10.11. Calculus

CompositeSimpsonsRule
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
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
Derivative (f,x0)

Attempt to calculate derivative by trying first symbolically and then numerically.

InfiniteProduct
InfiniteProduct (func,start,inc)

Try to calculate an infinite product for a single parameter function

InfiniteProduct2
InfiniteProduct2 (func,arg,start,inc)

Try to calculate an infinite product for a double parameter function with func(arg,n)

InfiniteSum
InfiniteSum (func,start,inc)

Try to calculate an infinite sum for a single parameter function

InfiniteSum2
InfiniteSum2 (func,arg,start,inc)

Try to calculate an infinite sum for a double parameter function with func(arg,n)

IsContinuous
IsContinuous (f,x0)

Try and see if a real-valued function is continuous at x0 by calculating the limit there

IsDifferentiable
IsDifferentiable (f,x0)

Test for differentiability by approximating the left and right limits and comparing

LeftLimit
LeftLimit (f,x0)

Calculate the left limit of a real-valued function at x0

Limit
Limit (f,x0)

Calculate the limit of a real-valued function at x0. Tries to calculate both left and right limits.

MidpointRule
MidpointRule (f,a,b,n)

Integration by midpoint rule

NumericalDerivative
NumericalDerivative (f,x0)

Aliases: NDerivative

Attempt to calculate numerical derivative

NumericalIntegral
NumericalIntegral (f,a,b)

Integration by rule set in NumericalIntegralFunction of f from a to b using NumericalIntegralSteps steps

NumericalLeftDerivative
NumericalLeftDerivative (f,x0)

Attempt to calculate numerical left derivative

NumericalLimitAtInfinity
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
NumericalRightDerivative (f,x0)

Attempt to calculate numerical right derivative

OneSidedFivePointFormula
OneSidedFivePointFormula (f,x0,h)

Compute one-sided derivative using five point formula

OneSidedThreePointFormula
OneSidedThreePointFormula (f,x0,h)

Compute one-sided derivative using three-point formula

RightLimit
RightLimit (f,x0)

Calculate the right limit of a real-valued function at x0

TwoSidedFivePointFormula
TwoSidedFivePointFormula (f,x0,h)

Compute two-sided derivative using five-point formula

TwoSidedThreePointFormula
TwoSidedThreePointFormula (f,x0,h)

Compute two-sided derivative using three-point formula