# Engineering Analysis I Mathematical Foundations MME 502

a syllabus

## Course description

An introduction to the mathematical foundations of advanced engineering analysis. The course prepares one for the further study of specific analytic techniques and begins with a survey of the mathematical fields and their applications to engineering analysis. Topics introduced in some detail include probability theory, statistics, Fourier analysis, solution of partial differential equations using methods including separation of variables, differential and vector calculus, and complex analysis. (Adapted from the course catalog.)

## General information

Office hours location
Zoom rn
Actual office location
CH 103C
Location
Cebula 101
Times
M 5:00–6:50 pm
zoom.us/j/96550417120
unlisted playlist
Moodle
moodle.stmartin.edu

secrets

## Textbooks

(Kr) Erwin Kreyszig. Advanced Engineering Mathematics. Tenth Edition. Wiley, 2011. (Required. Old editions ok, but homework from Tenth.)

## Slack

Everyone is required to join the messaging service called “Slack.” We’ll use it to communicate with each other during the semester. The Slack team you need to join is called drrico. That’s a signup link. Be sure to join the channels #502-general-2019 and #502-homework-2019.

## Homebrew texts and notes

A partial text (with fill-ins) I’m writing will be posted on the Mathematical Foundations of Engineering Analysis page.

I’m writing this as we go, so each day of class please check the website and print the lecture(s) for that day, only. I’ll announce on Slack which need to be printed for each class.

## Video lectures

I will post videos of the live lectures on my YouTube channel. I recommend subscribing and familiarizing yourself with the playlist for this course.

## Schedule

The following schedule is tentative and will be updated as the course proceeds.

day lecture videos week reading due
Course introduction
01.01 Truth
01.02 Foundations of mathematics
1 Kr Preface, Ch 9.1-5
02.00 Mathematical reasoning, logic, and set theory
02.01 Set theory
02.02 Logical connectives and quantifiers
2 Kr Ch 24
03.01 Probability and measurement
03.02 Basic probability theory
03.03.1 Independence and conditional probability
03.03.2 Independence and conditional probability example
03.04 Bayes' theorem
3 Kr 25 Ass. 1
03.05 Random variables
03.06 Probability density and mass functions
03.07 Expectation
03.08 Central moments
04.00 Statistics
4 Kr 25
04.01 Populations, samples, and machine learning
04.02 Estimation of sample mean and variance
04.03 Confidence
04.04 Student confidence
04.05 Multivariate probability and correlation
5 Kr Ch 9.6-9, 10
05.00 Vector calculus
05.01 Divergence, surface integrals, and flux
05.02 Curl, line integrals, and circulation
6 Kr Ch 11 Ass. 2
05.04 Stokes and divergence theorems
7 Kr Ch 11
06.01.1 Fourier series
06.01.2 Fourier series example
8 Kr Ch 12 Ass. 3
06.02 Fourier transform from the fourier series
06.03 Generalized fourier series and orthogonality
9 Kr Ch 12
07.00 Partial differential equations intro
07.01 Classifying PDEs
07.02.1 Sturm-liouville problems
07.02.2 Sturm-liouville problems example
10 Kr Ch 13, 17 Ass. 4
07.03 Separation of variables
07.04 The 1D wave equation
11 Kr Ch 13, 17
08.02 Constrained linear optimization
08.03 The simplex algorithm
12 Kr Ch 22, 23 Ass. 5
Thanksgiving 13
nlin Nonlinear analysis
nlin.ss Nonlinear state-space models
14
BONUS 15 Ass. 6
Final Exam 16

## Assignments

### Assignment 2: Probability and statistics

• Solution, pword: zt5w1rfEagH4O8DF4zi9x
• Kr problems 24.3: 12, 14;
24.4: 6;
24.5: 8, 12;
24.6: 10, 18;
24.7: 8, 12;
24.8: 8;
24.9: 6, 8, 14;
25.3: 6, 10, 14;
25.9: 6.
• Take the weekly homework quiz.

### Assignment 3: Differential and integral vector calculus

• Solution, pword: 04CSMXQ7t8c4jnh5cCa5xE
• Kr problems 9.7: 4, 18, 24;
9.8: 2, 10;
9.9: 8, 12, 16;
10.1: 2;
10.2: 4;
10.3: 18;
10.4: 2;
10.6: 2;
10.7: 10;
10.9: 6.
• Take the weekly homework quiz.

## Homework, quiz, & exam policies

### Homework & homework quiz policies

Weekly homework will be “due” on Fridays, but it will not be turned in for credit. However — and this is very important — each week a quiz will be given on Friday that will cover that week’s homework.

Quizzes will be available on moodle each Friday (as early as I can get them up), and must be completed by that evening (before midnight). Late quizzes will receive no credit.

Working in groups on homework is strongly encouraged, but quizzes must be completed individually.

### Exam policies

Calculators will be allowed. Only ones own notes and the notes provided by the instructor will be allowed. No communication-devices will be allowed.

No exam may be taken early. Makeup exams require a doctor’s note excusing the absence during the exam.

The final exam will be cumulative.

Total grades in the course may be curved, but individual homework quizzes and exams will not be. They will be available on moodle throughout the semester.

Participation and Homework Quizzes
30%
Final Exam
70%

secrets

Participation grades depend on filling in your notes and engagement in class discussions.

Cheating or plagiarism of any kind is not tolerated and will result in a failing grade (“F”) in the course. I take this very seriously. Engineering is an academic and professional discipline that requires integrity. I expect students to consider their integrity of conduct to be their highest consideration with regard to the course material.

Cheating is academic dishonesty as well as unprofessional for prospective teachers. Do not copy other students' assignments, have someone else write your papers or plagiarize published or unpublished materials, or submit work previously graded by other instructors. See Saint Martin's University Student Handbook. Students will be graded not only on their academic success, but on professional conduct as well. Students who fail to show professionalism in their academic or personal conduct (e.g. constant tardiness, excessive absences, and/or other unprofessional behavior) may earn a lower letter grade than the total of semester accumulated points, or may even earn a failing grade.

## Access and accommodations

Your experience in this class is important to me. If you have already established accommodations with Disability Support Services for Students (DSS), please communicate your approved accommodations to me at your earliest convenience so we can discuss your needs in this course.

If you have not yet established services through DSS, but have a temporary health condition or permanent disability that requires accommodations (conditions include but not limited to; mental health, attention-related, learning, vision, hearing, physical or health impacts), you are welcome to contact DSS at 360-438-4580 or dss.testing@stmartin.edu or smu.dss@stmartin.edu DSS offers resources and coordinates reasonable accommodations for students with disabilities and/or temporary health conditions. Reasonable accommodations are established through an interactive process between you, your instructor(s) and DSS. It is the policy and practice of the Saint Martin’s University to create inclusive and accessible learning environments consistent with federal and state law.

## Sexual misconduct/sexual harassment reporting

Saint Martin’s University is committed to providing an environment free from sex discrimination, including sexual harassment and sexual violence. There are Title IX/sexual harassment posters around campus that include the contact information for confidential reporting and formal reporting. Confidential reporting is where you can talk about incidents of sexual harassment and gender-based crimes including sexual assault, stalking, and domestic/relationship violence. This confidential resource can help you without having to report your situation to the formal reporting process through unless you request that they make a report. Additional information and or reports can be made to the Title IX Team here on campus through the Dean of Students – Ms. Melanie Richardson, Associate VP of Human Resources – Ms. Cynthia Johnson, Public Safety – Mr. Will Stakelin, or the Provost/Vice President of Academic Affairs, Dr. Kate Boyle. Please be aware that in compliance with Title IX and under the Saint Martin’s University policies, educators must report incidents of sexual harassment and gender-based crimes including sexual assault, stalking, and domestic/relationship violence. If you disclose any of these situations in class, on papers, or to me personally, I am required to report it.

## University sanctioned activities

If a student is absent from class due to university sanctioned activities, such as sports, it is the student's responsibility to request that the absence be excused, otherwise, the absence will be recorded as unexcused. Absent students are responsible for catching up with the class, and if any assignments are due on the day of the absence, it is the student's responsibility to turn in the assignments on time (prior to class). Assignments may be submitted as an attachment to email: fumie@stmartin.edu. Please request the policy handout, “Requirement for receiving Excused Absence” on the first day of the class if you think this policy might apply to you.

## Center for Learning, Writing, and Advising

The Center for Student Learning, Writing and Advising is an integrated learning assistance program that offers services for students at all levels of achievement in pursuit of intellectual growth and academic excellence! The Center offers peer tutoring, study support, first year/early major advising, and writing support. Please investigate ways in which to support your learning.

## COVID-19 Policies

1. Students and faculty perform self-check for COVID-19 symptoms before coming to class Students and faculty should perform a self-check each day before coming to campus, and stay away from campus if they are ill. Students who are ill should inform faculty. Faculty who are ill should arrange for a communication plan with students if they need to miss class. Faculty are encouraged to give a gentle reminder at the beginning of each face-to-face class that students experiencing symptoms listed on the checklist should elect to remove themselves from campus. Anyone diagnosed with COVID-19, or living with/caring for someone diagnosed with COVID-19, should notify the Office of Public Safety.
2. Support for students who are unable to attend classes for any reason due to COVID-19 (including illness, travel restrictions, and quarantine): Faculty should attempt to make reasonable accommodations for students who are unable to attend classes or complete coursework due to the pandemic. Students adversely impacted by COVID-19 should notify their faculty and academic advisor to arrange for accommodations as soon as they become aware that they will be needed. Another alternative is to use the Saints Care form on the SMU website.
3. Attendance: This attendance policy consists of two elements. One relates to support of contact tracing efforts throughout this period of COVID-19 potential threats. The second relates to the use of attendance as a course grading element.
1. For tracking purposes, if needed, in all face-to-face courses faculty should maintain a record of attendance throughout the semester. The attendance needs to be taken by voice call or faculty recognition of students attending each individual session. Records should be kept via the Self-Service attendance feature or some other record the instructor maintains and can produce on demand should an inquiry be necessary for tracing purposes. Attendance should not be taken by passing around an attendance sheet or having students sign in as they enter the classroom as this handling could compromise attendees.
2. In an effort to support students who are considered high-risk or vulnerable as defined by public health officials and/or are unable to attend due to concerns about illness, campus safety, or need to care for familial obligations, attendance should not be used as a grade element during the Fall or any subsequent semesters affected by continuing COVID-19 requirements.
5. Social Distancing in the Classroom: Faculty, students, and guests must maintain minimum physical distancing whenever possible of six feet between all on-campus personnel, including with visitors, and where physical distancing cannot be maintained, implement administrative or engineering controls to minimize exposure.
6. Classroom arrangement: Desks and tables will be placed in a fixed manner to allow for a minimum of six feet between students seated in their desks, and from the faculty leading the class. Desks may not be re-arranged or shifted. When directing students into smaller discussion or work groups, faculty need to ensure that students maintain the six-foot physical distancing standard. Students also need to continue to use PPE (cloth facial coverings or face shields) during these activities. Recognizing that use of small group activities while enforcing physical distancing may have an impact on classroom volume, faculty are encouraged to take this into consideration when planning classroom activities.
7. Passing out/collecting paper materials: Faculty should avoid distributing and collecting “handouts” or printed materials by hand. Ideally, the materials are uploaded to the class Moodle site before class. Some classes may need to have students bring digital devices to class. Exceptions will be made for tests that cannot be delivered electronically. When tests are hand-administered and hand-collected, faculty and students should take precautions to reduce the risk of transmission. For example, faculty may wish to use disposable gloves while handing out and collecting tests. Students should not pass tests to other students. Students and faculty may wish to use hand sanitizer before and after handling tests.
8. Cleaning: Classrooms and laboratories will be cleaned and disinfected regularly and thoroughly by custodial staff. However, because many people will be using these spaces throughout the day, students and faculty should protect themselves by disinfecting the area and objects they will come into contact with. Students and faculty should also be considerate of others and clean up and disinfect their work area as much as possible before they leave the room. a. Upon entry into the classroom, faculty and students should disinfect surfaces in their immediate area where they will be sitting: chair, stool, desk, table, computer workstation, etc., using the appropriate cleaning products available in the classroom as follows: i. Copy machine/computer screen/smartboards: screen cleaning solution ii. Other surfaces, including keyboard/mouse: disposable wipes (e.g., Clorox wipes); iii. Used wipes should go in the garbage receptacles provided in the classroom b. Special instructions for laboratories: department-specific laboratory cleaning and disinfecting protocols must be followed. In addition, students and faculty should disinfect their work area upon arrival, as indicated above c. Before leaving the classroom, faculty should disinfect the whiteboard, computer/electronic equipment, and other surfaces they have touched (faculty will be provided with their own whiteboard markers and erasers material) d. Sanitizing stations will be available at building entrances and exits, as well as other designated areas. Students and faculty are encouraged to wash hands frequently and/or carry their own hand sanitizer. Note: each classroom will have a cleaning/disinfecting kit with appropriate solutions and applicators (spray bottle, sanitizing wipes, towels, hand sanitizer). Faculty and students are encouraged to also bring their own hand sanitizer and sanitizing wipes.
9. Food and beverages: Because consuming food and beverages require removal of the mask, no food or beverages can be consumed in the class. If students or faculty must drink water or eat during class, they should step outside the classroom. Faculty may wish to consider giving refreshment breaks during courses that meet longer than 50 minutes.
10. Storage of personal items (jackets, bags, umbrellas, etc.): Items such as backpacks, bags, umbrellas, and articles of clothing, should be kept in areas close to their owner. Shared lockers or common storage areas should not be used since these areas could lessen social distancing. Spaces under student chairs or desks are the best places to store these types of items.
11. Emergency drills and events (fire, active shooter, etc.): Continue training opportunities and exercises. The COVID-19 environment provides trainers a real-time opportunity for training students, faculty, and staff.
12. Compliance: Compliance with these policies is covered by regulations stipulated in the university contract signed by students. Students who violate these regulations repeatedly or egregiously may be referred to the Dean of Students.

## Correlation of course & program outcomes

In keeping with the standards of the Department of Mechanical Engineering, each course is evaluated in terms of its desired outcomes and how these support the desired program outcomes. The following sections document the evaluation of this course.

### Desired course outcomes

Upon completion of the course, the following course outcomes are desired:

1. Students will demonstrate the ability to use the fundamentals of advanced engineering analysis mathematics.
2. Students will demonstrate the ability to solve partial differential equations with the method of separation of variables.
3. Students will demonstrate the ability to use Fourier analysis.
4. Students will demonstrate the ability to use differential vector calculus.
5. Students will demonstrate an understanding of probability and statistics and how they relate to truth.
6. Students will demonstrate an understanding of the meaning of “truth” in the context of engineering analysis, with its foundations in mathematical, physical, and philosophical analysis.

### Desired program outcomes

In accordance with ABET’s student outcomes, our desired program outcomes are that mechanical engineering graduates have:

1. an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics
2. an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors
3. an ability to communicate effectively with a range of audiences
4. an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts
5. an ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives
6. an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions
7. an ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

### Correlation of outcomes

The following table correlates the desired course outcomes with the desired program outcomes they support.

desired program outcomes
1 2 3 4 5 6 7
desired course outcomes 1