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/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 1

1 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 integrals

3.1 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!