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I just (barely) passed what is known as my university's hardest first year physics course: electricity and magnetism. We didn't use differential equations, but

I just (barely) passed what is known as my university's hardest first year physics course: electricity and magnetism. We didn't use differential equations, but we had the same hand wave "just think about it" relationship with line integrals. The way my professor explained it was "we're engineers, not mathematicians, so we actually know what we're talking about". What he meant by this is that as engineers, we need to have intuition as to what an integral actually is rather than knowing how to prove things with them. To an extent, this is a good way to go about it. Really it's not at all useful to understand things like delta-epsilon as an engineer because those concepts really have no application. It's much more useful to just gain an intuition as to what you're actually doing when you're taking a line integral, and applying that to, for example, calculating an electric field strength as a result of an object. Physics teaches physics, not math.

selimthegrim 4y ago
Did this professor think conservative fields and independence of path were for schmucks too?
WalterBright 4y ago
My engineering and physics intuition came from understanding the math behind it. For example, I've seen a lot of handwavy explanations of how jet engines worked, but understanding eluded me until I went through the math in jet engine class.
- nobodyandproud 4y ago
  Different strokes for different folks. Michael Faraday was brilliant and driven, but his intuition did not come from understanding the math as he was famously math-illiterate. On a personal note, the subject I had the most trouble with was classic electromagnetism (calc-based freshman physics): It was the first time I hit a wall/limit on what I could grasp. The wall was because I could never couldn’t develop an intuition for the physics behind it.
  - dannymi 4y ago
    >The wall was because I could never couldn’t develop an intuition for the physics behind it. On the off chance that you can understand German, check out chapter 9.1.1 Fluidvolumen und Divergenz (until and including chapter 11 Erhaltung der Energie), in the book Einführung Theoretische Meteorologie by Michael Hantel (ISBN 978-3-8274-3055-7). It even uses a car analogy ;) You will understand fluid dynamics, and by extension electrodynamics, like you never did before. And it will teach you the physical intuition first. This book was such a lucky find for me ten years ago. Equation (11.3) is the fluid analogon to the continuity equation (in electrodynamics that is: ∂/∂t ρ + ∇⃗⋅J⃗ = 0)--and you can see how, physically, you get to it, and what the parts and the whole mean. Lots of diagrams and geometry and simple analogies make that take about 30 pages.
- deleted 4y ago
  [deleted]
- tekla 4y ago
  Can you elaborate? Im and Aero and while there is a defo a bunch of math involved suck, squeeze, bang, blow is pretty much the gist of how jet engines work and I don't find it really all that hand-wavy, its just a funny way of describing gas pressure and velocity graphs.
  - WalterBright 4y ago
    The hand-wavy explanations never explained why the exhaust went out the back rather than the front and the back.
    - melony 4y ago
      Do elaborate. The most funky differential I know comes from EE's Maxwell eqns (how capacitors work, and weird ideas about "ground").
      - WalterBright 4y ago
        The compressor up front produces enough pressure to prevent the exhaust going out that way. Another way to see it is you cannot start a turbine by dumping fuel in and igniting it. The turbine has to be spun up first, usually with an electric motor. The Me262 engines had an ingenious tiny gas engine in the nacelle which served that purpose, complete with a little handle to start it! Next time you're on a jet, watch them do the engine start. You can see it slowly gaining speed, then suddenly it dramatically speeds up - that's when the fuel gets squirted in and ignited. Anyhow, jet engines look deceptively simple. But they are real masterpieces of engineering.
colordrops 4y ago
I think you are just reiterating what the person I was replying to said. Makes sense, what I was saying is that it should be explained that there are differences with pure mathematics and that it's meant to be a pragmatic tool, and maybe even some of the reasoning as to why the differences are the way they are.

selimthegrim 4y ago

Did this professor think conservative fields and independence of path were for schmucks too?

WalterBright 4y ago

My engineering and physics intuition came from understanding the math behind it. For example, I've seen a lot of handwavy explanations of how jet engines worked, but understanding eluded me until I went through the math in jet engine class.

nobodyandproud 4y ago
Different strokes for different folks. Michael Faraday was brilliant and driven, but his intuition did not come from understanding the math as he was famously math-illiterate. On a personal note, the subject I had the most trouble with was classic electromagnetism (calc-based freshman physics): It was the first time I hit a wall/limit on what I could grasp. The wall was because I could never couldn’t develop an intuition for the physics behind it.
- dannymi 4y ago
  >The wall was because I could never couldn’t develop an intuition for the physics behind it. On the off chance that you can understand German, check out chapter 9.1.1 Fluidvolumen und Divergenz (until and including chapter 11 Erhaltung der Energie), in the book Einführung Theoretische Meteorologie by Michael Hantel (ISBN 978-3-8274-3055-7). It even uses a car analogy ;) You will understand fluid dynamics, and by extension electrodynamics, like you never did before. And it will teach you the physical intuition first. This book was such a lucky find for me ten years ago. Equation (11.3) is the fluid analogon to the continuity equation (in electrodynamics that is: ∂/∂t ρ + ∇⃗⋅J⃗ = 0)--and you can see how, physically, you get to it, and what the parts and the whole mean. Lots of diagrams and geometry and simple analogies make that take about 30 pages.
deleted 4y ago
[deleted]
tekla 4y ago
Can you elaborate? Im and Aero and while there is a defo a bunch of math involved suck, squeeze, bang, blow is pretty much the gist of how jet engines work and I don't find it really all that hand-wavy, its just a funny way of describing gas pressure and velocity graphs.
- WalterBright 4y ago
  The hand-wavy explanations never explained why the exhaust went out the back rather than the front and the back.
  - melony 4y ago
    Do elaborate. The most funky differential I know comes from EE's Maxwell eqns (how capacitors work, and weird ideas about "ground").
    - WalterBright 4y ago
      The compressor up front produces enough pressure to prevent the exhaust going out that way. Another way to see it is you cannot start a turbine by dumping fuel in and igniting it. The turbine has to be spun up first, usually with an electric motor. The Me262 engines had an ingenious tiny gas engine in the nacelle which served that purpose, complete with a little handle to start it! Next time you're on a jet, watch them do the engine start. You can see it slowly gaining speed, then suddenly it dramatically speeds up - that's when the fuel gets squirted in and ignited. Anyhow, jet engines look deceptively simple. But they are real masterpieces of engineering.

colordrops 4y ago

I think you are just reiterating what the person I was replying to said. Makes sense, what I was saying is that it should be explained that there are differences with pure mathematics and that it's meant to be a pragmatic tool, and maybe even some of the reasoning as to why the differences are the way they are.