but chaos is a fairly immature field and as far as I'm aware specific and useful applications to aerospace aren't widespread yet.

 

[woleka]

Thanks a lot, that was very helpful