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