Introduction to Numerical Analysis for Engineers
• Interpolation 4.1-4.4
– Lagrange interpolation 4.3 – Triangular families 4.4 – Newton’s iteration method 4.4 – Equidistant Interpolation 4.4
• Numerical Differentiation 6.1-6.2
• Numerical Integration 7.1-7.3
– Error of numerical integration
Mathews
Numerical Differentiation
Taylor Series
First order
x f(x)
h
n=1
x f(x)
h h
n=2
Numerical Differentiation
Second order
Second Derivatives
Numerical Integration
x f(x)
a b
Lagrange Interpolation
Equidistant Sampling
Integration Weights (Cote’s Numbers)
Properties
Numerical Integration
Trapezoidal Rule
Simpson’s Rule
x f(x)
h
f(x) n=2
n=1
Numerical Integration Error Analysis
x f(x)
h h
Trapezoidal Rule
Local Absolute Error
Global Error
Simpson’s Rule
Local Error Global Error