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calculus
| Show `curl\ curlbbF = \g\r\a\d\ div bbF - grad^2bbF`
where `grad^2 =
(del^2)/(delx^2) + (del^2)/(dely^2) + (del^2)/(delz^2)\ ` (Laplace
operator).Derive `grad^2bbE = 1/(c^2)(del^2bbE)/(delt^2)` and `grad^2bbH =
1/(c^2)(del^2bbH)/(delt^2)`
by applying the previously proven identity to the
Maxwells equations
for simple electromagnetic fields.
(i.e., `divbbE=0,
divbbH=0, curlbbE=- 1/c(delbbH)/(delt), curlbbH=1/c(delbbE)/(delt)`)
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No answers available [Answer]
2005-09-09
| Katsu (MLC Tutor)
katsu@mathtoearth.org |
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[ Answer ] |
calculus
combinatorics
| Let a special gamma function be defined for positive integers `n`
as,
`Gamma_s(n)=int_0^oo e^(-t)t^(n-1)dt`1) Derive `Gamma_s(1)=1`
by
calculating `Gamma_s(1)=int_0^oo e^(-t)dt` 2) Prove
`Gamma_s(n)=(n-1)Gamma_s(n-1)`
by using a partial integration. 3) Show
`Gamma_s(n)=(n-1)bb!`
where `(n-1)bb! =(n-1)*(n-2)cdots3*2*1` 4) Derive
`0bb! = 1`
by naturally defining `0bb! =Gamma_s(1)` as shown previously.
|
No answers available [Answer]
2005-09-10
| Katsu (MLC Tutor)
katsu@mathtoearth.org |
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[ Answer ] |
statistics
business statistics
| Given raw data of heights (from 70 inches to 90 inches) of all 412 NBA
players,
how many classes (bins) do you divide the data into for a histogram
and
what is your rationale for it?(There are many answers to this question
depending on the circumstances.
One guide may be to use the Sturges formula;
`c=1+3.3logn`,
where `c` is the total number of classes and `n` is the total
number of data points.)
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No answers available [Answer]
2005-09-11
| Katsu (MLC Tutor)
katsu@mathtoearth.org |
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[ Delete ]
[ Answer ] |
calculus
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