 E01E dot product for 2 vectors - gives scalar v1v2 = Σ(d= 1 to 2 or 3 : x1d*x2d)  E129 cross product for 2 vectors - gives vector v1v2 = 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 integranddl (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.