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xxx MAIN NOTATION
∇ vector differential operator “nabla”; ∇a is the gradient of a scalar a

b
integral; f(x) dx is the integral of a function f(x) over the interval [a, b]
a

contour integral (denotes an integral over a closed contour)
⊥ perpendicular
parallel
Roman alphabet

Arg z argument of a complex number z = x + iy;bydefinition, tan(Arg z)= y/x
arg z principal value of Arg z;by definition, arg z =Arg z,where –π <Arg z ≤ π
√ √ 2
a square root of a number a,defined by the property ( a ) = a
√ √
n
n
n a nth root of a number a (n=2, 3, ... , a≥0), defined by the property ( a ) =a
if a ≥ 0
|a| absolute value (modulus) of a real number a, |a| = a
–a if a < 0
a vector, a = {a 1 , a 2 , a 3 },where a 1 , a 2 , a 3 are the vector components
|a| modulus of a vector a, |a| = √ a ⋅ a
a ⋅ b inner product of vectors a and b, denoted also by (a ⋅ b)
a × b cross-product of vectors a and b
[abc] triple product of vectors a, b, c
(a, b) interval (open interval) a < x < b
(a, b] half-open interval a < x ≤ b
[a, b) half-open interval a ≤ x < b
[a, b] interval (closed interval) a ≤ x ≤ b
arccos x arccosine, the inverse function of cosine: cos(arccos x)= x, |x| ≤ 1
arccot x arccotangent, the inverse function of cotangent: cot(arccot x)= x
arcsin x arcsine, the inverse function of sine: sin(arcsin x)= x, |x| ≤ 1
arctan x arctangent, the inverse function of tangent: tan(arctan x)= x
arccosh x hyperbolic arccosine, the inverse function of hyperbolic cosine; also denoted
√
–1
2

by arccosh x =cosh x; arccosh x =ln x + x – 1 (x ≥ 1)
arccoth x hyperbolic arccotangent, the inverse function of hyperbolic cotangent; also
–1 1 x + 1
denoted by arccoth x =coth x; arccoth x = ln (|x| > 1)
2 x – 1
arcsinh x hyperbolic arcsine, the inverse function of hyperbolic sine; also denoted by
√
–1
2

arcsinh x =sinh x;arcsinh x =ln x + x + 1
arctanh x hyperbolic arctangent, the inverse function of hyperbolic tangent; also denoted
1
–1
by arctanh x =tanh x;arctanh x = ln 1 + x (|x| < 1)
2 1 – x
n

n!
k
C k binomial coefficients, alsodenotedby k , C = k!(n – k)! , k=1, 2, ... , n
n
n

1 1 1
C Euler constant, C = lim 1 + + + ··· + –ln n = 0.5772156 ...
n→∞ 2 3 n
cos x cosine, even trigonometric function of period 2π
1
cosec x cosecant, odd trigonometric function of period 2π:cosec x =
sin x
1
–x
x
cosh x hyperbolic cosine, cosh x = (e + e )
2
cot x cotangent, odd trigonometric function of period π,cot x =cos x/sin x
coth x hyperbolic cotangent, coth x =cosh x/sinh x
det A determinant of a matrix A =(a ij )