Louisiana Tech University ME 291

Winter 1995-96

Mechanical Engineering Computer Applications

Dr. Melvin R. Corley

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

Newsgroup for Class

Syllabus last revised on Feb. 12, 1996

Class Schedule

1. Introduction and Organization
• Th 11/16: Introduction and Course Policies
2. Programming and Fundamentals of Numerical Error Analysis
• Tu 11/21: Truncation and Roundoff Error (pp. 7-37)

Computer Problem #1

Refer to the figure on page 43 of your textbook. If the figure is inverted, the shaded area could represent the liquid remaining in a partially filled horizontal cylindrical tank. Write a program that accepts as inputs the tank diameter and length (in feet) and prints a 10 row by 10 column chart which converts dipstick measurements ranging from 0.0 to 9.9 units into gallons of liquid remaining in the tank. To demonstrate your program, choose the tank length to be 20 feet and the tank diameter to be 10 feet. You may also add other test cases to demonstrate special features of your program. (Due: 11/30)

3. Simultaneous Algebraic Equations
• Tu 11/28: Classical Direct Methods (pp. 47-69)
• Th 11/30: LU Decomposition (pp. 70-105)

Computer Problem #2

A concrete mix was designed to have the weight proportions of [cement : fine aggregates : coarse aggregates] as [1: 1.9 : 2.8] with a water-cement ratio of 7 gallons of water per sack of cement. A sack of cement weighs 94 lb. The weight densities of the materials are as follows: Cement--195 lb/ft^3, Fine aggregates--165 lb/ft^3, Coarse aggregates--165 lb/ft^3, Water--62.4 lb/ft^3. How much of each constituent is needed to produce 50 cubic yards of concrete? (Due: 12/19)

4. Interpolation and Approximation
• Tu 12/05: Polynomial Interpolation (pp. 113-142)
• Th 12/07: Spline Interpolation (pp. 145-163)
5. Numerical Differentiation and Integration
• Tu 12/12: Classical Integration Formulas (pp. 177-213)
• Th 12/14: Richardson Extrapolation (pp. 214-220)
6. Pre-Holiday Exam Week
• Tu 12/19: EXAM #1 (MathCAD Solutions: Problem 1, Problem 2, Problem 3, Problem 4
7. Nonlinear Equations
• Th 01/04: Bracketing Methods (pp. 249-267)

Computer Problem #3

8. Simultaneous Nonlinear Equations
• Tu 01/09: Generalized Newton's Method (pp. 283-286)
• Th 01/11: Applications to Curve Fitting (pp. 297-312)
9. Ordinary Differential Equations
• Tu 01/16: Single Step Methods (pp. 359-368(
• Th 01/18: Runge-Kutta Methods (pp. 369-375)
10. Applications of Initial Value Problems
• Tu 01/23: Higher Order R-K Methods (pp. 376-379)

Computer Problem #4

• Th 01/25: Multi-Step Methods (pp. 380-395)
11. Boundary Value Problems
• Tu 01/30: Shooting Method (pp. 396-406)
• Th 02/01: Applications
12. Modern Programming Paradigms
• Tu 02/06: OOP Techniques
• Th 02/08: Visual Programming
13. Final Exam Week
• Tu 02/13: EXAM #2 (MathCAD Solutions: Problem 1, Problem 2, Problem 3

Grading

EXAM #1

20%

EXAM #2

30%

Homework and Computer Problems

50%

Useful pointers for this course:

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

Thanks for visiting the Louisiana Tech ME 291 home page. You are the [an error occurred while processing this directive] visitor since November 15, 1995.

I hope you will visit again soon.