Waves: Books on Math & Physics for Real Analysis, Complex Analysis, etc.

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In summary, "Waves: Books on Math & Physics for Real Analysis, Complex Analysis, etc." is a collection of books that explore the fundamentals of mathematics and physics, specifically focusing on topics such as real analysis and complex analysis. These books provide readers with a comprehensive understanding of these advanced mathematical concepts and their applications in the fields of physics and engineering. They are a valuable resource for anyone looking to deepen their knowledge and skills in these subjects.
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dRic2
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Hi, I'm looking for a book that deals with the mathematics and the physics of waves (sound waves, electromagnetic waves, maybe optics). Basically just "classical waves" (I'm not very interested right know in the applications to quantum mechanics). My math background is (courses that I took):
real analysis
(introduction to) complex analysis
linear algebra
PDE (never had a formal course but I'm quite good in solving standard PDE with "decent" boundary conditions)
(introduction to) functional analysis
I'm looking for a book that deals with the basics but also offers insight on the matter. I prefer an "intuitive"/physical approach, but I don't dislike mathematical rigor.

Do you have any suggestions ?
 
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I really enjoyed the Young text in my undergrad.

https://www.amazon.com/dp/0070725217/?tag=pfamazon01-20

242227
 
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  • #3
Okay, that's weird. Definitely buy the $5.29 hardcover. Buying the $678.08 Paperback would appear to be a bad shopping decision...

WTH?
 
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  • #4
berkeman said:
Okay, that's weird. Definitely buy the $5.29 hardcover. Buying the $678.08 Paperback would appear to be a bad shopping decision...

WTH?
Such a huge price difference! A new hard cover book is $87.14 << paperback. Why is the latter so costly?
 
  • #5
Most likely just typos. LOL
 
  • #6
Waves, Berkeley Series Vol III by Crawford I used as a sophomore
There is a book Waves Physics by Stephen Nettle that may also be good but I think this is more deep.
I think the honors class as Sophomores may have used this one, but I think it is higher level.
 
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  • #7
mpresic3 said:
aves Physics by Stephen Nettle
I can't find this book...
 
  • #8
What do you think about "Almost all about waves" by J.R. Pierce?
 
  • #9
dRic2 said:
I can't find this book...
It was a typo, he meant: S. Nettel, Wave Physics
 
  • #10
Thanks!
 
  • #11
Demystifier said:
It was a typo, he meant: S. Nettel, Wave Physics
Sorry, Dr Nettel. I worked for Dr Nettel in 1980. Hard to believe I would ever spell his name wrong!
 
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Introduction to Wave Physics is a free textbook based on a standard, intermediate-level physics course on waves. It covers both scalar (acoustic) and vector (electromagnetic) waves up to three-dimensions in rectangular, cylindrical and spherical coordinates. It also addresses advanced topics including radiation, diffraction and scattering. It can be downloaded from https://www.researchgate.net/publication/349721510_Introduction_to_Wave_Physics or the book website . (Hard copies are also available on Amazon).

(The poster and author is Anthony Gerig, a physics professor at Viterbo University.)
 
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  • #13
mpresic3 said:
Waves, Berkeley Series Vol III by Crawford
I used this one too in undergrad. I really don't know how it compares to others listed.

Just looked on Ama$on, wow, over 40 USD used. I bought my copy new (still see $7.95 on the inside cover). It came with a little packet of colored gels and diffraction gratings.
 
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  • #14
How much physics have you learned? If you have only taken introductory level physics then I would recommend looking at:

The Physics of Waves by Georgi. The author has a free pdf posted at his site
https://sites.harvard.edu/hgeorgi/physics-of-wave-files/
Like a lot of general 'physics of waves' book it is written for students with less math background than you have. It assumes you have taken sequences in calculus and introductory physics.

For an intuitive introduction to electromagnetic waves I really like Bekefi and Barrett
https://www.amazon.com/dp/0262520478/?tag=pfamazon01-20
While it looks like it was typeset with an old typewriter, it really is a fantastic read.

If you know more physics, such as intermediate mechanics and/or electromagnetic theory, then there are other options. One general undergraduate-level book is Physics of Waves by Elmore and Heald
https://www.amazon.com/dp/0486649261/?tag=pfamazon01-20
In the preface the authors indicated it was written for students who had taken intermediate mechanics. It includes waves in elastic media and fluids, as well as electromagnetic waves. They do a pretty good job describing the physics and deriving wave equations for the different phenomena, and they introduce the concept of wave impedance which I find to be very helpful.

jason
 
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Related to Waves: Books on Math & Physics for Real Analysis, Complex Analysis, etc.

1. What is the difference between real analysis and complex analysis?

Real analysis is the study of functions of real numbers, while complex analysis is the study of functions of complex numbers. Complex analysis is an extension of real analysis, as complex numbers include both real and imaginary components.

2. How do waves relate to math and physics?

Waves are a fundamental concept in both math and physics. In math, waves are described by mathematical functions and are used to model various physical phenomena. In physics, waves are a form of energy transfer and are used to describe a wide range of natural phenomena, from sound and light to electromagnetic radiation and quantum mechanics.

3. What are some practical applications of real and complex analysis?

Real and complex analysis have numerous practical applications in fields such as engineering, physics, economics, and computer science. They are used to model and understand complex systems, make predictions, and solve problems in various industries.

4. How are real and complex analysis related to each other?

Real and complex analysis are closely related, as complex analysis is built upon the foundations of real analysis. Many concepts and techniques in real analysis, such as limits, derivatives, and integrals, have analogues in complex analysis. However, complex analysis also introduces new concepts, such as analytic functions and contour integrals, that are not present in real analysis.

5. What are some recommended books for learning about real and complex analysis?

Some popular books on real and complex analysis include "Principles of Mathematical Analysis" by Walter Rudin, "Complex Analysis" by Lars Ahlfors, and "Real and Complex Analysis" by Walter Rudin. Other resources, such as online courses and lecture notes, are also available for those interested in learning about these topics.

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