Question
What are prerequisites for a good understanding of a course in aerodynamics?
Answer
There is a macro-level subject that is unique to aerospace engineering which is usually called "aerodynamics" or "flight dynamics" and there is a more general micro-level one called "fluid and gas dynamics" that is shared with mechanical engineering and other engineering fields (it's basically a kind of applied Newtonian physics).
To understand basic aerodynamics at the macro level (lift, drag, thrust, angle of attack, yaw/pitch/roll dynamics) you need intermediate mechanics and enough linear algebra so you can handle matrix transforms between coordinate systems. If you are sneaky about it, you can even get away without doing any calculus I'd say.
To understand the micro stuff, you need (in addition to the above), advanced calculus, basic partial differential equations and some prior exposure to numerical computation. This is the subject that deals with computing things like the lift and drag of a wing section via first principles, shock waves in air intakes of jet engines, subsonic and supersonic flow dynamics, things like compressor stall, aeroelastic coupling and flutter, vortex shedding...
It is mainly an experimental/computational subject at an advanced level because the core equations, the Navier-Stokes equations are not solvable or even very well understood at the structural level (i.e., necessary/sufficient conditions). The N-S equations are among the Millenium Prize problems in mathematics, so that gives you an idea of how tough they are:
http://www.claymath.org/millenni...
To be a pilot, you need a fairly good understanding of the first kind, and a limited understanding of the second kind where it impacts actual flying decisions (for example, experienced pilots know under what conditions flutter or vortex shedding can occur and when it is dangerous).
To do aerospace engineering, you need a good understanding of both. At the more advanced levels, you will also need significant understanding of propulsion, structural mechanics and control theory. Aerospace engineering tends to be a highly integrated field because it is so focused on two specific classes of relatively distinct engineering objects (airplanes/rockets on the one hand, spacecraft on the other). Other engineering fields are less integrated because they are much broader in application.
To understand basic aerodynamics at the macro level (lift, drag, thrust, angle of attack, yaw/pitch/roll dynamics) you need intermediate mechanics and enough linear algebra so you can handle matrix transforms between coordinate systems. If you are sneaky about it, you can even get away without doing any calculus I'd say.
To understand the micro stuff, you need (in addition to the above), advanced calculus, basic partial differential equations and some prior exposure to numerical computation. This is the subject that deals with computing things like the lift and drag of a wing section via first principles, shock waves in air intakes of jet engines, subsonic and supersonic flow dynamics, things like compressor stall, aeroelastic coupling and flutter, vortex shedding...
It is mainly an experimental/computational subject at an advanced level because the core equations, the Navier-Stokes equations are not solvable or even very well understood at the structural level (i.e., necessary/sufficient conditions). The N-S equations are among the Millenium Prize problems in mathematics, so that gives you an idea of how tough they are:
http://www.claymath.org/millenni...
To be a pilot, you need a fairly good understanding of the first kind, and a limited understanding of the second kind where it impacts actual flying decisions (for example, experienced pilots know under what conditions flutter or vortex shedding can occur and when it is dangerous).
To do aerospace engineering, you need a good understanding of both. At the more advanced levels, you will also need significant understanding of propulsion, structural mechanics and control theory. Aerospace engineering tends to be a highly integrated field because it is so focused on two specific classes of relatively distinct engineering objects (airplanes/rockets on the one hand, spacecraft on the other). Other engineering fields are less integrated because they are much broader in application.