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Oct
1
comment The Best of Dover Books (a.k.a the best cheap mathematical texts)
Nice review. I'm curious, do you know of a book which has the improved proofs you mention in the review. I found his discussion of how the contraction mapping sets-up the inverse and implicit mapping theorems was pretty lucid. Maybe you've written something?
Sep
30
comment Using calculus to find inverse functions
Interesting circle of ideas, however, we usually try hard to change problems of calculus into problems of algebra. You are doing the opposite. So, I don't have too much hope for your method as differential equations are a bit harder to solve than algebraic equations in many instances.
Sep
30
awarded  Explainer
Sep
30
comment Best book ever on Number Theory
How did the semester go? I'm thinking of using some of the Sage in a elementary number theory course teach in the spring. Currently, my plan was to use Jones and Jones Elementary Number Theory supplemented by some examples/exercises from Stein. Thoughts?
Sep
30
comment The Best of Dover Books (a.k.a the best cheap mathematical texts)
For example? (not meaning to argue, just curious about your take on it)
Sep
28
comment Does $2^i$ exist, if so how do I calculate its value?
I edited this so I could reverse my vote. You convinced me.
Sep
28
revised Does $2^i$ exist, if so how do I calculate its value?
added 1 character in body
Sep
28
comment Does $2^i$ exist, if so how do I calculate its value?
@Fujoyaki granted. But, there are many additional solutions we ought to mention since the OP seems not to be aware of the difficulties of the bigger picture of complex powers.
Sep
28
answered How to explain to a high school student why a linear differential equation is linear?
Sep
28
comment Does $2^i$ exist, if so how do I calculate its value?
$1^i = e^{i\log(1)}=e^{i(\ln(1)+2\pi i\mathbb{Z})} = e^{-2\pi \mathbb{Z}}$. This is a set of values which forms a sequence of points on $\mathbb{R}$. In short, @Fujoyaki it is quite clear that this positive real base gives an infinite set of values. This is standard stuff. See any complex analysis text.
Sep
17
comment Problem 30 of GR8767 how is improper integral defined?
Yes. That's the method intended. We can twist this problem many different directions in view of the above comment.
Sep
17
accepted Problem 30 of GR8767 how is improper integral defined?
Sep
17
comment Problem 30 of GR8767 how is improper integral defined?
I had hoped there might be some slick countermeasure to direct calculation, but, on the other hand, it's not that bad. Thanks for your assistance, my student will appreciate it.
Sep
16
comment Problem 30 of GR8767 how is improper integral defined?
ah ha. I did not notice that, this would help, although, it remains to show why it must be zero. I assume there is some easy method? Care to add that to your answer, I'd accept it then.
Sep
16
asked Problem 30 of GR8767 how is improper integral defined?
Sep
15
comment Continuity and Differentability of a Partial derivative
I think, d,e,i, j are correct. Partial derivatives can exist, but, that doesn't say much about continuity due to the examples where all linear paths agree but quadratics differ. I hope someone comes along with some specific counter examples soon, I must run.
Sep
15
comment Is a horizontal line considered periodic?
Periods are ambiguous in other cases. For example, $\sin \theta$ has periods $2\pi k$ for any $k \in \mathbb{Z}$. Of course, you could pick a minimal period in that case. But, I don't see the problem. I mean, the constant function is part of the family of periodic functions built over any period. This is a good thing.
Sep
15
comment Geometric proof for triple vector product Jacobi identity
The basic geometric idea here is also used in this math.stackexchange.com/a/400732/36530
Sep
9
revised Geometric proof for triple vector product Jacobi identity
added picture and some organization
Sep
8
answered Geometric proof for triple vector product Jacobi identity