Louisiana Tech University

ME 292

Fall 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
Supplementary Text: Elementary Numerical Methods and C++, M.R. Corley. (Available for cost of duplication from College Discount Supply, Ruston)

Discussion group for class

Syllabus last revised on November 2, 1999

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

Click here to download program listings from the book. (Revised 04/20/1999)
 
 
 
 
 
 
 
 
 

Class Schedule

1. Introduction and Organization
   • F 09/03: Introduction, Course Policies, Coding Standards, Computer Program Report Format, Course Educational Objectives, DJGPP software installation instructions, programming tools for C++
   • Program #1 (due 09/10) Write a C++ program patterned after the one on page 1 of your textbook that introduces yourself to the instructor. The program should supply your name and a few facts about yourself, such as where you are from, what previous programming experience you have had, and other interesting stuff. The purpose of this assignment is see if you can successfully install and run the C++ compiler and follow the coding and report standards for the course.
   • M 09/06: Labor Day Holiday
2. C++ Basics
   • W 09/08: Writing the first program (pp. 1-19)
   • F 09/10: Constants and variables, data types (Notes)
   • Program #2 (due 09/17) Write a C++ program that illustrates common mathematical operations involving int, float, and double data types. Create int variables ia = 1, ib = 2, and ic = 3; float variables fa = 1.0, fb = 2.0, and fc = 3.0; and double variables da = 1.0, db = 2.0, and dc = 3.0. Your program should print out the results of several different expressions using the addition, subtraction, multiplication, and division operators with these variables. Be sure to include some expressions that involve integer division. Your discussion of results will be very important for this program.
   • M 09/13: Expressions (pp. 20-25)
   • W 09/15: Statements (pp. 25-30)
   • F 09/17: Selection and Repetition (pp. 30-37)
   • Program #3 (due 09/27) You are given the task of designing an industrial drying oven. Material that is 99% water is placed in the oven in 100 lbm batches. How many pounds of water must be removed for the moisture content to be reduced to 98%? Find the solution to this problem by setting up a repetition structure that successively subtracts a fixed amount of water until the desired moisture content is reached. Print a table of the moisture percentage as a function of the amount of water removed.
   • M 09/20: Repetition statements (pp. 30-57)
   • W 09/22: Functions (pp. 37-52)
   • F 09/24: Passing function arguments (pp. 37-52)
   • M 09/27: Working with projects (Notes)
   • Program #4 (due 10/04) The Maclaurin series expansion for sine(x) is:
     sine(x)= x - (x**3)/3! + (x**5)/5! - (x**7)/7! + . . .
     Write a C++ program that uses functions to compute this series two different ways. The first method simply computes each term as it is written and adds it to the total. (Note: you will have to write a factorial function.) The second method should exploit the fact that each succeeding term can be calculated by multiplying the preceding term by -x**2/(n*(n+1)). Test your program by computing the sine of 30, 60, 90, 450, 810, and 1170 degrees using 5, 10, 20, 40, and 60 terms of the series, respectively.
   • W 09/29: EXAM #1 (Here's a practice exam for your reference.)
3. Programming and Fundamentals of Numerical Error Analysis
   • F 10/01: Truncation and Roundoff Error (pp. 53-65)
   • M 10/04: Introduction to C++ classes for numerical computing (pp. 90-199)
   • Program #5 (due 10/11) You wish to measure the rainfall of an approaching thunderstorm, but all you have available is a galvanized pail having the following dimensions: base diameter - 8.5 inches, top diameter - 11 inches, height - 10 inches. Recognizing that the tapered wall of the pail will produce an inaccurate reading, you choose to make a calibrated depth gage for the bucket. Write a C++ program that will determine how far from the end of the gage you would place marks corresponding to rainfall amounts in increments of 0.5 inch.
4. Roots of non-linear equations
   • W 10/06: Bracketing and Iterative Methods (pp. 66-82)
   • F 10/08: Roots of Polynomials (pp. 82-89)
5. Direct Solution of Linear Equations
   • M 10/11: Gaussian Elimination (pp. 200-211)
   • Program #6 (due 10/20) Matrices are used extensively in computer graphics applications. For a brief introduction, click here. Write a C++ program that uses the enmvec and enmmat classes to construct a transformation matrix that will transform a 1 by 1 rectangle originally centered at position (6,0) so that its new center is at (-3,7). As the rectangle is moved, it grows in size by a factor of 2 and also rotates 15 degrees counterclockwise about its own center. Print out a sequence of transformation matrices that will accomplish this task and show the coordinates of the four corners of the rectangle after each step of the transformation. Construct a composite transformation matrix that does the entire sequence in one step. Print this matrix and apply it to the original data and show that the transformed rectangle is the same as the one obtained using the step by step approach.
   • W 10/13: LU Decomposition (pp. 211-222)
6. Iterative Solution of Systems of Equations and Eigenvalue Problems
   • F 10/15: Introduction to Classes
   • M 10/18: Jacobi and Gauss-Seidel Iteration (pp. 232-242)
7. Matrix Eigenvalue Problems (cont'd)
   • W 10/20: Power and Inverse Power Method (pp. 243-255)
   • Program #7 (due 10/27) A digital flowmeter samples the water velocity in a 12-inch schedule 40 cast iron water main every 5 minutes. Write a C++ program that will use the thirteen velocity measurements (ft/sec) below taken over a one-hour period to calculate the number of gallons of water supplied by the water main.
     DATA: 3.2, 3.8, 4.4, 4.5, 4.5, 5.2, 5.0, 5.4, 5.5, 5.2, 5.0, 4.8, 4.7
   • F 10/22: Jacobi Rotation and Householder Methods (pp. 256-272)
8. Interpolation and Data Fitting
   • M 10/25: EXAM #2
   • W 10/27: Interpolation and Data Fitting (pp. 273-290)
   • Program #8 (due 11/03) Write a C++ program that will find the coefficients of the least-squares polynomials of degree zero through twelve for the data used in Program #7. Plot the original data and the three best least-squares polynomial approximations (in your opinion). Justify your choices of the best curve fits. Do not use MathCad to generate publication quality plots! Spreadsheets such as Excel and Quattro generate much more professional looking plots.
9. Differentiation and Integration
   • F10/29: Sorting (pp. 290-296)
   • M 11/01: Differentiation and Newton-Cotes Integration (pp. 326-337)
10. Ordinary Differential Equations
    • W 11/03: Adaptive Integration and Gaussian Integration (pp. 338-372)
    • Program #9 (due 11/12)
    • F 11/05: Single Step Methods (pp. 371-382)
11. Applications of Initial Value Problems
    • M 11/08: Runge-Kutta Methods (pp. 382-389)
    • W 11/10: Multi-Step Methods (pp. 389-402)
12. Boundary Value Problems
    • F11/12: Shooting Method & Finite Difference Method (pp. 396-427)
    • M 11/15: EXAM #3

Grading

 

EXAM #1	20%
EXAM #2	20%
EXAM #3	25%
Homework and Computer Problems	35%

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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