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Numerical Integration

Numerical Integration. Four 2-variate Gaussians. Four 2-variate Gaussians. Gaussian pdf. Weight sum of Gaussian pdfs. myfx4.m. Plot 4G. plot_4G.m. Integration of 4G. demo_int_4G.m. Double integration. exp( cos (x)). plot_expcos.m. Definite Integration. demo_quad.m.

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Numerical Integration

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  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 • Get ss, a and b • Set fx to inline(ss); Set n • h = (b-a)/n; result = 1/2*(fx(a)+fx(b)); for i=1:n Add fx(a+i*h) to result • 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)) 數值方法2008, Applied Mathematics NDHU

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