E01E dot product for 2 vectors - gives scalar
v1v2 = Σ(d= 1 to 2 or 3 : x1d*x2d)
E129 cross product for 2 vectors - gives vector
v1v2 = det(d=2 or 3 : d d reshape link nj vij)
ni = unit orthogonal vector basis
∇ 2207 gradient (nabla or del) of scalar field f - gives vector
v = Σ(i=1 to D : ∂/∂xi(f)*ni )
∇ combo divergence (grad-dot) of vector field V - gives scalar
∇V = Σ(i=1 to 2 or 3: ∂/∂xi(Vi) )
∇ combo curl (grad-cross) of vector field v - gives vector
∇V= det(i=1 to 3 : i i reshape link ni ∂/∂xi(V) vi ...)
ni = unit orthogonal vector basis
∇′ gradient in particle/system frame
r_hat In Lucas's notation, an "^" or "hat" over a letter - denotes a unit vector in the direction of the vector
represented by the letter, eg r_h (r in Lucas writing) means a unit vector in the direction of vector r.
⊥ perpendicular to
# [Howell 17Aug2015 - in Lucas's "Universal force, volume 1" the variables t, c, n q are scalar, the rest are vector.
|r - v*t| In Lucas's book, this denotes the vector norm (usually written ||r - v*t||) rather than the absolute value of each component of a vector or matrix, as is the usual interpretation of |r - v*t|. The single verticle bars do usually denote the norm on the one-dimensional vector spaces formed by the real or complex numbers, for example |-3| (absolute value)
(see https://en.wikipedia.org/wiki/Norm_%28mathematics%29)
d[dt: x] total derivative of x with respect to t
dp[dt: x] partial derivative of x with respect to t
d^n[dt^n: x] nth total derivative of x with respect to t
dp^n[dt^n: x] nth partial derivative of x with respect to t
∫[ds: f] indefinite integral of f with respect to s
∫[ds, a to b: f] definite integral of f with respect to s, from a to b
∮[ds: f(t)] integral of f(t) over the closed [2D curve, 3D surface] S
∮[dl: f(l)] closed-loop integral f(l) wrt dl (pathway)
∮[dl: f(l)] closed-loop integral with dot product of integranddl (eg in Green's theorem etc)
∫ 222B integral
∫c 222E line integral closed
∬s 222C surface integral
∫∫∫v 2230 volume integral
△ 25B3 delta (change)
∆ 2206 delta (change)
∂ 2202 partial deriv
√ 221A square root
∝ 221D proportional
∞ 221E infinity
≈ 2248 approximately equal to
≠ 2260 not equal to
== 2250 identically equal to (should be "=" with dot over)
∆= 225C ??? (should be "=" with dot over)
≤ 2264 less than or equal to
≥ 2265 greater than or equal to
⊥ 22A5 perpendicular
' E094 prime often for RFp - particle reference frame
∘ 221E
∈ 2208 element of
Special note - the Unicode character for dotProduct has to be selected to show up in
[ ????????????????????
LibreWrite, pdf, kwrite, LibreCalc]
The character (Ctrl+Shift+U+E01E) works well so far.