The lectures were very easy to follow and the exercises fitted these lectures well. This course was not always very rigorous, but a great introduction to complex analysis nevertheless. Thank you!
Derivations are generally clear and easy to follow, some are abit less intuitive but Dr Petra Bonfert-Taylor makes the effort to explain it in a way that is easy for me to understand.
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I like it
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Area of special interest for me, and what I was hoping to prepare myself for in this course, for example include
1. Nyquist stability criterion, as it relates to classical approach to analysis and design of the control systems,
2. Fourier, Laplace and Z-transforms, with rigorous approach to definition of the region of convergence, and generalized functions transformations,
Nyquist stability criterion actually comes from residue theorem, so with addition of the week 7, that goal is partially fulfilled.
Actually, without week 7, this course would not have much of the sense at all. To include topics like Julia and Mandelbrot sets, and even Riemann Hypothesis, while skimping on Cauchy’s Theorem and Integral Formula, and actually to completely left out Residue Theorem and its applications altogether… well that would be pure "l'art pour l'art".
From each sentence, this course instructor knowledge and expertise clearly shines, but so does the fascinations with pretty, fractal like, pictures or open problems in mathematics. From that kind of fascinations the greatest results in mathematics came. Complex analysis is one of those gems, so don’t cut corners on it.
Most of the proofs are just sketched, or omitted altogether. That is really unfortunate, because proofs of the complex analysis theorems are really good way to gain in depth understanding of the subject meter. Very much like in vector calculus, the approach and ideas in those proofs, have universal applicability in wide range of engineering areas. To state complex analysis theorem without proof is like teaching student a recipe to solve differential equitation, without teaching him to properly set the equitation together with appropriate boundary conditions.
創建者 simon w•
much of the course is excellent, I found some better aids along the way which gave well worked out examples; the peer assessed exercises were very good but the standard shown by some participants seemed low in terms of presentation (neatness, clarity of argument) the final exam was quite hard and even if one achieves a pass mark of > 80% it is not possible to see exactly where one went wrong. I found the course stimulated my personal research : https://learn.lboro.ac.uk/archive/olmp/olmp_resources/pages/wbooks_fulllist.html I also greatly appreciated the presentation in "Visual Complex Analysis" by Tristan Needham Clarendon Press Oxford
my background : Calculus at School until 18, 1 year maths for sciences at Uni, Khan Academy Maths in the last 5 years, Intro to Math Thinking Keith Devlin Coursera
創建者 Joshua H•
Its an overall satisfactory course. It balances the understanding of functions in the complex plane and the processing of functions in the complex plane. Throughout this course, there are in depth (as in depth as an introductory course can be) mention of topics such as properties and implications of analytic functions, transformations, residue calculus, power series, and more. Apart from this, the only drawback is the occasional omission of proofs. In general, there is always an attempt to either prove a given theorem, or at least give an idea as to how it would be proved, but quite often the student is entrusted to apply a theorem without fully understanding it. All-in-all, I would recommend this course to others.
Everything in the course was explained in great detail and clarity, and the assignments that were assigned for the course provided educational value. However, I feel that the quizzes and the problems on them were considerably more difficult than most of the example problems that were gone over during the lectures, and that can be a problem considering you need at least a 4/5 (80%) to pass each quiz (each quiz consisting of 5 questions at the time I'm writing this).The difficulty spike being slightly too high is the only problem that I experienced in this course, and aside from that, everything else was great!
This is a very good course. Professor Bonfert-Taylor only uses slides so it is a traditional maths course (for awesome non-traditional maths courses on Coursera Cf Jim Fowler calculus 1 and 2). However, the content is very homogeneous in terms of level of difficulty, the progression is perfect and she explains everything there is on each one of the slides. It's a pity she doesn't try to appeal to our geometrical intuition (I know it's less easy to do than in real analysis, but still, it would have been helpful in some places).
創建者 Santiago R R•
A really tough and complete introduction to complex analysis. With the added lectures about the residue theorem and Laurent series, the course feels really useful and fun to apply.
The pop-up questions seem a bit out of place for me, and confused me more times than they helped me comprehend the concept at hand.
Besides that, this was really a great experience, and one of the most challenging and fun math courses I have done here in Coursera.