1. 數值方法 2008, Applied Mathematics NDHU 1 Numerical Integration

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

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

4. 數值方法 2008, Applied Mathematics NDHU 4 Gaussian pdf

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

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

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

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

9. 數值方法 2008, Applied Mathematics NDHU 9 Numeric calculus for double integrals

10. 數值方法 2008, Applied Mathematics NDHU 10 Example Approx. integral2.230985141404140 True Integral2.230985141404130 demo_ex2_4G.m 2.230985172585607 by dblquard.m

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

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

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

14. Example 數值方法 2008, Applied Mathematics NDHU 14 function of x:x.^2+2*x-5 fx1 = Inline function: fx1(x) = 1./3.*x.^3+x.^2-5.*x

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

16. 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.

17. 數值方法 2008, Applied Mathematics NDHU 17

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

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

20. 數值方法 2008, Applied Mathematics NDHU 20 Mesh

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

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

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

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

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

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

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

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 28

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

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

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 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 數值方法 2008, Applied Mathematics NDHU 31 f(x)=exp(cos(x))