Louisiana Tech University

ME 291

Winter 1999

Mechanical Engineering Computer Applications

Instructor: Dr. Melvin R. Corley

Textbook: An Introduction to Numerical Methods in C++, B.H. Flowers, Oxford, 1995, ISBN 0-19-853863-4

Discussion group for class

Syllabus last revised on February 3, 1999

Click here to view errata in PDF format.(Revised 12/22/1998)

Click here to download program listings from the book. (Revised 12/22/1998)
 
 
 
 
 
 
 
 
 

Class Schedule

1. Introduction and Organization
   • Th 12/03: Introduction, Course Policies, Coding Standards, Computer Program Report Format, programming tools for FORTRAN and C++
   • Program #1 (due 12/10): 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. You can find algorithms for computing machine epsilon by searching the Internet.
2. Programming and Fundamentals of Numerical Error Analysis
   • Tu 12/08: Truncation and Roundoff Error (pp. 53-65)
   • Th 12/10: Introduction to C++ classes for numerical computing (pp. 90-199)
   • Program #2 (due 12/18)
3. Roots of non-linear equations
   • Tu 12/15: Bracketing and Iterative Methods (pp. 66-82)
   • Th 12/17: Roots of Polynomials (pp. 82-89)
   • Program #3 (due 01/15)
4. DECEMBER 19 - JANUARY 3 
5. Direct Solution of Linear Equations
   • Tu 01/05: Gaussian Elimination (pp. 200-211)
   • Th 01/07: LU Decomposition (pp. 211-222)
6. Iterative Solution of Systems of Equations and Eigenvalue Problems
   • Tu 01/12: Jacobi and Gauss-Seidel Iteration (pp. 232-242)
   • Th 01/14: Power and Inverse Power Method (pp. 243-255)
   • Program #4 (due 01/29)
7. Matrix Eigenvalue Problems (cont'd)
   • Tu 01/19: Jacobi Rotation and Householder Methods (pp. 256-272)
   • Th 01/21: EXAM #1
8. Interpolation and Data Fitting
   • Tu 01/26: Interpolation and Data Fitting (pp. 273-290)
   • Th 01/28: Sorting (pp. 290-296)
   • Program #5 (due 02/12)
9. Differentiation and Integration
   • Tu 02/02: Differentiation and Newton-Cotes Integration (pp. 326-337)
   • Th 02/04: Adaptive Integration and Gaussian Integration (pp. 338-372)
10. Ordinary Differential Equations
    • Tu 02/09: Single Step Methods (pp. 371-382)
    • Th 02/11: Runge-Kutta Methods (pp. 382-389)
    • Program #6 (due 03/02)
11. Applications of Initial Value Problems
    • Tu 02/16: HOLIDAY
    • Th 02/18: Multi-Step Methods (pp. 389-402)
12. Boundary Value Problems
    • Th 02/23: Shooting Method (pp. 396-406)
    • Tu 02/25: Finite Difference Methods (pp. 413-427)
    • Tu 03/02: EXAM #2

Grading

 

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

Useful pointers for this course:

• Installation guide for DJGPP FORTRAN/C++ compiler
• Guide to Available Mathematical Software (GAMS)
• Numerical Algorithms Group
• Netlib
• IMSL
• RKSUITE
• Solving ODE's

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