calculus1 http://www.openmath.org/cd/calculus1.ocd 2003-04-01 official 2001-03-12 2 0 arith1 fns1 interval1 list1 transc1 relation1 quant1 logic1 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 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 partialdiff 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 int 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: lambda x:diff(lambda y:integral(lambda z:f(z))(y))(x) = lambda x:f(x) An example which represents the equation: integral(x +-> sin(x)) w.r.t. x = x +-> -cos(x) defint 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: