- en D9Ti gratuite" [Upgrade of the
functions of the D9 and D9Ti free].
AlphaDxD (in French). 5
January 2011.
Archived from the
original on 18 May 2022...
- en D9Ti gratuite" [Upgrade of the
functions of the D9 and D9Ti free].
AlphaDxD (in French). 2011-01-05.
Archived from the
original on 2022-05-18. Retrieved...
-
equation x 2
d 2 y
d x 2 + x
d y
d x + ( x 2 − α 2 ) y = 0 {\displaystyle x^{2}{\frac {
d^{2}y}{
dx^{2}}}+x{\frac {dy}{
dx}}+\left(x^{2}-\
alpha ^{2}\right)y=0}...
- )
d x ∧
d y + g ( x , y , z )
d z ∧
d x + h ( x , y , z )
d y ∧
d z ) . {\displaystyle \int _{S}\left(f(x,y,z)\,
dx\wedge dy+g(x,y,z)\,dz\wedge
dx+h(x...
- _{a}^{b}{\frac {\partial }{\partial \
alpha }}f(x,\
alpha )\,
dx+f(b,\
alpha ){\frac {db}{
d\
alpha }}-f(a,\
alpha ){\frac {da}{
d\
alpha }}.} The
general form of Leibniz's...
-
Friedrich Gauss, the
integral is ∫ − ∞ ∞ e − x 2
d x = π . {\displaystyle \int _{-\infty }^{\infty }e^{-x^{2}}\,
dx={\sqrt {\pi }}.}
Abraham de
Moivre originally...
- L ( x , f ( x ) , f ′ ( x ) )
d x , {\displaystyle J[f]=\int _{a}^{b}L(\,x,f(x),f'{(x)}\,)\,
dx\,,}
where f ′(x) ≡ df/
dx. If f is
varied by
adding to it...
-
scalar α: ∫ − ∞ ∞ δ ( α x )
d x = ∫ − ∞ ∞ δ ( u )
d u | α | = 1 | α | {\displaystyle \int _{-\infty }^{\infty }\delta (\
alpha x)\,
dx=\int _{-\infty }^{\infty...
- }f\,\psi \,
dx,}
which is
often denoted by
D f ( ψ ) . {\displaystyle
D_{f}(\psi ).} This new
action ψ ↦
D f ( ψ ) {\textstyle \psi \mapsto
D_{f}(\psi )}...
-
notation as
d d x ( u ⋅ v ) =
d u
d x ⋅ v + u ⋅
d v
d x . {\displaystyle {\frac {
d}{
dx}}(u\cdot v)={\frac {du}{
dx}}\cdot v+u\cdot {\frac {dv}{
dx}}.} The rule...
