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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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    I disagree that complex analysis doesn't fit. Complex numbers are the language of waves and a good understanding of even the simple harmonic oscillator requires complex numbers to be appreciated and used in its most efficient form. On the topic of material for waves, if you are comfortable already with complex number and linear algebra, then the lectures notes for this class [http://www.its.caltech.edu/~xcchen/courses/physics12a.html] are excellent. The assignments can be a bit annoying are for the most part very good. – SescoMath Jul 21 '20 at 02:55
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    @PhysMath I'm taking that class next fall – joshuaronis Jul 21 '20 at 03:42

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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  • Thanks mihir. Yep, I know now that about complex analysis...I edited my question a bit to explain better what I'm looking for. I'll take a look at those notes! – joshuaronis Jul 21 '20 at 15:38