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NUMERICAL METHOD

NUMERICAL METHOD. Introduction. Definition : The study of approximation techniques for solving mathematical problems, taking into account the extent of possible errors. Why use Numerical Methods?. To solve problems that cannot be solved exactly. Why use Numerical Methods?.

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NUMERICAL METHOD

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  1. NUMERICAL METHOD

  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. Steps in Solving aMathematical Problem

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

  7. Mathematical Procedures

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

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

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

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

  13. Simultaneous Linear Equations Find the velocity profile, given Three simultaneous linear equations

  14. Interpolation What is the velocity of the rocket at t=7 seconds?

  15. Regression Thermal expansion coefficient data for cast steel

  16. Regression (cont)

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

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

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