數值方法 2008, Applied Mathematics NDHU 1 Numerical Integration

數值方法 2008, Applied Mathematics NDHU 2 Four 2-variate Gaussians

數值方法 2008, Applied Mathematics NDHU 3 Four 2-variate Gaussians

數值方法 2008, Applied Mathematics NDHU 4 Gaussian pdf

數值方法 2008, Applied Mathematics NDHU 5 Weight sum of Gaussian pdfs

數值方法 2008, Applied Mathematics NDHU 6 myfx4.m

數值方法 2008, Applied Mathematics NDHU 7 Plot 4G plot_4G.m

數值方法 2008, Applied Mathematics NDHU 8 Integration of 4G demo_int_4G.m Double integration

數值方法 2008, Applied Mathematics NDHU 9 exp(cos(x)) plot_expcos.m

數值方法 2008, Applied Mathematics NDHU 10 Definite Integration demo_quad.m

數值方法 2008, Applied Mathematics NDHU 11 Symbolic integration demo_int.m

數值方法 2008, Applied Mathematics NDHU 12 Example function of x:x.^2+2*x-5 fx1 = Inline function: fx1(x) = 1./3.*x.^3+x.^2-5.*x

數值方法 2008, Applied Mathematics NDHU 13 Numerical integration - quadrature

數值方法 2008, Applied Mathematics NDHU 14 Counter example >> demo_int function of x:(1-sin(x.^2)).^(1/3) Warning: Explicit integral could not be found.

數值方法 2008, Applied Mathematics NDHU 15

數值方法 2008, Applied Mathematics NDHU 16 plot_sin13.m

數值方法 2008, Applied Mathematics NDHU 17 Numerical integration demo_quad2.m

數值方法 2008, Applied Mathematics NDHU 18 Mesh

數值方法 2008, Applied Mathematics NDHU 19 Lower and upper sum

數值方法 2008, Applied Mathematics NDHU 20 Lower sum : lower bound

數值方法 2008, Applied Mathematics NDHU 21 Upper sum : upper bound

數值方法 2008, Applied Mathematics NDHU 22 Composite Trapezoid rule

數值方法 2008, Applied Mathematics NDHU 23 Uniform mesh

數值方法 2008, Applied Mathematics NDHU 24 Associate error

數值方法 2008, Applied Mathematics NDHU 25 Partition size

數值方法 2008, Applied Mathematics NDHU 26 Procedure: Composite Trapezoid rule 1. Get ss, a and b 2. Set fx to inline(ss); Set n 3. h = (b-a)/n; result = 1/2*(fx(a)+fx(b)); for i=1:n Add fx(a+i*h) to result Add fx(a+i*h) to result 4. Return result*h

數值方法 2008, Applied Mathematics NDHU 27 Simpson rule for numerical integration

數值方法 2008, Applied Mathematics NDHU 28 Exercise Due to 12/19 ► Implement the composite Trapezoid rule for numerical integration, including flow chart and Matlab codes ► Implement the composite Sympson rule for numerical integration, including flow chart and Matlab codes ► Test your matlab function with the following integration ► * Test your matlab function with definite integration of the weight sum of four Gaussian pdfs ► * Compare your results with those obtained by using quad.m f(x)=exp(cos(x))