Calculus

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