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Next year I'm planning to start on my bachelor's in physics, however, I have already started taking some undergraduate courses in mathematics and next semester I will have to choose between complex analysis and differential equations - I will take the other course at some other time, but that will at least be a year away.

I know both subjects are important in physics, but my question is which subject will have the largest impact when I start on my bachelor's degree.

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closed as primarily opinion-based by Emilio Pisanty, Qmechanic Oct 22 '18 at 23:47

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ I'm voting to close this question as off-topic because it is about career advice. $\endgroup$ – Emilio Pisanty Oct 22 '18 at 20:55
  • $\begingroup$ In the standard beginner undergrad sequence complex analysis will essentially never be used. It may come up a couple times a year when they give you the value of an integral and say "by the way, you can prove this with complex analysis". $\endgroup$ – knzhou Oct 22 '18 at 21:07
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Complex analysis is unlikely to be of any use at all in undergraduate physics classes. Differential equations are used constantly. All of physics is expressed in terms of differential equations, such as Maxwell's equations and the Schrodinger equation.

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As an undergraduate, having a decent understanding of complex numbers, rather than complex analysis, goes far. Complex analysis - complex functions and integrals of complex functions in the complex plane and power series of complex functions and the multiple of theorems, etc... - is not very useful in an undergraduate curriculum, unless it is an advanced undergrad curriculum.

However, what's more useful for an undergrad is a good understanding of the complex plane and how to use it to make problems easier. The main application is in quantum mechanics, where we are dealing with complex numbers and functions ubiquitously. Most of the relevant information necessary for introductory quantum mechanics regarding complex numbers is usually covered by an intro. text book, and I strongly recommend David McynTyre's book, and/or Griffith's book. For more mathematical treatments of complex numbers, see this post.

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