CompositeSimpsonsRule (f,a,b,n)
Integration of f by Composite Simpson's Rule on the interval [a,b] with n subintervals with error of max(f'''')*h^4*(b-a)/180, note that n should be even.
See Planetmath for more information.
CompositeSimpsonsRuleTolerance (f,a,b,FourthDerivativeBound,Tolerance)
Integration of f by Composite Simpson's Rule on the interval [a,b] with the number of steps calculated by the fourth derivative bound and the desired tolerance.
See Planetmath for more information.
Derivative (f,x0)
Attempt to calculate derivative by trying first symbolically and then numerically.
InfiniteProduct (func,start,inc)
Try to calculate an infinite product for a single parameter function.
InfiniteProduct2 (func,arg,start,inc)
Try to calculate an infinite product for a double parameter function with func(arg,n).
InfiniteSum (func,start,inc)
Try to calculate an infinite sum for a single parameter function.
InfiniteSum2 (func,arg,start,inc)
Try to calculate an infinite sum for a double parameter function with func(arg,n).
IsContinuous (f,x0)
Try and see if a real-valued function is continuous at x0 by calculating the limit there.
IsDifferentiable (f,x0)
Test for differentiability by approximating the left and right limits and comparing.
LeftLimit (f,x0)
Calculate the left limit of a real-valued function at x0.
Limit (f,x0)
Calculate the limit of a real-valued function at x0. Tries to calculate both left and right limits.
MidpointRule (f,a,b,n)
Integration by midpoint rule.
NumericalDerivative (f,x0)
Aliases: NDerivative
Attempt to calculate numerical derivative.
NumericalIntegral (f,a,b)
Integration by rule set in NumericalIntegralFunction of f from a to b using NumericalIntegralSteps steps.
NumericalLeftDerivative (f,x0)
Attempt to calculate numerical left derivative.
NumericalLimitAtInfinity (_f,step_fun,tolerance,successive_for_success,N)
Attempt to calculate the limit of f(step_fun(i)) as i goes from 1 to N.
NumericalRightDerivative (f,x0)
Attempt to calculate numerical right derivative.
OneSidedFivePointFormula (f,x0,h)
Compute one-sided derivative using five point formula.
OneSidedThreePointFormula (f,x0,h)
Compute one-sided derivative using three-point formula.
RightLimit (f,x0)
Calculate the right limit of a real-valued function at x0.
TwoSidedFivePointFormula (f,x0,h)
Compute two-sided derivative using five-point formula.
TwoSidedThreePointFormula (f,x0,h)
Compute two-sided derivative using three-point formula.