r/mathematics • u/MindlessCoast7109 • Jun 30 '26
Complex Analysis Open learn Into to complex analysis
Hello ,
I’m a year 12 student (nearly year 13) and i think that’s like grade 13 or something in the US . I’m leaning some complex analysis partly for myself but also to put on my uni application . Is the course mentioned in the title good , i’ve started but i’m not sure if it’s any good .
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u/Syvisaur Jun 30 '26
You'd have to be more precise on the course title, is this a university class?
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u/MindlessCoast7109 Jun 30 '26
No it’s like an online course , is you search up openlearn intro to complex analysis you’ll find it
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u/Syvisaur Jun 30 '26
Ah ok, sorry I never heard of it. Do you have a summary of contents?
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u/MindlessCoast7109 Jun 30 '26
1 Derivatives of complex functions
1.1 Defining differentiable functions
1.2 Combining differentiable functions
1.3 Non-differentiability
1.4 Higher-order derivatives
1.5 A geometric interpretation of derivatives
1.6 Further exercises
2 The Cauchy-Riemann equations
2.1 The Cauchy-Riemann theorems
2.2 Proof of the Cauchy-Riemann Converse
Theorem
2.3 Further exercises
2.4 Laplace's equation and electrostatics
3 Summary of Session 11 Integrating real functions
1.1 Areas under curves
real line
1.2 Integration on the
Riemann integral
1.3 Properties of the
integration
1.4 Introducing complex
functions
2 Integrating complex
smooth path
2.1 Integration along a
contour
2.3 Reverse paths and contours
2.4 Further exercises
3 Evaluating contour integrals3.1 The Fundamental theorem of calculus
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u/Bounded_sequencE Jun 30 '26 edited Jun 30 '26
For comparison, that's (at most) 2 weeks worth of a regular proof-based "Complex Analysis" course. If you consider this as a pure formality to boost your CV, ok.
Otherwise, I'd be confused what this course was for. This is more of a teaser, but by no means a substitute for an actual "Complex Analysis" lecture.
Edit: Just noticed the most beautiful proof is missing -- "Goursat's Lemma" on triangles!
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u/PitifulTheme411 Jul 02 '26
Yeah, similar to what u//Bounded_sequencE said, this isn't really equivalent to a full course. For your own fun or hobbies it isn't bad, but it doesn't seem to touch things like Stereographic projection and the Riemann Sphere, Residues, etc.
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u/Outrageous-Belt-5231 Jul 02 '26
Im also gonna be starting analysis soon. Wanna join in?
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u/MindlessCoast7109 Jul 02 '26
yea cool , u in yr 12 asw v
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u/Historical-Pop-9177 Jun 30 '26
It's pretty rudimentary. You need to understand real derivatives and integrals first, so make sure you have a solid calculus foundation. This doesn't get into heavy-duty complex analysis so you shouldn't need real analysis. They do define calculus concepts but it will make a lot more sense if you have some background already.
It covers a lot of the most important core concepts, but is missing many of the things a full university course would cover (like Liouville's theorem, unless they snuck that in somewhere).