The conventions used on these pages are:

1. Italics represent scalars;
2. Bold italics represent vectors;
3. Bold represent unit vectors or tensors;
4. Upright text represents Booleans or matrices.

oo

means infinity.

=a

means exactly a (usually by definition).

~a

means approximately a.

<a

means less than a.

>a

means greater than a.

a--b

means somewhere between a and b.

a...b

means varies between a and b.

+-a

means plus or minus a; that is, a or -a.

-a [footnote 1]

means negative a.

a + b

means a plus b.

a - b [1]

means a minus b.

a +- b

means a plus b and a minus b.

a -+ b

means a minus b and a plus b.

a b

means a times b.

a/b

means a divided by b.

a^b

means a to the power b.

a^1/2

means a to the power one-half, or the square root of a.

a == b

means a is defined as b.

a = b

means a is equal to b.

a != b

means a is not equal to b.

a ~= b

means a is approximately equal to b.

a < b

means a is less than b.

a <= b

means a is less than or equal to b.

a << b

means a is much less than b.

a > b

means a is greater than b.

a >= b

means a is greater than or equal to b.

a >> b

means a is much greater than b.

a o= b

means a is proportional to b; that is, there exists some k such that a = k b.

a -> b

means a approaches b.

f(a)

means f is a function of a.

f[b]

means that, for f(a), f is evaluated at a = b.

da/db

means the derivative of a with respect to b.

@a/@b

means the partial derivative of a with respect to b.

o

means the zero vector.

i

means the unit x-axis basis vector

j

means the unit y-axis basis vector

k

means the unit z-axis basis vector

-v [1]

means negative v; that is, (-1) v.

u + v

means u plus v.

u - v [1]

means u minus v.

u +- v

means u plus v and u minus v.

u -+ v

means u minus v and u plus v.

u dot v

means the vector dot product of u and v.

u cross v

means the vector cross product of u and v.

r v

means the scalar vector product of r and v.

v/r

means the scalar vector quotent of v and r; that is, (1/r) v.

norm v

|v|

means the norm (or magnitude) of v.

v²

means the norm square of v; that is, v dot v or |v|².

u == v

means u is defined as v.

u = v

means u is equal to v.

u != v

means u is not equal to v.

u |= v

means u and v are parallel vectors; that is, there exists some k such that u = k v.

u /= v

means u and v are perpendicular vectors; that is, u dot v = 0.

unit v [footnote 2]

means a unit vector in the direction of v; that is, the vector v == unit v == v/|v|.

F(a)

means F is a function of a.

F[b]

means that, for F(a), F is evaluated at a = b.

dF/dr

means the derivative of F with respect to r.

@F/@r

means the partial derivative of F with respect to r.

grad F

means the gradient of F ("del F").

div F

means the divergence of F ("del dot F").

curl F

means the curl of F ("del cross F").

I

means the identity matrix.

-M

means negative M; that is, (-1) M.

M + N

means M plus N.

M - N

means M minus N.

r M

means r times M.

M N

means M times N.

v M

means v times N.

M v

means M times v.

M^-1

means the inverse of M.

M^T

means the transpose of M.

M^H

means the Hermitian transpose of M.

tr M

means the trace of M.

det M

means the determinant of M.

Mⁿ

means M to the power n; that is, M multiplied by itself n - 1 times.

~P [footnote 3]

means the logical negation of P ("not P").

P & Q

means the conjunction of P and Q ("P and Q").

P | Q

means the inclusive disjunction of P and Q ("P or Q").

P ^ Q

means the exclusive disjunction of P and Q ("P exclusive-or Q").

P : Q

means P implies (or entails) Q ("if P, then Q"; "Q if P").

P :: Q

means P is equivalent to Q ("if P, then and only then Q"; "Q if and only if P").

P ~& Q

means the negative conjunction of P and Q ("P not-and Q").

P ~| Q

means the negative inclusive disjunction of P and Q ("P not-or Q").

P ~^ Q

means the negative exclusive disjunction of P and Q ("P not-exclusive-or Q").

P ~: Q

means P does not imply (or entail) Q ("it is not the case that if P, then Q"; "it is not the case that Q if P").

P ~:: Q

means P is negatively equivalent to Q ("it is not the case that if P, then and only then Q"; "it is not the case that Q if and only if P").