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May
31
comment Why is integration so much harder than differentiation?
Just for the record: Penrose discusses these matters on p. 103-120. Yet he gives no good reason why this is so (esp. for the symbolic case).
May
16
accepted integral transforms: why do roots in frequency domain correspond to eigenvalues in time domain (and how does it help solve differential equations)?
May
15
comment What is the importance of eigenvalues/eigenvectors?
+1: This is the clearest explanation I have seen so far about the connection between systems of differential equations and eigenvectors - impressive!
May
15
asked integral transforms: why do roots in frequency domain correspond to eigenvalues in time domain (and how does it help solve differential equations)?
May
13
awarded  Cleanup
May
13
revised Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds
deleted 23 characters in body
May
13
revised Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds
rolled back to a previous revision
May
13
accepted Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds
May
13
comment Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds
Ah, now I understand - Thank you!
May
13
comment Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds
+1 - why can you use the same average speed after the first leg? The length of the round trips is reducing constantly (or the other way round: why do you have to wait for the first leg to be completed?) In a way the situation seems to be structurally the same after the first leg.
May
13
comment Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds
gave the easy way a thought: do you think that it works when the dog is running back and forth at different speeds?
May
13
comment Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds
+1 for the anecdote! When it is so famous under what name does it normally go? And where can I find step-by-step solutions for both ways?
May
13
revised Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds
deleted 3 characters in body
May
13
asked Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds
May
12
accepted Difference between metric and norm made concrete: The case of Euclid
May
12
comment Difference between metric and norm made concrete: The case of Euclid
I think I finally got it - Thank you to everybody!
May
12
comment Connections between metrics, norms and scalar products (for understanding e.g. Banach and Hilbert spaces)
@Theo: You are right! Thank you very much for that hint! I switch constantly between both languages. I found that oftentimes the part that is missing for a proper understanding in one language is to to be found in the other. There are so many texts in German that are not translated and of course the other way round. BTW: The site of Dirk Werner is to be found here: page.mi.fu-berlin.de/werner99 - there are some free texts, e.g. this one about Fixpunktsätze that seems to be very understandable too: page.mi.fu-berlin.de/werner99/skripte/fixpunkte.pdf
May
12
comment Difference between metric and norm made concrete: The case of Euclid
@Qiaochu: Thank you. Perhaps my confusion stems from the fact that on the one hand, as you say, you can do it either way, on the other hand there is this hierarchy between metric spaces and normed spaces (every normed space is a metric space but not the other way round). It seems like a contradiction to me...?!?
May
12
comment Difference between metric and norm made concrete: The case of Euclid
@user6312: Thank you - could you please give an example of a simple metric that is not translation invariant?
May
12
asked Difference between metric and norm made concrete: The case of Euclid