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I'm learning differential equations and waves - following online courses and reading some textbooks - and I find that quite often, the use of Phasors, equations combining sinusoidal waves of different amplitudes and frequencies (the derivation of beats)...etc...they're explained really briefly, without a lot of diving deeper into them, and then applied.

Is there a specific "math" which I could study, or textbook I could read, that presents these subjects more explicitly? The more geometric and intuitive the math book is, the better! I tried looking for "wave mathematics" but...found mostly really advanced books. Complex Analysis didn't seem to fit either.

All and any recommendations are welcome.

Edit:

Books on the differential equations of waves are helpful...but, that's not really what I meant. What I really want is something that starts simpler.

What led me to asking this question is that it took me a long time to understand the geometric intuition for how to combine waves of the same amplitude but different frequencies (for which this - https://www.jstor.org/stable/27965328?seq=1 - helped quite a bit) and I still don't understand at all how to combine them if they have different amplitudes!

Is there not anything simpler than a differential equations approach, or perhaps a book that DOES go into the differential equations, but also does so explaining each step, instead of skipping over the "basic" math of waves?

Thanks again.

joshuaronis
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2 Answers2

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Berkeley Physics Course vol. 3 is all about waves: https://www.amazon.com/Waves-Berkeley-Physics-Course-Vol/dp/0070048606

I personally prefer the chapters reviewing waves in the book Optics, from E. Hecht: https://www.amazon.com/Optics-5th-Eugene-Hecht/dp/0133977226

Good luck with your studies! :)

Karl Pilkington
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I found this to a more in-depth mathematical look into the physics of waves: https://www.people.fas.harvard.edu/~hgeorgi/onenew.pdf It covers a lot of the topics covered in Ph 12a.

Also, complex analysis is the analysis/calculus of complex-valued functions. It is slightly different than the study of complex numbers required for waves such as complex exponentials, Euler's formula etc.

mihirb
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