Math 5070

MATH 5070 - Numerical Analysis I

The analysis and use of numerical algorithms for the solution of nonlinear equations, systems of linear equations, interpolation, numerical differentiation and integration.

Note: Open to upper-level undergraduate and graduate students.

Prerequisites and Corequisites: Prerequisite: MATH 3740 (with grade of “C” or better) and a computer programming language beyond Basic, (e.g., Fortran or C).

Credits: 3 hours

 

• Students should know how IEEE arithmetic works, including number representations and rounding.

• Students should know the basics of computation using Scilab, using functions in Scilab, and how to make files so that others can reproduce their work.

• Students should know and be able to use error analysis, machine epsilon, rounding, absolute and relative error, and the condition of a problem.

• Students should be able to find the roots of a function of 1 variable using bisection, the secant method, and Newton's method. Students should be able to find the numerical errors for such methods.

• Students should be able use Gaussian elimination and other methods for solving linear systems of equations and know how to find and use the condition number for a matrix to understand possible errors. Students should also be able to show how many steps or operations are required to solve linear systems.

• Students should know how to interpolate using polynomials in different forms and understand the errors for such interpolations. Students should also know how to interpolate using cubic splines.

• Students should know how to derive formulas for numerical derivatives estimates and their errors. This includes Richardson extrapolation.

• Students should be able to do numerical integration using Newton-Cotes formulas and Gaussian quadrature.

 

The prerequisite for this class is Math 3740 at WMU. It is important that you have some experience with computer programming.

You are responsible for all material in the text and all material presented in class. This includes any material not in the text and all material in the text that was not presented in class.  A list of topics may be available.

It is expected that you will spend at least 3 to 4 hours outside class for every hour in class. Even though roll will not be taken, you are expected to attend all classes.

A list of expectations may be available.

You are expected to follow all university policies.

The last day to withdraw is October 28, 2024. A tentative schedule may be available.

 

All cameras, cell phones, wireless devices, mp3/mp4 type media players, and similar devices are to be turned off and put away while you are in the classroom. If you ask, you may get an exception for note taking. This means taking written notes, not recording the class. Use of one of these devices during a quiz/exam is forbidden and will be considered cheating.

 

A list of problems to work will be on this web site. You are responsible for all of the problems. If you have any questions about problems, please ask them in class or in office hours.

All written homework will be submitted as a PDF file through a dropbox in e-learning. Submit all written assignments as a single PDF file containing the solutions to all of the assigned problems. The problems must be legible and in order of section and the numerical order, e.g. section 2.1 problem 1, section 2.1 problem 5, section 2.2 problem 2,... All pages in your PDF must be the same size. If a signed statement is required for the assignment, it is to be the first page of your submission with a written, not typed, signature. Do not submit a zip file. Your name must be in the name of the file. Make certain that you have clicked the submit button for the dropbox in e-learning.

If you are using a cell phone to scan your documents it is strongly suggested that you use Adobe Scan or Microsoft Lens. These both give higher quality scans than I have seen from CamScan. If your assignment is hard to read, it may be returned without being graded.

 

There will be a number of computer assignments and projects beyond the problems in the text. The assignments will be posted in the dropbox section of elearning. The assignments are to be done using Scilab 2024.

All Scilab assignments are to be submitted as a single Scilab *.sce file. Your name must be included in the file name. Any assignments submitted as zip files will not be graded. Further instructions will be included in the drop box. Failure to follow the instructions may mean your assignment will not be graded.

 

Three exams plus a final exam will be given given. The tentative dates for the exams are September 26, October 31, and November 26, 2022.

 

The final exam will be given on Tuesday, December 10, 2024 at 8 to 10 a.m. in the usual class room. It will be comprehensive.

 

All exams will following the following outline: 50% of the questions are things you must be able to do, 25-30% of the problems are things you should be able to do, and 20-25% of the questions are more difficult. It is not uncommon for averages to be around 60% or lower.

To pass this class with a "C" you must demonstrate that you can do all the required material. Averages for a "C" may go down to 50%. Averages for a "A" may go down to 80%.

The distribution of grades is as follows. The final exam is worth 30%, the other exams are worth 13.3% each, and the total from the homework and computer assignments is worth 30%.