i 
The square root of minus one. 
f(x) 
The value of the function f at argument x. 
sin(x) 
The value of the sine function at argument x. 
exp(x) 
The value of the exponential function at argument x. This is often
written as e^{x}. 
a^x 
The number a raised to the power x; for rational x is defined
by inverse functions. 
ln x 
The inverse function to exp x. 

Same as a^x. 

The power you must raise b to in order to get a; 
cos x 
The value of the cosine function (complement of the sine) at argument
x. 
tan x 
Works out to be 
cot x 
The value of the complement of the tangent function or 
sec x 
Value of the secant function, which turns out to be 
csc x 
Value of the complement of the secant, called the cosecant. It
is 
asin x 
The value, y, of the inverse function to the sine at argument
x. Means x = sin y. 
acos x 
The value, y, of the inverse function to cosine at argument x.
Means x = cos y. 
atan x 
The value, y, of the inverse function to tangent at argument x.
Means x = tan y. 
acot x 
The value, y, of the inverse function to cotangent at argument
x. Means x = cot y. 
asec x 
The value, y, of the inverse function to secant at argument x.
Means x = sec y. 
acsc x 
The value, y, of the inverse function to cosecant at argument
x. Means x = csc y. 

A standard symbol for angle. Measured in radians unless stated
otherwise. Used especially for
when x, y, and z are variables used to describe point in three dimensional space. 
i, j, k 
Unit vectors in the x y and z directions respectively. 
(a, b, c) 
A vector with x component a, y component b and z component c. 
(a, b) 
A vector with x component a, y component b. 
(a, b) 
The dot product of vectors a and b. 

The dot product of vectors a and b. 

The dot product of vectors a and b. 
v 
The magnitude of the vector v. 
x 
The absolute value of the number x. 

Used to denote a summation, usually the index and often their
end values are written under it with upper end value above it. For example the
sum of j for j=1 to n is written as This
signifies 1 + 2 + … + n. 
M 
Used to represent a matrix or array of numbers or other entities. 
v> 
A column vector, that is one whose components are written as a
column and treated as a k by 1 matrix. 
<v 
A vector written as a row, or 1 by k matrix. 
dx 
An "infinitesimal" or very small change in the variable
x; also similarly dy, dz, dr etc... 
ds 
A small change in distance. 

The variable or
distance to the origin in spherical coordinates. 
r 
The variable
or distance to the z axis in three dimensions or in polar coordinates. 
M 
The determinant of a matrix M (whose magnitude is the area or
volume of the parallel sided region determined by its columns or rows). 
M 
The magnitude of the determinant of the matrix M, which is a volume
or area or hypervolume. 
det M 
The determinant of M. 

The inverse of the matrix M. 

The vector product or cross product of two vectors, v and
w. 

The angle made by vectors v and w. 

The scalar triple product, the determinant of the matrix formed
by columns A, B, C. 

A unit vector in the direction of the vector w; it means
the same as . 
df 
A very small change in the function f, sufficiently small that
the linear approximation to all relevant functions holds for such changes. 

The derivative of f with respect to x, which is the slope of the
linear approximation to f. 
f ' 
The derivative of f with respect to the relevant variable, usually
x. 

The partial derivative of f with respect to x, keeping y, and
z fixed. In general a partial derivative of f with respect to a variable q is
the ratio of df to dq when certain other variables are held fixed. Where there
is possible misunderstanding over which variables are to be fixed that information
should be made explicit. 

The partial derivative of f with respect to x keeping r and z
fixed. 
grad f 
The vector field whose components are the partial derivatives
of the function f with respect to x, y and z: ;
called the gradient of f. 

The vector operator ,
called "del". 

The gradient of f; its dot product with
is the directional derivative of f in the direction of w. 

The divergence of the vector field w; it is the dot product of
the vector operator with
the vector w, or . 
curl w 
The cross product of the vector operator with
the vector w. 

The curl of w, with components . 

The Laplacian, the differential operator: . 
f "(x) 
The second derivative of f with respect to x; the derivative of
f '(x). 

The second derivative of f with respect to x. 

Still another form for the second derivative of f with respect
to x. 

The kth derivative of f with respect to x; the derivative of
. 
T 
Unit tangent vector along a curve; if curve is described by r(t),. 
ds 
A differential of distance along a curve. 

The curvature of a curve; the magnitude of the derivative of its
unit tangent vector with respect to distance on the curve: . 
N 
A unit vector in the direction of the projection of normal
to T. 
B 
A unit vector normal to the plane of T and N, which
is the plane of curvature. 

The torsion of a curve; . 
g 
The gravitational constant. 
F 
The standard symbol for force in mechanics. 
k 
The spring constant of a spring. 

The momentum of the ith particle. 
H 
The Hamiltonian of a physical system, which is its energy expressed
in terms of ,
position and momentum. 
{Q, H} 
The Poisson bracket of Q and H. 

An antiderivative of f(x) expressed as a function of x. 

The definite integral of f from a to b. When f is positive and
a < b holds, then this is the area between the x axis the lines y = a, y =
b and the curve that represents the function f between these lines. 
L(d) 
A Reimann sum with uniform interval size d and f evaluated at
the left end of each subinterval. 
R(d) 
A Reimann sum with uniform interval size d and f evaluated at
the right end of each subinterval. 
M(d) 
A Reimann sum with uniform interval size d and f evaluated at
the maximum point of f in each subinterval. 
m(d) 
A Reimann sum with uniform interval size d and f evaluated at
the minimum point of f in each subinterval. 