I really appreciated this thorough approach. It was really well-paced. The examples, and the fact that you worked through them assuming the viewer has very little knowledge, helps so much!
Petra, I've noticed elsewhere on the net that there are some alternative ways to visualize (graph) complex functions. The mapping method is a nice one, as it really puts the emphasis on the overall behavior of the function, and it lets one see the inverse mapping easily. I am already thinking it is the most useful out of all the visualization options because of that. But another method I've seen involves a 2D picture of the domain, filled in using color, where Re(f(w)) -> brightness and Im(f(w)) -> hue. Some graphs I've seen made this way are very pretty! Yet another method I've seen involves 3D graphs, with w (two-dimensions) graphed against Re(f(w)) (one dimension) in one color, creating a surface, and against Im(f(w)) in another color, creating a second surface. This can look good in computer animation if the surfaces are shown translucent and with some shading added to better show how they curve. I don't really have a specific question about them, but am wondering if you have any general comments on these other methods for the visualization of complex functions? What would you tell a student about the advantages and disadvantages of each method? Also, it would be nice to see comparisons of basic functions viewed by each of the different methods, especially where there are things about the function easily seen via one method that are not as easily seen via another, along with good commentary on the matter. Do you know if a good resource for this already exists, or would you be interested in making a video on it for us?
Thank you, I always think that studying complex analysis is complex but that's something I wanted long time ago, and I feel confident that if I complete your course I would have good hold on the subject
Hello mam ...it is a very beautiful lecture and very helpful thank u mam ... But mam I am weak in real analysis and topology kindly suggest me a website for these two courses I shall be very thankful ..any one
Wonderful lecture.
Love your videos
I really appreciated this thorough approach. It was really well-paced. The examples, and the fact that you worked through them assuming the viewer has very little knowledge, helps so much!
Please make videos on other topics as well
The animations are very. They are very helpful in solidifying the concepts.
I love the little subtleties and foreshadowing in these videos. 12:06 is basically the nyquist stability criterion.
Amazing work! You explain in a very good way.
You have an adorable voice. Thanks for sharing this video! Helped a lot with my class.
you just ruined the vibe bro
@@eclipse-xl4ze vibe check
Petra, I've noticed elsewhere on the net that there are some alternative ways to visualize (graph) complex functions.
The mapping method is a nice one, as it really puts the emphasis on the overall behavior of the function, and it lets one see the inverse mapping easily. I am already thinking it is the most useful out of all the visualization options because of that.
But another method I've seen involves a 2D picture of the domain, filled in using color, where Re(f(w)) -> brightness and Im(f(w)) -> hue. Some graphs I've seen made this way are very pretty!
Yet another method I've seen involves 3D graphs, with w (two-dimensions) graphed against Re(f(w)) (one dimension) in one color, creating a surface, and against Im(f(w)) in another color, creating a second surface. This can look good in computer animation if the surfaces are shown translucent and with some shading added to better show how they curve.
I don't really have a specific question about them, but am wondering if you have any general comments on these other methods for the visualization of complex functions? What would you tell a student about the advantages and disadvantages of each method? Also, it would be nice to see comparisons of basic functions viewed by each of the different methods, especially where there are things about the function easily seen via one method that are not as easily seen via another, along with good commentary on the matter. Do you know if a good resource for this already exists, or would you be interested in making a video on it for us?
So well explained, clear, understandable. Thank you so much!
Thank you, I always think that studying complex analysis is complex but that's something I wanted long time ago, and I feel confident that if I complete your course I would have good hold on the subject
Absolutely great video, this kind of explanation is what I needed to fully understand this tricky stuff
WOW this is really well explained . You are good
competence is surely appreciable
Thank you very much for uploading these videos! Theyre really helpful! :)
Fun. Reminds me of computer science love for iterated composition. Next
Reminds me of successor functions from lambda calculus.
Great explanation thanks Petra Bonfert Taylor
You are awesome :D !!
Well explained :)
11:09 ish isnt it the case that the lengths dont increase if the radius is less than 1 as exponent of decimal yields smaller decimal?
Are the slides available? If so how can I get them. This is so much better than Churchill's book.
thank you mam
Great video, but that f n of z looks like the notation for taking nth derivative of f.
Hello mam ...it is a very beautiful lecture and very helpful thank u mam ... But mam I am weak in real analysis and topology kindly suggest me a website for these two courses I shall be very thankful ..any one
Pls give the name of book