# ME205: Numerical Methods for Engineers

## Course Syllabus for "ME205: Numerical Methods for Engineers"

Please note: this legacy course does not offer a certificate and may contain broken links and outdated information. Although archived, it is open for learning without registration or enrollment. Please consider contributing updates to this course on GitHub (you can also adopt, adapt, and distribute this course under the terms of the Creative Commons Attribution 3.0 license). To find fully-supported, current courses, visit our Learn site.

### Learning Outcomes

Upon successful completion of this course, the student will be able to:

• Quantify absolute and relative errors.
• Distinguish between round-off and truncation errors.
• Interconvert binary and base-10 number representations.
• Define and use floating-point representations.
• Quantify how errors propagate through arithmetic operations.
• Derive difference equations for first and second order derivatives.
• Evaluate first and second order derivatives from numerical evaluations of continuous functions or table lookup of discrete data.
• Describe situations in which numerical solutions to nonlinear equations are needed
• Implement the bisection method for solving equations.
• Implement both Newton-Raphson and secant methods.
• Describe the difference between Newton-Raphson and secant methods.
• Demonstrate the relative performance of bisection, Newton-Raphson, and secant methods.
• Define and identify special types of matrices.
• Perform basic matrix operations.
• Define and perform Gaussian elimination to solve a linear system.
• Identify pitfalls of Gaussian elimination.
• Define and perform Gauss-Seidel method for solving a linear system.
• Use LU decomposition to find the inverse of a matrix.
• Define and perform singular value decomposition; explain the significance of singular value decomposition.
• Define interpolation.
• Define and use direct interpolation to approximate data and find derivatives.
• Define and use Newton’s divided difference method of interpolation.
• Define and use Lagrange and spline interpolation.
• Define regression.
• Perform linear least-squares regression and nonlinear regression.
• Derive and apply the trapezoidal rule and Simpson’s rule of integration.
• Distinguish Simpson’s method from the trapezoidal rule.
• Estimate errors in trapezoidal and Simpson integration.
• Derive and apply Romberg and Gaussian quadrature for integration.
• Define and distinguish between ordinary and partial differential equations.
• Implement Euler’s methods for solving ordinary differential equations.
• Investigate how step size affects accuracy in Euler’s method.
• Implement and use the Runge-Kutta 2nd order method for solving ordinary differential equations.
• Apply the shooting method to solve boundary-value problems.
• Define Fourier series and the Fourier transform.
• Find Fourier coefficients for a given data set or function and domain.
• Describe the finite element method for one-dimensional problems.

### Course Requirements

In order to take this course, you must:

√    Have frequent broadband Internet access.

√    Have the ability/permission to install plug-ins or software (e.g. Adobe Reader or FLASH (see for solutions)).

√    Have the ability to download and save files and documents to a computer.

√    Have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.).

√    Be competent in the English language.

√    Have read the Saylor Student Handbook

√    Have completed the following courses from “The Core Program” of the Mechanical Engineering discipline: ME101, ME102, ME001/MA101, ME002/MA102, and ME003/MA221.

### Course Information

Welcome to ME101.  Below, please find general information on this course and its requirements.

Course Designers: Anonymous and Stephen Gibbs, Ph.D.

Peer Reviewers: Stephen Gibbs, Ph.D.

Primary Resources:  This course is composed of a range of different free, online materials. However, the course references the following free, online resources from academic institutions that are key to completing this course:

Requirements for Completion: In order to complete this course, you will need to work through each unit and all of its assigned materials.  Pay special attention to Unit 1, as this unit lays the groundwork for understanding the more advanced, exploratory material presented in the latter units. You will also need to complete:

• Unit 1 Quizzes
• Unit 2 Quizzes
• Unit 3 Quizzes
• Unit 4 Quizzes
• Unit 5 Quizzes
• Unit 6 Quizzes
• Unit 7 Quizzes
• Unit 8 Quizzes
• Unit 9 Quizzes
• Subunit 2.4 Assignment
• Subunit 4.6 Assignment
• Subunit 6.4 Assignment
• Subunit 8.2 Assignment
• The Final Exam

Each unit contains an assessment exercise and quizzes from the University of South Florida’s Holistic Numerical Methods Institute.  Please give time to these; they are the best way to test your knowledge and learn.

Note that you will only receive an official grade on your Final Exam.  However, in order to adequately prepare for this exam, you will need to work through the unit multiple choice quizzes and assignments listed above.

In order to “pass” this course, you will need to earn a 70% or higher on the Final Exam. Your score on the exam will be tabulated as soon as you complete it.  If you do not pass the exam, you may take it again.

Time Commitment: You should be able to complete this course in approximately 128 hours of study and creative effort.  Each unit includes a “time advisory” that lists the amount of time you are expected to spend on each subunit.  These should help you plan your time accordingly.  It may be useful to take a look at these time advisories and to determine how much time you have over the next few weeks to complete each unit, and then to set goals for yourself. For example, Unit 1 should take you 17 hours. Perhaps you can sit down with your calendar and decide to complete subunit 1.1 (a total of 2 hours) on Monday night; subunit 1.2 (a total of 3 hours) on Tuesday night; half of subunit 1.4 (about 2 hours) on Wednesday night; the remainder of subunit 1.4 (about 2 hours) on Thursday night; etc.

Tips/Suggestions: Most of the materials for this course are easy to read or study quickly; it is easy to convince yourself prematurely that you understand the material. Re-reading may be a useful technique to help better understand the material.  Most students learn this sort of material best by implementing example calculations either by hand or by machine. In fact, many students really begin to understand the underlying mathematics only after implementing numerical calculations by machine.

We encourage you to also take notes as you work through the course materials.  These notes will be useful as you prepare for your Final Exam.