Mathematics necessary for Radiometry, Photometry, Thermodynamics

[rdgn]

What are the math concepts I have to learn for Radiometry, Photometry and Thermodynamics (all Calculus-based) as applied in building science (engineering, architecture, etc.).

I'm almost done with Multivariable Calculus and I'm aware that MV Calculus is necessary, but what specific calculus topics? (I'm already done with line integrals, double, triple, surface, haven't done flux yet).
Is a study of differential equations necessary?
Do I need to study some math beyond Calc III?
Would polar/spherical/cylindrical coordinates systems be necessary? (Almost all the math I've done was in cartesian coordinates so I barely remember other coordinate systems).

I've been skimming through some sources to get an idea of what I'll be seeing and there are still some symbols that I'm not sure what they mean, e.g.
\frac{1}{\pi R^2}\int_{S_{v}}^{ }cos\phi dS

Looks like a line integral but I'm not sure If this is in cartesian or polar, etc. coordinates, and I don't know what the fraction means. I also encounter that fraction 1 over something quite a lot so I'm sure there's a concept behind it that I don't know of. Thanks!

 

[Mark44]

What are the math concepts I have to learn for Radiometry, Photometry and Thermodynamics (all Calculus-based) as applied in building science (engineering, architecture, etc.).

I'm almost done with Multivariable Calculus and I'm aware that MV Calculus is necessary, but what specific calculus topics? (I'm already done with line integrals, double, triple, surface, haven't done flux yet).
Is a study of differential equations necessary?
Do I need to study some math beyond Calc III?

Relative to the building sciences disciplines you mentioned, I would guess that study beyond the calculus topics you listed isn't necessary. However, for thermodynamics at anything beyond an introductory level, differential equations would be used, including partial differential equations (PDE).

Would polar/spherical/cylindrical coordinates systems be necessary? (Almost all the math I've done was in cartesian coordinates so I barely remember other coordinate systems).

I've been skimming through some sources to get an idea of what I'll be seeing and there are still some symbols that I'm not sure what they mean, e.g.
\frac{1}{\pi R^2}\int_{S_{v}}^{ }cos\phi dS

Without knowing the context, I can't say, other than to guess this is a surface integral, where dS represents an infitesimal area element

Looks like a line integral but I'm not sure If this is in cartesian or polar, etc. coordinates,

Because of the $\cos(\phi)$ integrand, it appears to me to be in spherical coordinates, but that wouldn't necessarily be the case.

and I don't know what the fraction means.

It's the reciprocal of the area of a circle of radius R.

I also encounter that fraction 1 over something quite a lot so I'm sure there's a concept behind it that I don't know of.

 

[rdgn]

Thanks!

Just a follow-up. I remember now where I encountered integrals where there was 1/something before the integral. It was when I was reading things about Cauchy: https://en.wikipedia.org/wiki/Cauchy's_integral_formula.

Although I'm quite sure I won't be studying complex analysis, I was wondering if the reciprocal 1/pi*r^2 has anything to do with Cauchy's complex analysis, or any prerequisite calculus topics. (here's the context of the formula btw, which I don't understand because apparently it requires an understanding of flux: http://www.grasshopper3d.com/group/ladybug/forum/topics/discussion-sky-view-factor).

I also forgot to add Fluid Mechanics to my question.
I assume PDEs are as far as I need to learn for Fluid Mechanics?