Department of Physical Science and Engineering
Engineering Program
Welcome to Introductory Numerical Methods!
EGR 205 Introductory Numerical Methods
Reference No. 9276
Spring 2007

INSTRUCTOR: Dr. Scott D. Johnson, Associate Professor, Engineering Coordinator, Physical Sciences and Engineering


OTHER LOCATIONS: CH-308 (Faculty Resource Room) and CH-100 (Department)

PHONE NUMBERS: 301-386-7536 (Office) or 301-322-0420 (Department Main Line)


To facilitate e-mail communication with me, please include the following code: CCGP07 along with the course designation (EGR 205) in the subject of any e-mails to me during the Spring 2007 semester.

Example: EGR205: Need help on roots of equations: CCGP07


OFFICE HOURS: MW 7:15-7:45pm; TTh 5:35-7:30pm, by appointment all other times


The understanding of a variety of numerical methods is crucial to solving most high-level applications in engineering, physics, chemistry, and biology. This course, recognizing this fact, emphasizes case studies in a number of areas including mechanical, civil, environmental, electrical, aerospace, chemical, and biological engineering. Subjects to be studied include error analysis, roots of non-linear equations, systems of linear equations, optimization, curve fitting including splines, Fourier analysis, modeling, numerical differentiation and integration, and numerical solving of differential equations including, but not limited to, predictor-corrector methods and finite element analysis. Extensive surveys of a number of advanced subjects include digital filters, molecular dynamics, percolation, and Monte Carlo simulation methods. Some new mathematical concepts will be introduced in the class. A number of software packages important to engineering are surveyed with primary emphasis on MATLAB.


MAT 242, EGR 101 and some knowledge of computer programming.


Upon successful completion of the course a student will be able to

  1. Give an error on solutions to numerically solved problems and qualify that error.

  2. Demonstrate the ability to use the appropriate numerical methods to solve complex science or engineering problems.

  3. Use a software package to aid in the solution of a complex science or engineering problem.

  4. Solve for the roots, minimum, and maximum of an equation, solve a system of equations,fit a curve to a set of data, and perform numerical differentiation and integration.

  5. Perform a rudimentary Fourier analysis.

  6. Demonstrate an understanding of the numerical techniques to solve differential equations.


Numerical Methods for Engineers 5th Edition. Chapra,Steven and Canale, Raymond. McGraw-Hill. (2006).
MATLAB Tutorial CD: Learning MATLAB Superfast .  Daku, Brian.  John Wiley & Sons (2005).


Pocket Book for Technical Writing for Engineers and Scientists 3rd Edition .  Finkelstein, Leo.  McGraw-Hill (2007).
Schaum's Outline of Numerical Analysis 2nd Edition.  Scheid, Francis.  McGraw-Hill (1989).


  1. Pens, Pencils, Eraser, Straight edge, Paper, and Calculator are required for every class.


As with any class an amount of time at least equivalent to two times the credit hours is expected to be performed for homework and labs. Please allot sufficient time for homework.

Homework will be assigned each week including the first week.


Evaluation of student performance is to be based on:

  1. Unannounced quizzes and homework will account for approximately 25% of the semester grade. Homework consists of essays that are to be written in standard English format and problem sets.

  2. Four extensive projects will be assigned that will constitute 60% of the total grade. These projects are to be an original individual work. A grade of zero will be given to anyone who copies their projects.

  3. A four to five page essay surveying the material in the course. This essay is to include not just the methods but a practical guide on to when to use different numerical methods. This is worth approximately 15% of the semester grade.This project is to be an original individual work. A grade of zero will be given to anyone who copies their projects.


  1. Homework is due at the start of class (or before) except for in-class projects.

  2. Laboratory work is to be submitted in appropriate binders follow any standard laboratory format (this will be reviewed in class).

  3. Make-up homework, quizzes, and/or tests are up to the discretion of the teacher (excused absences only). No makeup will be possible for laboratory work, sufficient time should be available to recover if an absence is necessary.


New topics are to be covered each week and include but are not limited to the following subjects. This outline is subject to change.

Week 1 Introduction to Computational Methods: MATLAB and other programs ; IMSL, LAPACK, PPPACK and other libraries

Week 2 Modeling and Error Analysis

Week 3 Roots of Equations

Week 4 Roots of Equations

Week 5 Linear Algebraic Equations

Week 6 Linear Algebraic Equations

Week 7 Optimization

Week 8 Optimization

Week 9 Curve Fitting

Week 10 Fourier Analysis

Week 11 Numerical Differentiation

Week 12 Numerical Integration

Week 13 Differential Equations

Week 14 Finite Differences and Finite Element method

Week 15 Simulation methods: Molecular Dynamics, Monte Carlo, and Percolation

A new chapter should be read each week usually following the title of the topic above. Problems will be based off of the reading.

Quizzes will all be unannounced so be prepared.

Tests will be announced a week before and will depend on our progress in the classroom.


  1. Food and drink in limited quantities (snacks, not meals) are permitted in restricted areas (not near electronics) and will be revoked if proper cleanliness is found wanting.

  2. Cell phones must be in vibrate mode and are only to be answered for emergencies (step outside please).

  3. Common courtesy is to apply at all times.


Last day to apply for spring graduation

Thursday, February 15

President's Day. COLLEGE CLOSED

Monday, February 19

Last day to change from "audit to credit" or "credit to audit" for full-semester classes

Friday, February 23

Midterm - middle of semester; class will speed up

Tuesday, March 20

Spring break. COLLEGE CLOSED for the week.

Saturday-Friday, April 7 to April 13

Last day to withdraw from full-semester classes

Friday, April 20

Last Day of regular classes for the Spring Semester

Wednesday, May 9

Final exam period/last week of classes

Monday, May 14


Computer programming maybe done in class (CH-307) on the portable PCs during designated time periods.