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calculus1
http://www.openmath.org/cd
http://www.openmath.org/cd/calculus1.ocd
2014-04-01
official
2009-04-01
5
0
Author: OpenMath Consortium
SourceURL: https://github.com/OpenMath/CDs
This CD is intended to be compatible with the calculus operations
in Content MathML.
Integration is just for the univariate case and is either definite
or indefinite.
diff
application
This symbol is used to express ordinary differentiation of a unary
function. The single argument is the unary function.
diff(lambda y:a(y) + b(y))(x) = diff(lambda y:a(y))(x) + diff(lambda y:b(y))(x)
diff(lambda y:a(y) * b(y))(x) = diff(lambda y:a(y))(x) * b(x) +
a(x) * diff(lambda y:b(y))(x)
This represents the equation:
derivative(x + 1.0) = 1.0
nthdiff
application
This symbol is used to express the nth-iterated ordinary differentiation of
a unary function. The first argument is n, and the second the unary function.
partialdiff
application
This symbol is used to express partial differentiation of a function
of more than one variable. It has two arguments, the first is a list of
integers which index the variables of the function, the second is the function.
An example to represent the equation:
\partial^2{xyz}/ \partial{x}\partial{z} = y
1
3
partialdiffdegree
application
This symbol is used to express partial differentiation of a function
of more than one variable. It has three arguments, the first is a list of
integers which give the degrees by which the function is differentiated
by the corresponding variable. The second is the total degree (which should
therefore be the sum of the values in the first list, but may be
given symbolically). The third is the function.
An example to represent the equation:
\partial^2{xyz}/ \partial{x}\partial{z} = y
1
0
1
2
int
application
This symbol is used to represent indefinite integration of unary functions.
The argument is the unary function.
application of integrate followed by differentiate is the identity
function, that is:
diff(lambda y:integral(lambda z:f(z))(y)) = f
An example which represents the equation:
integral(x +-> sin(x)) w.r.t. x = x +-> -cos(x)
defint
application
This symbol is used to represent definite integration of unary
functions. It takes two arguments; the first being the range (e.g. a
set) of integration, and the second the function.
for all a,b | integral from a to b = -integral from b to a
for all a < b < c | integral over [a,c] = integral over [a,b] +
integral over [b,c]
An example to represent the definite integration of sin(x) between the points
-1.0 and 1.0.
An example to represent the definite integration of f(x), for x in the
set C: