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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. Numeric calculus for double integrals. demo_ex2_4G.m. Example.

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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. Numeric calculus for double integrals 數值方法2008, Applied Mathematics NDHU

  10. demo_ex2_4G.m Example 2.230985172585607 by dblquard.m 數值方法2008, Applied Mathematics NDHU

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

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

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

  14. 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

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

  16. 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

  17. 數值方法2008, Applied Mathematics NDHU

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

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

  20. Mesh 數值方法2008, Applied Mathematics NDHU

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

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

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

  24. Composite Trapezoid rule 數值方法2008, Applied Mathematics NDHU

  25. Uniform mesh 數值方法2008, Applied Mathematics NDHU

  26. Error Analysis 數值方法2008, Applied Mathematics NDHU

  27. Partition size 數值方法2008, Applied Mathematics NDHU

  28. Composite Trapezoid rule • input s, a and b • f = inline(s); Set n • h = (b-a)/n; ans= 1/2*(f(a)+f(b)) • for i=1:n-1 add f(a+i*h) to ans • ans= ans*h 數值方法2008, Applied Mathematics NDHU

  29. Flow Chart Input s,a,b f = inline(s); Set n h = (b-a)/n; ans = 1/2*(f(a)+f(b)) for i=1:n-1 add f(a+i*h) to ans ans= ans*h EXIT 數值方法2008, Applied Mathematics NDHU

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

  31. Exercise • Draw a flow chart to illustrate integration by the composite Trapezoid rule • Implement the composite Trapezoid rule for numerical integration, including flow chart and Matlabcodes • 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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