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How would I go about self learning real/Complex analysis and PDE’s. Which topics are prerequisites? Any book recommendations?

I know basic linear algebra (matrices, vectors, vector calculus which is part of calculus), good calculus, and decent multi variable calculus (multi variable integrals and calculus, directional derivatives, optimisation).

What other topics do I need to learn for real/Complex analysis and PDE’s? And what are some good books for those topics+Analysis+PDE’s?

Simplex1
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  • Related discussion here and here. – Pedro Feb 08 '19 at 09:37
  • How theoretical and/or hardcore do you wish to go? On a scale from light, late-night reading to Rudin? In all seriousness I have a number of recommendations, but it depends heavily on how invested you are and what your goals are – Brevan Ellefsen Feb 14 '19 at 01:03
  • @BrevanEllefsen I don't wish to go too hardcore. Probably 6-7/10 in theoretical/hardcore. My goals are to have PDE's and real/complex analysis knowledge so I can move on to Stochastic calculus (which I understand requires probability/stats and stochastic processes, and perhaps linear algebra). I know that complex analysis isn't necessary, however, I wish to learn signal processing. – Simplex1 Feb 14 '19 at 06:14
  • @Simplex1 got it. OK, cheap textbooks I've enjoyed that take a nice mix of application and theory: for complex analysis, "Fundamentals of Complex Analysis with Applications to Physics and Engineering" by Saff and Snider. For Real Analysis, either Abbot's "Understanding Analysis" for a first approach and "Principles of Mathematical Analysis" by Rudin for a more comprehensive and deeper study. – Brevan Ellefsen Feb 14 '19 at 06:36
  • @Simplex1 depending on how much probability theory you wish to learn, I'd recommend focusing less on complex analysis and more on things like Measure Theory though. Again, depends a bit on what you wanna learn Stochastic Calculus for. Oh, and concerning PDE's I'm afraid I cannot give a good recommendation there. It's not a field I've done enough with to recommend one text over another :/ As an alternative to what I've written above, the Princeton series of books by Stein and Shakarchi flow together pretty well and have a big emphasis on Harmonic/Fourier Analysis... – Brevan Ellefsen Feb 14 '19 at 06:41
  • ... and importantly get into some decent meadure theory if I recall correctly. A bit tougher intros to real and complex analysis than the intro texts I listed above, but could be good to read concurrently to get a deeper idea of what's going on. Side note, one thing that's kicked me in the butt time and time again is not studying enough linear algebra and intuiting enough multivariable calculus. Make sure you're solid on both. For linear algebra, I found the textbooks Linear Algebra Done Right, and Linear Algebra Done Wrong to both be good for someone who already took a first course. – Brevan Ellefsen Feb 14 '19 at 06:44

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