MATH470 - Measurement Theory
Course Code: MATH470 Course ID: 4549 Credit Hours: 3 Level: Undergraduate
This course covers the study of basic topics in analysis with emphasis on methods and measurement. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations. (Prerequisite: MATH305)
|Registration Dates||Course Dates||Session||Weeks|
|05/21/21 - 10/29/21||11/01/21 - 12/26/21||Fall 2021 Session I||8 Week session|
|08/31/21 - 02/04/22||02/07/22 - 04/03/22||Winter 2022 Session I||8 Week session|
After successfully completing this course, you will be able to accomplish the following course objectives (CO):
- CO-1: Review mathematical preliminaries necessary to measure and analyze the effects of various errors associated with the computations.
- CO-2: Analyze the errors associated with the computations of solutions for equations in one variable and the convergence of sequences and series.
- CO-3: Differentiate between interpolation and approximation methods in order to measure the error involved in using these methods.
- CO-4: Differentiate between methods for differentiation and integration on order to measure the error involved in using these methods.
- CO-5: Differentiate between various methods for solving initial-value problems for ordinary differential equations in order to measure the error involved in using these methods.
- CO-6: Differentiate between direct methods for solving systems of linear equations in order to measure the error involved in using these methods.
- CO-7: Analyze singular value decompositions in order to measure the error involved.
Forum Assignments: The University requires weekly contact from each student. This requirement can be met by submitting chapter Journals and by participating in the Forums. A total of 20% of the final grade will be based on participation in eight forum topics within seven Forums. It is expected that Forum posts are written in complete sentences using correct grammar and spelling. Any post that requires research must be accompanied by a proper APA style citation of the references used. There are many citation tutorials available on the web, but citefast.com works well and can be used quickly, efficiently, and gives the student the ability to save the resource.
Written Assignments: Written homework is assigned to provide you an opportunity to practice what you have read. It gives the professor a summative means by which to determine the level of understanding that a student has achieved. Your homework problems can be written up directly in the assignment text box using the equation editor to enter any mathematics. However, if you prefer, you could also choose to write up your solutions in a Word document using the Equation Editor to enter mathematics or scan your hand written solutions. Or work the problems in a spreadsheet. If you choose the latter two options, make sure that your hand written solutions are clearly numbered and readable. In either case, you would attach your files to the appropriate drop box.
There are 8 weekly written assignments for a total of 50% of the final course grade. If the student is having difficulty with a problem, he/she should check the companion website for additional resources and/ ask questions about a similar problem in the text in the appropriate Weekly Question forum.
Learning Journal: A very important component of your learning experience is to be able to reflect on what you have learned. The purpose of keeping a weekly journal is to enhance your learning through the process of writing and thinking about your experiences. During each week you will be responsible for keeping a written record (journal) of your lesson notes, observations, thoughts about your learning experience, and questions. At the end of the week you will be asked to submit the journal.
There are 8 weekly journals for a total of 30% of the final grade.
Your journal should be written as a 3-column table with the following headings: Definitions, Algorithms, and Questions. For each section covered in this chapter, provide the following information:
- Definition heading: list pertinent definitions and proof writing tools that you read about in this module;
- Algorithm heading: provide a brief summary of any algorithms presented in the chapter.
- Questions heading: list any questions regarding the material you had in this module.
Definition: list pertinent definitions and proof writing tools that you read about in this module
Algorithm: provide a brief summary of any algorithms presented in the chapter
Questions: list any questions regarding the material you had in this module
Evaluation is based on homework assignments, journals, and discussion board participation. The student is assessed on the level of conceptual understanding and technical application of the various topics of Measurement Theory in Numerical Analysis.
Final course evaluation will be based on the following breakdown of each time of Learning Activity.
|APUS Honor Code and Pledge||1.00 %|
|Week 1: Introductions||2.22 %|
|Week 1: Mathematical preliminaries and measure of error||2.22 %|
|Week 2: Equations of one variable, rates of convergence, and measure of error||2.22 %|
|Week 3: Interpolation Methods and Measure of Error||2.22 %|
|Week 5: Methods of differentiation, integration, and measure of error||2.22 %|
|Week 6: Methods for solving initial-value problems and measure of error||2.22 %|
|Week 7: Direct methods for solving systems of linear equations and measure of error||2.22 %|
|Week 8: Singular value decomposition and measure of error||2.22 %|
|Week 8: COURSE WRAP UP||2.22 %|
|Week 1: Written Homework Exercises||6.25 %|
|Week 2: Written Homework Exercises||6.25 %|
|Week 3: Written Homework Exercises||6.25 %|
|Week 4: Written Homework Exercises||6.25 %|
|Week 5: Written Homework Exercises||6.25 %|
|Week 6: Written Homework Exercises||6.25 %|
|Week 7: Written Homework Exercises||6.25 %|
|Week 8: Written Homework Exercises||6.25 %|
|Week 1: Learning Journal||4.29 %|
|Week 2: Learning Journal||4.29 %|
|Week 3: Learning Journal||4.29 %|
|Week 5: Learning Journal||4.29 %|
|Week 6: Learning Journal||4.29 %|
|Week 7: Learning Journal||4.29 %|
|Week 8: Learning Journal||4.29 %|
The Numerical Analysis Companion Website contains a plethora of supplementary resources including power points, video clips where available, algorithm program files written in MAPLE, MATLAB, C, JAVA, MATHEMATICA, FORTRAN, and PASCAL, sample tests, and the first two chapters of the Student Study Guide.
NUMERICAL ANALYSIS Companion Website: the link is listed in the table below.
In addition to the required course text, the following public domain web sites are useful. Please abide by the university’s academic honesty policy when using Internet sources as well. Note web site addresses are subject to change.
NUMERICAL ANALYSIS Companion Website
Dr. R.L. Burden's Website
Dr. A.M. Burden's Website
NPTEL: e-Learning Courses from the IITs and IISc
Holistic Numerical Methods
|Book Title:||Numerical Analysis, 9th Ed - the VitalSource e-book is provided inside the classroom|
|Electronic Unit Cost:||$32.00|
Not current for future courses.