ME 5040 A (CRN: 90479)
Mechanical Engineering: Adv Engineering Analysis I (A)
3 credit hours
About ME 5040 A
Analytical methods for the solution of partial differential equations in engineering mechanics and physics, including: eigenfunction expansions; Fourier series; Sturm-Liouville theory and special functions. Prerequisite: Graduate student in engineering, mathematics, or physical sciences or Instructor permission.
Notes
Prereq: Graduate standing in Engineering, Mathematics, Physical Science, or with instructor permission; Open to Degree and PACE students
Section URL
https://aisweb1.uvm.edu/pls/owa_prod/bwckschd.p_disp_detail_sched?term_in=202609&crn_in=90479
Section Description
SYLLABUS
Course: ME 5040 (90479) - Advanced Engineering Analysis I
Credits: 3
Meeting Time and Place: FALL 2026, TTh 4:25-5:40 pm, PLB 220
Instructor: D. Huston, 201E Votey, 656-1922, dryver.huston@uvm.edu, office hours MW 4:00 – 5:00 pm or by appointment, email is preferred over Teams messages.
Pre-requisites or co-requisites: Graduate standing in engineering or physical science
Course Description:
• Purpose: to cover essentials of engineering analysis at a graduate level in one semester.
• Topics covered:
o Real analysis – Chapters 1-4
o Fourier, Laplace and related transforms – Chapters 5, 6
o Complex variables – Chapters 11-15
o Linear analysis – Chapters 17-20
o Ordinary differential equations – Chapters 21-23
o Partial Differential Equations – Chapters 26-28
• How the course topics relate to each other: The knowledge accumulation is linear. Most of the later topics require understanding of the previous topics.
• Course structure: primarily lectures with occasional review sessions; students attend classes, complete weekly homework assignments, midterm tests, final exam and term paper.
Course Learning Objectives: Students who successfully complete this course will have a working knowledge of the covered topics and a facile ability to learn more advanced topics in engineering analysis.
Required and Optional Course Materials:
Text (Required): Foundations of Applied Mathematics, M. Greenberg, Dover, ISBN 978-0-486-49279-7, or Prentice-Hall, ISBN 0-13-329623-7
Supplemental Texts (Optional):
Schaum's Outline of Advanced Mathematics for Engineers and Scientists 1st Edition, by Murray R. Spiegel, ISBN:0071635400
Schaum's Outline of Advanced Calculus, 3rd Edition, by Robert C. Wrede, Murray R. Spiegel ISBN-13: 978-0071623667
Mathematics for the Physical Sciences, by Herbert S. Wilf, Dover, 1962 – posted online
Section Expectation
Student Learning Accommodations:
In keeping with University policy, any student with a documented disability interested in utilizing accommodations should contact SAS, the office of Disability Services on campus. SAS works with students and faculty in an interactive process to explore reasonable and appropriate accommodations, which are communicated to faculty in an accommodation letter. All students are strongly encouraged to meet with their faculty to discuss the accommodations they plan to use in each course. A student's accommodation letter lists those accommodations that will not be implemented until the student meets with their faculty to create a plan.
Contact SAS:
A170 Living/Learning Center;
802-656-7753;
access@uvm.edu
http://www.uvm.edu/access
University Policies and Values:
This course follows and adheres to all University policies and values. Details are posted at:
https://www.uvm.edu/ctl/designing-and-teaching-courses/syllabus-resources/syllabus-policies-and-values/
The Green and Gold Promise clearly articulates the expectations that UVM has for students, faculty, and staff to remain compliant with all COVID-19 recommendations from the federal CDC, the State of Vermont, and the City of Burlington. This include following all rules regarding facial coverings and social distancing when attending class. If you do not follow these guidelines, I will ask you to leave the class. If you forget your mask, you cannot enter the class and should go back and retrieve your mask. The Code of Student Conduct outlines policies related to violations of the Green and Gold Promise. Sanctions for violations include fines, educational sanctions, parent notification, probation, and suspension
Evaluation
Grading Criteria/Policies:
• Administration: Homework 10%, midterm exams 30%, final exam 30%, and term paper 30%.
• Late coursework submission policy: 10% reduction in grade per day late.
Assessments (Graded Work):
• Midterm and final exams are closed book and in-class. No electronic devices permitted, except simple calculators. One 8.5 x 11 in2 sheet of prepared notes allowed.
• Term paper is a minimum length of 20 pages on a topic relevant to this course. The topic must be approved by the instructor. Term paper is due the last day of classes this semester at 11:59 pm.
• This is a 5000-level course.
Use of Artificial Intelligence (AI) and other external resources:
• The bulk of the homework assignments are designed to not use AI tools for solutions. All use of AI and other external resources must be disclosed. There will be opportunities for the use of novel AI methods in the term paper.
Course Evaluation: All students will be asked to complete an anonymous and confidential evaluation of the course at its conclusion. The information will be considered in the continued efforts to improve the course.
Important Dates
Note: These dates may change before registration begins.
Courses may be cancelled due to low enrollment. Show your interest by enrolling.
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| Last Day to Drop | |
| Last Day to Withdraw with 50% Refund | |
| Last Day to Withdraw with 25% Refund | |
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Resources
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