Louisiana Tech University ME 291

Summer 1997

Mechanical Engineering Computer Applications

Textbook: An Introduction to Numerical Computations, 2nd edition, Yakowitz and Szidarovszky, Macmillan, 1989, ISBN 0-02-430821-

Discussion group for class

Syllabus last revised on August 7, 1997

Class Schedule

1. Introduction and Organization
• Th 06/05: Introduction, Course Policies, Coding Standards, programming tools for FORTRAN and C++
• Program #1 (due 06/12): Write a program that will compute the value of machine epsilon for both single precision (float) and double precision (double) arithmetic. (Extra credit: calculate machine epsilon for extended precision (long double).) Your main program should be a driver that calls functions to evaluate machine epsilon in their respective precision. These functions should be patterned after the routine shown in Table 1.5 of your textbook, but yours should work correctly.
2. Programming and Fundamentals of Numerical Error Analysis
• Tu 06/10: Truncation and Roundoff Error (pp. 7-37)
• Th 06/12: Introduction to vmpclass.h
3. Simultaneous Algebraic Equations
• Tu 06/17: Classical Direct Methods (pp. 47-69)
• Program #2 (due 06/26)
• Th 06/19: LU Decomposition (pp. 70-105)
4. Interpolation and Approximation
• Tu 06/24: Polynomial Interpolation (pp. 113-142)
• Th 06/26: Spline Interpolation (pp. 145-163)
• Program #3 (due 07/15): Work problem 19 on page 224 of your textbook.
5. Numerical Differentiation and Integration
• Tu 07/01: Classical Integration Formulas (pp. 177-213)
• Th 07/03: HOLIDAY
6. Adaptive Integration
• Tu 07/08: Richardson Extrapolation (pp. 214-220)
• Th 07/10: EXAM #1
7. Nonlinear Equations
• Tu 07/15: Bracketing Methods (pp. 249-267)
• Th 07/17: Other methods (pp. 268-282)
• Program #4 (due 07/31)
8. Simultaneous Nonlinear Equations
• Tu 07/22: Generalized Newton's Method (pp. 283-286)
• Th 07/24: Applications to Curve Fitting (pp. 297-312)
9. Ordinary Differential Equations
• Tu 07/29: Single Step Methods (pp. 359-368)
• Th 07/31: Runge-Kutta Methods (pp. 369-375)
10. Applications of Initial Value Problems
• Tu 08/05: Higher Order R-K Methods (pp. 376-379)
• Th 08/07: Multi-Step Methods (pp. 380-395)
• Program #5 (due 08/15): A regulation baseball having a circumference of 9.5 inches and weighing 5.25 ounces is "launched" by a batter from a position exactly 2 feet above home plate. We wish to determine the minimum launch velocity that will place the baseball exactly on the top of the center field fence which is 420 ft. from home plate. The required launch velocity is dependent on the angle of departure from home plate. Assume the drag coefficient for the ball is 0.5. The drag force can be calculated as 0.5 * Cd * A * v^2, where A is the projected area of the ball and v is the speed of the ball. Be sure to use consistent units. Write and execute a program that will solve the dynamic equations for this system for launch angles ranging from near theoretical minimum to near 90 degrees. Make a graph of minimum launch velocity versus launch angle. Run your program for both a field at sea level and one at 5,000 ft. above sea level (Coors Field).
11. Boundary Value Problems
• Tu 08/12: Shooting Method (pp. 396-406)
• Th 08/14: EXAM #2

Grading

 

EXAM #1	20%
EXAM #2	30%
Homework and Computer Problems	50%

 

Useful pointers for this course:

• Numerical Algorithms Group
• Netlib
• IMSL
• Hints on using RKF45
• RKF45.cpp and rkf45.h

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