What Additional Math Skills Are Essential for Studying Undergrad Optics?

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Discussion Overview

The discussion centers on the mathematical skills necessary for studying undergraduate optics, particularly in relation to the topics outlined in a course description. Participants explore the adequacy of calculus and vector calculus, as well as the potential need for additional mathematical concepts such as linear algebra and electromagnetic theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses skepticism about the sufficiency of the math prerequisites listed for the optics course, suggesting that linear algebra may be necessary.
  • Another participant mentions the importance of Bessel functions in diffraction and suggests that some knowledge of electromagnetic theory could be beneficial.
  • A recommendation for basic linear algebra, particularly matrix multiplication, is made as an additional requirement for studying optics.
  • It is noted that knowledge of Fourier series and transforms, as well as surface integrals in polar coordinates, may be important for non-geometric optics topics.
  • For geometric optics, a solid understanding of the sine theorem and basic trigonometry is deemed sufficient by one participant.
  • Hecht's "Optics" is recommended as a standard undergraduate textbook, with some uncertainty expressed regarding its coverage of lasers.
  • A question is raised about whether introductory or advanced electromagnetic theory is more appropriate to take before studying optics.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of additional mathematical skills beyond those listed in the course description. There is no consensus on whether linear algebra or advanced electromagnetic theory is essential, indicating ongoing debate regarding the prerequisites for studying optics.

Contextual Notes

Some participants highlight the potential limitations of the course's math prerequisites, suggesting that the requirements may not fully encompass the mathematical tools needed for a comprehensive understanding of optics.

torquemada
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My physics dept offers an optics class with the following descriptive summary:

Geometric optics, periodic and non-periodic waves; Doppler effect; interference and diffraction, diffraction gratings; theory of polarization of light; fiber optics and introduction to lasersIt says the math you need is just calc sequence through multivariable calc, and only part of vector calc, not all of it.

My physics program doesn't require a linear algebra course, so i don't trust them. is there any other math i should know of that i'll need for undergrad optics, given the topics listed above? thanks

also does anyone know of a good undergrad optics text? thanks
 
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You'll probably fall over Bessel function in diffraction. Some electromagnetic theory might also help. I think you should do fine with the math you listed.
A very good undergraduate textbook for Optics: Hecht's "Optics". I think it covers all what you listed (small doubt about lasers but I'm 96.7% sure it covers it a bit at least).
 
I recommend some basic linear algebra, especially matrix multiplication, in addition to the listed mathematical prerequisites. Then you should be set. :)
 
fluidistic said:
You'll probably fall over Bessel function in diffraction. Some electromagnetic theory might also help. I think you should do fine with the math you listed.
A very good undergraduate textbook for Optics: Hecht's "Optics". I think it covers all what you listed (small doubt about lasers but I'm 96.7% sure it covers it a bit at least).

Thanks to you and all who replied. Do you mean though intro E&M or is it better to take advanced E&M before optics?
 
You'll need to know how to multiply matrices for polarization problems, Fourier series and transforms, basic surface integral in polar coordinates, and some idea of Bessel functions for all the non-geometric optics. For geometric optics a solid command of the sine theorem, basic trig etc. is sufficient. You should know all the basics of EM theory and EM waves though, that will help.

Hecht seems to be the standard, but I'd go with whatever your professor basis his notes off of.
 

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