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Unformatted text preview: 4/10/2011 1 • Integration • Trapezoidal rule • Riemann’s integral • Simpson’s rule • Matlab built in functions for integration Lecture 18: Numerical integration • Error analysis Integration For a function f , The “integral of f from a to b ” is the area under the graph of the function. If f is continuous, then the area is well defined, as the common limit of upper and lower sums. The integral is denoted If a function g is the primitive of f , namely for all x , then the fundamental theorem of calculus gives that the integral of f can be computed by evaluating g Integration x f x g b But finding primitives can be hard… In many cases of engineering and scientific (and economics, etc) interest – the functions do not have known primitives, so… – the integral (area) must be approximated by a finite number of function evaluations. ) ( ) ( ) ( a g b g dx x f a Discretization grid Exactly like in numerical differentiation, one creates a discrete grid on...
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- Spring '08
- Numerical Analysis, Riemann, trapezoidal integration