MATH460 - Principles of Applied Mathematics
Course Code: MATH460 Course ID: 4548 Credit Hours: 3 Level: Undergraduate
The process of expressing scientific principles, experiments, and conjectures in mathematical terms. Topics include: gathering reliable data, exposing underlying assumptions, variables, relationships, levels, refining of models, and stochastic models. Deterministic versus stochastic models. (Prerequisite: MATH305)
|Registration Dates||Course Dates||Session||Weeks|
|07/27/21 - 12/31/21||01/03/22 - 02/27/22||Winter 2022 Session B||8 Week session|
|10/26/21 - 04/01/22||04/04/22 - 05/29/22||Spring 2022 Session B||8 Week session|
After successfully completing this course, you will be able to:
CO-1: Find the Fourier series of periodic functions and the trigonometric polynomials for which the square error with respect to the function is minimum on a finite interval.
CO-2: Represent a function as a Fourier Sine or Cosine integral to find the transform of a function.
CO-3: Solve a Partial Differential Equation of the one dimensional wave equation by the method of separating variables
CO-4: Examine Heat Equations by Fourier series and Integrals.
CO-5: Differentiate complex valued functions using Cauchy-Riemann Equations, exponentials, logarithms, and general powers.
CO-6: Analyze the Cauchy integral Theorem, Cauchy integral Formula, and the Taylor series expansion of analytic functions to find line integrals.
CO-7: Find the Laurent series of a function to determine the poles and essential singularities.
CO-8: Solve boundary value problems for Laplace's equation by using conformal mapping.
Please refer to the Course Outline section of this syllabus for the weekly reading assignments. While reading assignments are not graded, it is very important that you read the assigned material and work practice problems as necessary and appropriate.
A link to online lectures and practice problems keyed to the textbook chapters is provided by Connect Math. It will appear near the bottom of the list of tools. Once clicked, a pop-up window will open and silently log the student into the Connect Math site where work can begin without having to login or type in any credentials.
The forums are designed for students to provide information and ask questions on course content for the week. Your forum posts must meet the minimum requirement for the number of posts and the content for that assignment. These forums should not be used to discuss specific exam questions, but can be used to ask questions relative to practice exercises, practice tests, and textbook problems.
These forums will be a very important part of your learning. Please plan to spend time working on your answers. Reviewing your classmates’ proofs – making corrections and learning the material.
Three significant posts are required per forum. Posts should be made as indicated in the forum instructions. Be sure to click on the link “Read Full Description” so that you will be familiar with each forum requirement and the grading rubric. (A significant post generally contains at least 100 words—single sentence responses such as “Now I understand” or “Thank you for your help” do not constitute significant posts.) Your replies should note any confusing steps within a stated proof.
Grading for each forum will follow the point structure outlined in the description for each forum.
Introductory Forum: It is very important that you submit and participate in the Introduction Forum. Please introduce yourself to me and the class. Share where you work or plan to work after completing your program, your family, and any hobbies or special interests. Also tell us why you are taking this course and what you hope to gain from obtaining your degree. In addition, please take a look at the course objectives in the syllabus and discuss the relevance to your career goals.
Instructions: Your initial post should be at least 250 words. Please respond to at least 2 other students. Responses should be a minimum of 100 words. This forum submission serves as your official entry into the course and this is why we have drawn special attention to this assignment. You will be reminded of this Forum again in the Week 1 Lesson Module, but please keep in mind that this Introduction Forum must be submitted by 11:55 p.m., ET, on Sunday of Week 1 to maintain your registration in the course.
Please be sure to ask each other (and/or your professor) questions about practice problems, practice test questions or other textbook material in the Open Questions Forum! Please do not divulge only answers, but provide assistance in developing solutions for problems as well. This will help you learn through explaining and help your classmates find where they are missing the point. Teamwork is encouraged in working practice problems so that you can learn through sharing problem-solving techniques. If you are unsure of a problem, please ask about it in the Open Questions Forum so that everyone can share in the conversation.
Unit Tests and Quizzes:
Numbered unit tests and quizzes are found via the navigation link labeled "Tests & Quizzes.” Please complete each test and quiz by the due date noted in the syllabus and in the classroom. These are open-book and open-note tests, but are not collaborative efforts.
Students must plan and manage competing demands and priorities on their time and are expected to submit classroom assessment/forums on time. The instructor will post assessment/forum due dates and times in the Weekly Announcements.
Students are expected to submit classroom assignments by the posted due date and to complete the course according to the published class schedule. For late assignments, students need to contact the faculty member ahead of time about their individual situation.
Students’ course grades will be posted as soon as the instructor receives and evaluates the Final Project. Official grades will continue to be issued by the University on the grade report form. Instructors have 7 days from the end of the semester to submit their grades to the University.
The points earned on the graded course assignments will determine the course grade. The final grade in the course will be based on total points. Grades will be assigned based on the following composite scores:
|Quiz 1||5.00 %|
|Quiz 2||5.00 %|
|Quiz 3||5.00 %|
|Quiz 4||5.00 %|
|Quiz 5||5.00 %|
|Quiz 6||5.00 %|
|Quiz 7||5.00 %|
|Forum 1 (Introduction)||2.00 %|
|APUS Honor Code and Pledge||1.00 %|
|Week 1- Fourier Series||2.00 %|
|Forum 2||2.00 %|
|Forum 3||2.00 %|
|Forum 4 (Mid term check)||2.00 %|
|Forum 4||2.00 %|
|Forum 5||2.00 %|
|Forum 6||2.00 %|
|Forum 7||2.00 %|
|Forum 8 (Feedback)||2.00 %|
|Unit Tests||30.00 %|
|Test 1||10.00 %|
|Test 2||10.00 %|
|Test 3||10.00 %|
|Final project||15.00 %|
|Final Project||15.00 %|
In addition to the required course texts, 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.
|Site Name||Web Site URL/Address|
|MIT Open Courseware||http://ocw.mit.edu/courses/mathematics/18-075-advanced-calculus-for-engineers-fall-2004/lecture-notes/|
|Advanced Engineering Mathematics||https://course.ie.cuhk.edu.hk/~engg2012a/|
|Advanced Math For Engineers||http://www-personal.umich.edu/~wangzuoq/450Su11/|
|Book Title:||Advanced Engineering Mathematics, 10th ed - e-book available in the APUS Online Library|
|Publication Info:||Wiley Lib|
Not current for future courses.