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Sep
18
comment Second Derivatives Using Implicit Differentiation
muad: "express $\frac{\mathrm{d}^2 y}{\mathrm{d}x^2}$ in terms of $x$ and $y$", per the OP. In other words, what is $y^{\prime\prime}(x)$ in terms of $x$ and $y$.
Sep
18
answered Second Derivatives Using Implicit Differentiation
Sep
18
comment A question on FLT and Taniyama Shimura
I mean for instance, modular functions can take the nome $q=\exp(i\pi\tau)$ (and apparently sometimes this is squared for convenience) or a ratio of periods $\tau$ as argument, which ties in intimately to elliptic functions (and then theta functions as well)... right?
Sep
18
comment A question on FLT and Taniyama Shimura
Hmm,the precious little I know is something like: Weierstrass functions are doubly periodic (elliptic) , and their having a period parallelogram allows the embedding of the corresponding lattice into the projective plane. I sort of got lost on why having a Weierstrass parametrization does not correspond to having a modular parametrization. Aren't modular functions just elliptic functions with transformed arguments?
Sep
18
comment A question on FLT and Taniyama Shimura
To be frank, Chandru, this is one of your better questions. :)
Sep
18
comment A question on FLT and Taniyama Shimura
Robin, please correct my impression of the whole setup if I'm wrong: what Frey did amounted to constructing a "weird" elliptic curve that, if it did not have an associated modular form, would imply the falsity of TSC and thus FLT. Meaning, what Ribet essentially did to settle the ε conjecture was to show that the Frey curve does have an associated modular form.
Sep
18
comment A question on FLT and Taniyama Shimura
Non-expert's question: the parametrization of an elliptic curve as $(x\;y)=(\wp\left(u;g_2,g_3\right)\;\wp^{\prime}\left(u;g_2,g_3\right))$ is a modular parametrization?
Sep
18
answered Cartesian Equation for the perpendicular bisector of a line
Sep
18
revised Cartesian Equation for the perpendicular bisector of a line
edited tags
Sep
18
awarded  Civic Duty
Sep
18
comment Inverse of an invertible triangular matrix (either upper or lower ) is triangular of the same kind
Just a tiny terminology note: $N$ in your answer would be termed a "strictly upper triangular matrix"; the definition of "strictly lower triangular matrix" is similar.
Sep
17
comment Why is an integral of a complex function defined as a line integral?
Even the garden-variety definite integral can be though of as a line integral, except that the contour is a single line segment, as opposed to a circle or even fancier curves.
Sep
17
comment Find the Volume Enclosed by Terrain and a Certain Sea Level
Just to show how a Bézier surface works, here's some old stuff I did in Mathematica: library.wolfram.com/infocenter/MathSource/4930 . Here, the "teapot" does not pass through the points, but the points do control the shape of the "teapot". For the purpose of finding volumes, this isn't what you want.
Sep
17
comment Where to go after calculus?
+1 for the suggestion to study history; it can be illuminating to find out why things in math are the way they are now, as well as gain a deep appreciation of the fact that mathematics is a human endeavor: actual humans with individual strengths and weaknesses helped mold mathematics as we now know it.
Sep
17
comment How to solve DE that relate values of derivatives at different points?
@whuber: I found books.google.com/books?id=5n2sN8rBU28C which corroborates your statement, though the usage I was accustomed to would be like the way the term was used in books.google.com/books?id=BUg4AAAAIAAJ&pg=PA192 and books.google.com/books?id=huuO6mKbVoEC&pg=PA214 . I suppose we are reading different books. :)
Sep
17
comment Find the Volume Enclosed by Terrain and a Certain Sea Level
As I said, Bézier treats your data as a convex hull instead of points to interpolate. Bicubic interpolation is standard fare, but without seeing what the data looks like, I don't want to give a definite recommendation.
Sep
17
comment Distributions of point charges
I can do no better than point out dx.doi.org/10.1088/0305-4470/31/3/014 and dx.doi.org/10.1098/rspa.2001.0913 .
Sep
17
comment Inverse of an invertible triangular matrix (either upper or lower ) is triangular of the same kind
A further hint: look up "forward elimination" and "backsubstitution", and figure out how to use these to find the inverse of a triangular matrix.
Sep
17
comment Inverse of an invertible triangular matrix (either upper or lower ) is triangular of the same kind
Why not try a constructive proof? Better yet, look at the 2-by-2 case first, and figure out how you can generalize your observations from it.
Sep
17
revised Inverse of an invertible triangular matrix (either upper or lower ) is triangular of the same kind
edited tags