Transcription of Chapter 5: Numerical Integration and Differentiation
{{id}} {{{paragraph}}}
Example: biology
Chapter 5: Numerical Integration and Differentiation
Chapter 5: Numerical Integration and DifferentiationPART I: Numerical IntegrationNewton-Cotes Integration FormulasThe idea of Newton-Cotes formulas is to replace a complicated function or tabu-lated data with an approximating function that is easy to baf(x)dx bafn(x)dxwherefn(x) =a0+a1x+a2x2+..+ Trapezoidal RuleUsing the first order Taylor series to approximatef(x),I= baf(x)dx baf1(x)dxwheref1(x) =f(a) +f(b) f(a)b a(x a)1 ThenI ba[f(a) +f(b) f(a)b a(x a)]dx= (b a)f(b) +f(a)2 The trapezoidal rule is equivalent to approximating the area of the trapezoidalFigure 1: Graphical depiction of the trapezoidal ruleunder the straight line connectingf(a)andf(b).
Chapter 5: Numerical Integration and Differentiation PART I: Numerical Integration Newton-Cotes Integration Formulas The idea of Newton-Cotes formulas is to replace a complicated function or tabu-lated data with an approximating function that is easy to integrate. I = Z b a f(x)dx … Z b a fn(x)dx where fn(x) = a0 +a1x+a2x2 +:::+anxn. 1 The ...
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: