PAROLE IN INGLESE ASSOCIATE CON «LEIBNITZ'S RULE»
Leibnitz's rule
leibnitz
rule
gottfried
wilhelm
leibniz
german
philosopher
mathematician
mathematics
several
results
concepts
attributed
algebra
algebraic
structure
formula
inefficient
method
calculating
determinants
expression
from
wolfram
mathworld
kaplan
integrals
depending
parameter
advanced
reading
addison
wesley
differentiating
this
wasn
sure
where
else
stick
collins
always
noun
finding
derivative
functions
first
answers
lbnitsz
compute
solved
study
definite
which
have
potential
fetching
question
aieee
then
∂θ
∂b
∂a
employed
especially
when
dealing
with
vertical
bottom
topography
surface
height
z=eta
integration
limits
journal
applied
mechanics
appl
mech
pages
history
received
april
revised
december
july
finite
differences
numerical
analysis
studied
analogous
exists
given
nbsp
higher
engineering
10 LIBRI IN INGLESE ASSOCIATI CON «LEIBNITZ'S RULE»
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Leibnitz's rule nella seguente selezione bibliografica. Libri associati con
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1
Calculus of Finite Differences and Numerical Analysis
Leibnitz's Rule. We have studied Leibnitz's rule for finding n derivative of the
product of two functions u and v as Dn (wv) = nDn(v)+ nCx{Du)Dn~ '(v)+ nC2(D2u
)Dn~ 2(v)+ ...+ nCn(Dnu)v. An analogous formula exists for differences and is
given ...
Prof. P. P. Gupta, Sanjay Gupta, G. S. Malik
2
Higher Engineering Mathematics
Note: Leibnitz's rule is applicable even when one of the limits of integration is
infinite. Worked Out Examples Example 1: Apply Leibnitz's rule £;f_^i eax dx.
Solution: Here /(< rb(a) eax dx ot)= I J-2 = / f(x, a)dx, so b(a) = —a, a(a) Ja(a) —2a
-f(x, ...
3
Linear Difference Equations
We have studied Leibnitz's rule for finding n derivative of the product of two
functions u and v as If (mv) = uD" (v) + "Cj (Dm) D"~1 (v) + nC2 (Z)2w) Z)71~2 (v) .
+ ...+nCn(Dnu)v. An analogous formula exists for differences and is given by An (
uv) ...
Dr. R.K. Gupta, D.C. Agarwal
4
Engineering Mathematics-I (For Wbut)
X y = jf(t)sm[k(x-t)]dt. The upper limit in this integral involves the parameter x. So,
using Leibnitz's Rule, we have X Jx = j~[f(t)sin[k(x-t)}dt o +/(*) sin[*(jc-*)] — (*) dx _
/(0)sin[*(x-0)]^(0) X = / #"(f)cos[*(*-0]*< 0 Using once more the Leibnitz's Rule, ...
5
Engineering Mathematics
sin a. 2 Integrating with respect to a, we get F(a) = — ^cos a + c. But F(0) = 0,
therefore, EXAMPLE 5.86 By successive use of Leibnitz's Rule to fxmdx, J, o
evaluate J ^(logjc)"^. 7T 7T 0 = -- + corc = -. 2 2 Solution. We have Hence, F(<x) =
--cosa ...
Solution: Applying Leibnitz's rule y„(e")n -Inx +nС1(еx)„-\(\nx)\ •.. + nс„(еx)(\пx)„. [
MM. 2005] Solution: Differentiating y w.r.t. x, yi = -a • sin(ln л) • ( - I + b • cos(ln x)- -
\xj x xy\ = —a sin(lnл) + ...
7
Geological Storage of CO2: Modeling Approaches for ...
Leibnitz's rule applies to the derivative of integrals. In the simplest case, we
consider the function h(x,y), which is integrated with respect to its first variable
over a domain bounded by two functions f1(x) and f2(x). Leibnitz's rule now
formalizes ...
Jan Martin Nordbotten, Michael A. Celia, 2011
8
Engineering Mathematics I: For Uptu
So, using Leibnitz's Rule, we have X o +/(*) sm[k{x - x)] — (x) dx _/(0)sin[^-0)]£(0)
X = J kf{t) cos[*(jc - t)]dt. 0 Using once more the Leibnitz's Rule, we get X g = /![*/(,)
cosW*-*, 0 + kf(x) cos[k(x — x)\ — (x) dx -^(0)cos[*(x-0)]£(0). x = -k2 J /(f) sm[k(x ...
Applying Leibnitz's rule with u = sin x, v = x2 d" d"~[ yn = sin , • x + nc , r (sin x) • 2x
dx" ' dx"~' yi = —a • sin(ln x) • I - I + b • cos(ln*) • - \ X f xyi = —a sin(ln x) + b cos(ln
x). Differentiating Xy2 + yi=—a • cos(ln x) • b sin(ln x) • - x x jc2>'2 + xyi ...
10
Demand Uncertainty in International Trade
since exp(-u)g(-u)d-u = 0. dv^.H^ requires use of Leibnitz's Rule: dv2{x*H) _ dx*
H S ^H(x*H)g(x*H) + / expx H Jx* exp(u)g{u)du Since tth(x*h) = 0 and exp(u)g{u)
du > 0 dv2(x*H) = (1-6) f S exp x*H dx H exp(u)g{u)du < 0 dxt, dx* To find —^r^-, ...
