Syllabus for MME 502
Engineering Analysis I Mathematical Foundations

Fall 2019

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 (CH 103C/Zoomington)
By appointment
Cebula 105
MWF 2:00–3:15 pm



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


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.


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

day lecture videos week reading due
Course introduction
01.01 Truth
1 Kr Preface, Ch 9.1-5
01.02 Foundations of mathematics
02.00 Mathematical reasoning, logic, and set theory
02.01 Set theory
02.02 Logical connectives and quantifiers
2 Kr Ch 24 Ass. 1
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
03.05 Random variables
03.06 Probability density and mass functions
03.07 Expectation
03.08 Central moments
04.00 Statistics
3 Kr 25 Ass. 2
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
05.00 Vector calculus
05.01 Divergence, surface integrals, and flux
05.02 Curl, line integrals, and circulation
4 Kr Ch 9.6-9, 10 Ass. 3
05.03 Gradient
05.04 Stokes and divergence theorems
06.01.1 Fourier series
06.01.2 Fourier series example
5 Kr Ch 11 Ass. 4
06.02 Fourier transform from the fourier series
06.03 Generalized fourier series and orthogonality
07.00 Partial differential equations intro
07.01 Classifying PDEs
6 Kr Ch 12 Ass. 5
07.02.1 Sturm-liouville problems
07.02.2 Sturm-liouville problems example
7 Kr Ch 13, 17 Ass. 6
Complex analysis
Optimization 8 Kr Ch 22, 23 Ass. 7


Assignment 1: Review of vectors

Assignment 2: Probability and statistics

Assignment 3: Differential and integral vector calculus

Assignment 4: Fourier analysis

Assignment 5: Analytic PDE solution

Assignment 6: Complex analysis

Assignment 7: Optimization

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

Exams typically will be take-home. If you require any specific accommodations, please contact me.

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.

Grading policies

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
Final Exam


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

Academic integrity policy

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.

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 or 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. Our confidential reporting faculty are: Dr. Emily Coyle, Psychology, and Dr. Rico Picone, Mechanical Engineering. 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. [As one of your two confidential support people, I am not, but this statement applies, otherwise.]

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