>>7803705 Yeah similar to what they've said in the thread already. Mostly calc 1-3, differential equations, maybe some linear algebra.
Before looking at complex analysis, investigate some real analysis.
Don't jump into Rudin. Baby Rudin is good for junior and senior level math undergrads. Anything past that is a for grad students as a thorough reference tool.
Out of that list you'll want to do PDE's, but I wouldn't suggest doing that until you've done both ODE's and multivariable calc. The last two subjects you listed are usually part of a Numerical Analysis class. Make sure you're at least intermediate in some programming language by the time you make it to numerical.
These are some of my favorite topics but keep in mind these are mostly junior and senior level undergrad math courses and if you're not at that level you have plenty of time to get there and work up a solid base. It's useless if you just rush to the topic and only understand half of it.
>>7804714 Complex analysis is the extrapolation of real analysis to the complex numbers. Also most complex analysis texts will require you to know things that were fundamentally proven in real analysis.
Lastly, having a rigorous, proof-based course is sort of necessary if you want to be successful in any kind of analysis class.
Depends on whether you want to learn complex analysis as a mathematician or for some applied purpose. A lot of school offer complex analysis as a "for scientists and engineers" class (whereas real analysis is always a rigorous, proof-based course) because the ideas are used quite frequently (mainly physics and EE) but obviously these students rarely have any exposure to mature mathematics. Same thing with PDEs, but a slightly higher level - you can solve basic PDEs with just Calc and DiffEq (would also recommend knowledge of LinAlg concepts), you can babby-tier analyze them with undergrad analysis, but if you really want to start analyzing PDEs you need at least a semester of grad analysis, preferably with exposure to functional analysis. I'm not well versed with numerics, but from what I gathered it's a similar idea - you can implement algorithms with superficial understanding for sure, but if you want to analyze numerical schemes (understand how well they compute solutions, accuracy vs run time stuff, stability, implicit vs explicit, etc.) you definitely need some sort of exposure to analysis.
The problem is when you list these 4 topics, which are prevalent to physical sciences/engineering, it isn't clear whether you want to learn them from an applied or analytical purpose.
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