Part Six Numerical Differentiation and Integration Motivation You encounter differentiation and integration every day !
Numerical Differentiation and Integration
You encounter differentiation and integration every day!
Differentiation:Almost all physical processes/phenomena are best cast in differentiation formExample: Newtons 2nd law: F = (dv/dt)m Heat conduction: Heat flux = -k’ (dT/dx) Our parachutist problem: dv/dt = (mg – cv)/m
Integration:Integration is commonplace in science and engineering
Urban area River cross-section Windblow on rocket
Differentiation: rate of change of a dependent variable with respect to an independent variable.
Integration: the integral of the function f(x) with respect to the independent variable x, evaluated between the limits x = a to x = b.
Example: numerical integration
There exist much more efficient and accurate numerical methods than these two! They are the ones we are to learn!