Reddit reviews Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics (3rd Edition)

Learn math first. Physics is essentially applied math with experiments. Start with Calculus then Linear Algebra then Real Analysis then Complex Analysis then Ordinary Differential Equations then Partial Differential Equations then Functional Analysis. Also, if you want to pursue high energy physics and/or cosmology, Differential Geometry is also essential. Make sure you do (almost) all the exercises in every chapter. Don't just skim and memorize.

This is a lot of math to learn, but if you are determined enough you can probably master Calculus to Real Analysis, and that will give you a big head start and a deeper understanding of university-level physics.

Saff and Snider is great for applied complex analysis. In my opinion it strikes a perfect balance between accessibility and rigor for a first course on the subject.

Visual Complex Analysis is another good choice, but it might be a little more advanced than what you're interested in.

The first half of Lang might also be a good choice, but Lang takes a slightly more formal, proof-based approach.

I've also skimmed through Brown and Churchill, which looks quite good but is prohibitively expensive.

Finally, you can find many cheap (~$10) books on the subject by Dover. The only one I've looked at is Knopp, which is quite formal and light on computation, but might be a good supplement. Here's another Dover book with outstanding Amazon reviews.

Complex analysis is both very elegant and very useful. Best of luck with your class!

If you're after a solid understanding of math, I recommend learning from actual math books. Keep "mathematical methods" books for reference and review. Some recommendations:

Linear Algebra by Lang

Fundamentals of Complex Analysis by Saff and Snider

Fourier Series and Boundary Value Problems by Brown and Churchill

These books will be significantly more rigorous than Boas, but maybe seeing everything developed carefully will be easier for you to understand.

I don't know where you are in physics, but if you've got any quantum mechanics classes coming up, then I would focus on linear algebra, as it is very important. (And not just the finite-dimensional R^n stuff...make sure you understand vector spaces of possibly infinite dimension over general fields, and C in particular.) For classical mechanics and electromagnetism, vector calculus is probably the most important, but things like Fourier analysis and residue integration can show up anywhere.

That's probably enough Calc to get started with it, but you haven't had a proof-oriented course yet so the way the material is approached, the progression, and the style of problems you'll have to solve may be a little foreign to you.

Reviews on Amazon point to this book as a good introduction, but it doesn't get to analytic continuation. You'll need to be familiar with the techniques taught in an analysis course before diving into a deeper book.

I used this one: http://www.amazon.ca/Fundamentals-Analysis-Applications-Engineering-Mathematics/dp/0139078746