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Welcome to EML3041: Computational Methods. SIT IN FIRST FOUR ROWS ONLY My name is Dr. Kaw.

Welcome to EML3041: Computational Methods. SIT IN FIRST FOUR ROWS ONLY My name is Dr. Kaw. Introduce yourself to the person on your left and right! Say one thing (nothing personal) about yourself to them! At home, go thru the piazza announcements.

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Welcome to EML3041: Computational Methods. SIT IN FIRST FOUR ROWS ONLY My name is Dr. Kaw.

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  1. Welcome to EML3041: Computational Methods. • SIT IN FIRST FOUR ROWS ONLY • My name is Dr. Kaw. • Introduce yourself to the person on your left and right! Say one thing (nothing personal) about yourself to them! • At home, go thru the piazza announcements. • All is well that ends well; well-begun is half-done. • No cell phones, laptops or other distractions. Daydreamers and sleepers will not be disturbed! http://nm.MathForCollege.com

  2. Introduction to Scientific Computing http://nm.MathForCollege.com Transforming Numerical Methods Education for STEM Undergraduates http://nm.MathForCollege.com

  3. My advice • If you don’t let a teacher know at what level you are by asking a question, or revealing your ignorance you will not learn or grow. • You can’t pretend for long, for you will eventually be found out. Admission of ignorance is often the first step in our education. • Steven Covey—Seven Habits of Highly Effective People http://nm.MathForCollege.com

  4. Why use Numerical Methods?

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

  6. Why use Numerical Methods? • To solve problems that are intractable to solve exactly!

  7. Steps in Solving anEngineering Problemhttp://nm.MathForCollege.com http://nm.MathForCollege.com

  8. Problem Description Mathematical Model Solution of Mathematical Model Using the Solution How do we solve an engineering problem? http://nm.MathForCollege.com

  9. Example of Solving an Engineering Problem http://nm.MathForCollege.com

  10. Bascule Bridge THG http://nm.MathForCollege.com

  11. Bascule Bridge THG Hub Trunnion Girder http://nm.MathForCollege.com

  12. Trunnion-Hub-Girder Assembly Procedure Step1. Trunnion immersed in dry-ice/alcohol Step2. Trunnion warm-up in hub Step3. Trunnion-Hub immersed in dry-ice/alcohol Step4. Trunnion-Hub warm-up into girder http://nm.MathForCollege.com

  13. Problem After Cooling, the Trunnion Got Stuck in Hub http://nm.MathForCollege.com

  14. Why did it get stuck? Magnitude of contraction needed in the trunnion was 0.015” or more. Did it contract enough? http://nm.MathForCollege.com

  15. Video of Assembly Process Unplugged Version VH1 Version http://nm.MathForCollege.com

  16. Consultant calculations http://nm.MathForCollege.com

  17. Is the formula used correct? http://nm.MathForCollege.com

  18. The Correct Model Would Account for Varying Thermal Expansion Coefficient http://nm.MathForCollege.com

  19. Can You Roughly Estimate the Contraction? Ta=80oF; Tc=-108oF; D=12.363” http://nm.MathForCollege.com

  20. Can You Find a Better Estimate for the Contraction? Ta = 80oF Tc = -108oF D = 12.363" http://nm.MathForCollege.com

  21. Estimating Contraction Accurately Change in diameter (D) by cooling it in dry ice/alcohol is given by Ta = 80oF Tc = -108oF D = 12.363" http://nm.MathForCollege.com

  22. So what is the solution to the problem? One solution is to immerse the trunnion in liquid nitrogen which has a boiling point of -321oF as opposed to the dry-ice/alcohol temperature of -108oF. http://nm.MathForCollege.com

  23. Revisiting steps to solve a problem 1) Problem Statement: Trunnion got stuck in the hub. 2) Modeling: Developed a new model 3) Solution: 1) Used trapezoidal rule OR b) Used regression and integration. 4) Implementation: Cool the trunnion in liquid nitrogen. http://nm.MathForCollege.com

  24. THE END http://nm.MathForCollege.com http://nm.MathForCollege.com

  25. Introduction to Numerical MethodsMathematical Procedures http://nm.MathForCollege.com http://nm.MathForCollege.com

  26. 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 http://nm.MathForCollege.com

  27. Nonlinear Equations How much of the floating ball is under water? Diameter=0.11m Specific Gravity=0.6 http://nm.MathForCollege.com

  28. Nonlinear Equations How much of the floating ball is under the water? http://nm.MathForCollege.com

  29. Differentiation What is the acceleration at t=7 seconds? http://nm.MathForCollege.com

  30. Differentiation What is the acceleration at t=7 seconds? http://nm.MathForCollege.com

  31. Simultaneous Linear Equations Find the velocity profile, given Three simultaneous linear equations http://nm.MathForCollege.com

  32. Interpolation What is the velocity of the rocket at t=7 seconds? http://nm.MathForCollege.com

  33. Regression Thermal expansion coefficient data for cast steel http://nm.MathForCollege.com

  34. Regression (cont) http://nm.MathForCollege.com

  35. Integration Finding the diametric contraction in a steel shaft when dipped in liquid nitrogen. http://nm.MathForCollege.com

  36. Ordinary Differential Equations How long does it take a trunnion to cool down? http://nm.MathForCollege.com

  37. Additional Resources For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, MathCad and MAPLE, blogs, related physical problems, please visit http://nm.MathForCollege.com/topics/introduction_numerical.html

  38. THE END http://nm.MathForCollege.com

  39. Passing this course http://nm.MathForCollege.com

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