Numerical integration and differentiation

Concepts

• Trapezoidal rule 10 exercisesThe trapezoidal rule is a quadrature method that approximates the definite integral of a function f on [a,b] by replacing the cur…
• Simpson's rule 10 exercisesSimpson's rule is a numerical quadrature method that approximates ∫_a^b f(x) dx by integrating a quadratic polynomial that interp…
• Gaussian quadrature 10 exercisesNumerical integration method that chooses optimal nodes x_i and weights w_i to approximate an integral with the highest possible…
• Finite differences for derivatives 10 exercisesFinite differences are approximations of the derivatives of a function f from its values at discrete points separated by a step h…
• Riemann integral from Real analysis 10 exercisesA bounded function f on [a,b] is integrable if the supremum L(f) of its lower sums and the infimum U(f) of its upper sums, over p…