MATH582

diff_backward(f, x; h = sqrt(eps(Float64)))

Compute the backward finite difference approximation of the derivative of f at point x.

Arguments

• f::Function: A univariate real-valued function.
• x::Real: The point at which to approximate the derivative.
• h::Real: Step size (default: sqrt(eps(Float64))).

Returns

• An approximation of f′(x) using the backward difference: $f'(x) ≈ (f(x) - f(x - h)) / h$

Example

diff_backward(log, 2.0)

diff_central(f, x; h = cbrt(eps(Float64)))

Compute the central finite difference approximation of the derivative of f at point x.

Arguments

• f::Function: A univariate real-valued function.
• x::Real: The point at which to approximate the derivative.
• h::Real: Step size (default: cbrt(eps(Float64))).

Returns

• An approximation of f′(x) using the central difference: $f'(x) ≈ (f(x + h/2) - f(x - h/2)) / h$

Example

diff_central(exp, 1.0)

diff_forward(f, x; h = sqrt(eps(Float64)))

Compute the forward finite difference approximation of the derivative of f at point x.

Arguments

• f::Function: A univariate real-valued function.
• x::Real: The point at which to approximate the derivative.
• h::Real: Step size (default: sqrt(eps(Float64))).

Returns

• An approximation of f′(x) using the forward difference: $f'(x) ≈ (f(x + h) - f(x)) / h$

Example

diff_forward(sin, π/4)