1. 1 NUMERICAL METHOD

2. 2 Introduction Definition : The study of approximation techniques for solving mathematical problems, taking into account the extent of possible errors.

3. Why use Numerical Methods? To solve problems that cannot be solved exactly

4. Why use Numerical Methods? To solve problems that are intractable!

5. 5 Steps in Solving a Mathematical Problem

6. 6 How do we solve a mathematical problem? Problem Description Mathematical Model Solution of Mathematical Model Using the Solution Prosedure/ Numerical

7. 7 Mathematical Procedures

8. 8 Nonlinear Equations Differentiation Simultaneous Linear Equations Curve Fitting –Interpolation –Regression Integration Ordinary Differential Equations Other Advanced Mathematical Procedures: –Partial Differential Equations –Optimization –Fast Fourier Transforms

9. 9 Nonlinear Equations How much of the floating ball is under water? Diameter=0.11m Specific Gravity=0.6

10. 10 Nonlinear Equations How much of the floating ball is under the water?

11. 11 Differentiation What is the acceleration at t=7 seconds?

12. 12 Differentiation Time (s)5812 Vel (m/s)106177600 What is the acceleration at t=7 seconds?

13. 13 Simultaneous Linear Equations Find the velocity profile, given Three simultaneous linear equations Time (s)5812 Vel (m/s)106177600

14. 14 Interpolation What is the velocity of the rocket at t=7 seconds? Time (s)5812 Vel (m/s)106177600

15. 15 Regression Thermal expansion coefficient data for cast steel

16. 16 Regression (cont)

17. 17 Integration Finding the diametric contraction in a steel shaft when dipped in liquid nitrogen.

18. 18 Ordinary Differential Equations How long does it take a trunnion to cool down?