ECIV 301

Programming & Graphics

Numerical Methods for Engineers

Lecture 27

Numerical Integration & Differentiation

Motivation

x

xfxxf

x

y ii

Motivation

x

xfxxf

x

y ii

Motivation

x

xfxxf

dx

dy ii

x

0lim

Motivation

b

a

dxxfI

AREA BETWEEN a AND b

Motivation

)()( tydt

dtv

Motivation

b

a

dxtvty

Motivation

Motivation

Calculate Derivative

Given

MotivationGiven

Calculate

Think as Engineers!

In Summary

INTERPOLATE

In SummaryNewton-Cotes Formulas

Replace a complicated function or tabulated data with an approximating

function that is easy to integrate

b

a

n

b

a

dxxfdxxfI

nn

nnon xaxaxaaxf

111

In Summary

Also by piecewise approximation

b

ax

x

x

n

b

a

i

i

i

dxxf

dxxfI

1

Closed/Open Forms

CLOSED OPEN