1. The taylor series and Numerical Differentiation
Fisika Komputasi
The taylor series and Numerical Differentiation
Computational Physics

2. The Taylor Series
(1)
f (x)
f (x0) x x0

3. The Taylor Series Nilai fungsi pada titik x0+Dx (2)
(3)

4. The Taylor Series

5. The Taylor Series

6. EXAMPLE 1

7. EXAMPLE 1

8. Numerical Differentiation
Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point.
In numerical analysis, numerical differen-tiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.

9. Numerical Differentiation
Forward Difference Approximation of the First Derivative
h is called the step size

10. Numerical Differentiation
Backward Difference Approximation of the First Derivative

11. Numerical Differentiation
Centered Difference Approximation of the First Derivative
(-)

12. Numerical Differentiation
Finite Difference Approximations of Higher Derivatives +

13. Numerical Differentiation
Finite Difference Approximations of Higher Derivatives
(1)
(2)
Equation (2) can be multiplied by 2 and subtracted from Eq. (1) to give
The second forward finite divided difference.

14. Numerical Differentiation
The second backward finite divided difference.
The second centered finite divided difference.

15. Numerical Differentiation

16. Numerical Differentiation

17. Numerical Differentiation

18. Numerical Differentiation

19. Derivative from difference tables

21. Derivative from difference tables

22. Derivative from difference tables

23. NUMERICAL DIFFERENTIATION PROBLEMS

24. NUMERICAL DIFFERENTIATION PROBLEMS

25. NUMERICAL DIFFERENTIATION
PROBLEMS

26. NUMERICAL DIFFERENTIATION PROBLEMS

27. Numerical Differentiation

28. Numerical Differentiation

29. Numerical Differentiation