# 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

Virtual office hours (zoom, make appointment!)
By appointment
Virtual office hours appointments
make appointment
Location
Cebula 201A
Times
W 5:00–6:50 pm
us02web.zoom.us/j/81106978094
Moodle
moodle.stmartin.edu

secrets

## Textbooks

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

## Discord

Everyone is required to join the messaging service called “Discord.” We’ll use it to communicate with each other during the semester. The Discord server you need to join is called drico. That’s an invitation link. Be sure to join the channel #502.

## Homebrew texts and notes

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

## Video lectures

I have posted videos of the 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
Analytical/symbolic versus numerical analysis
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
TBA 13
nlin Nonlinear analysis
nlin.ss Nonlinear state-space models
14
BONUS 15 Ass. 6
Final Exam 16

## Assignments

These may be updated throughout the term. They are set at the beginning of the week before the assignment is due.

### 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.

## Development environment

The following development environment will be used for all class examples and assignments. The three primary pieces of software, Anaconda (Python), Git, and VS Code are available for free on all major operating systems. All of this except VS Code is installed on engineering lab computers (including those in the classroom).

### Anaconda

Anaconda is a distribution of Python that includes the conda package and environment manager.

Download and install Anaconda. The default Anaconda environment is base, which is fine to use as long as you don’t want to work on multiple projects.

To edit or create an environment, on Windows open the Anaconda Prompt app, or on macOS, open the Terminal app. To create a new environment, use the command

conda create --name <environment-name> python=3.11 numpy scipy matplotlib sympy


The Python version is specified and the final arguments here are a list of packages to install (those given here are what I recommend as a default).

To install additional packages, make sure your environment is activated first (base is automatically activated):

conda activate <environment-name>


To install additional packages to the activated environment, use the installation formula (e.g., those here). For instance, to install the sympy package,

conda install conda-forge::sympy


All though it can cause compatibility issues if it is mixed with conda install packages, you can install packages with pip to an Anaconda environment. For instance,

pip install engcom


If an environments.yml file is provided by someone (maybe me) with a Python version and several packages to install, move that file to your current working directory (or cd to its location) and execute the command

conda env create -f environment.yml


### Git

Git is an amazing version control tool for code development and collaboration. I use it for everything.

Install Git from the instructions here.

### VS Code

This is currently the most popular code editor/integrated development environment (IDE) for many programming languages and tasks.

#### Setting up your VS Code environment

Do the following to set up your VS Code environment:

1. Download and install VS Code. It is available on all major platforms. It can be installed on your user account on a lab computer.
2. Open VS Code.
3. Under the “Extensions” tab (left-side navigation), install the Python extension.
4. Windows users: type ctrl+ to open a terminal. Click the dropdown next to the + sign and select “Select Default Profile.” From the dropdown, select “Git Bash.”
5. Type ctrl+shift+P (macOS cmd+shift+p), type Python: Select Interpreter, and press Enter. Select from the list the python.exe file in an anaconda directory with the name base (or an environment you created). This selects the Anaconda environment base.
6. Create a new file with ctrl+N. Write the following in the file:

 import numpy as np
import sympy as sp
import scipy
import matplotlib.pyplot as plt

print("Hello, world!")

7. Click the “play” button in the top right (Run Python File in Dedicated Terminal). The terminal should display the output Hello, world!.

## Machine Learning Packages

Here are some helpful machine learning packages.

### CVXPY for Convex Optimization

The convex optimization package CVXPY is excellent for optimization problems. (Here is the documentation.) Install it in your conda environment with the following command:

conda install -c conda-forge cvxpy


### Keras with TensorFlow

I recommend using Keras with a TensorFlow backend for building neural networks.

Install these packages into your conda environment (unfortunately we have to use pip instead of conda` for these, making the environment a bit fragile). The installation is different for each OS. The installation instructions are here.

## 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.

Homework Quizzes
30%
Final Exam
70%

secrets

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.

What is academic integrity? Saint Martin's University is a community of faculty, students and staff engaged in the exchange of ideas in the ongoing pursuit of academic excellence. Essential to our mission is a focused commitment to scholarly values and intellectual integrity, and a respect for the ideas, beliefs and work of others. This commitment extends to all aspects of academic performance. All members are expected to abide by ethical standards both in their conduct and their exercise of responsibility to themselves and toward other members of the community. As an expression of our shared belief in the Benedictine tradition, we support the intellectual, social, emotional, physical and spiritual nurturing of students.

What is academic dishonesty? Saint Martin's University defines academic dishonesty as violating the academic integrity of an assignment, test and/or evaluation of any coursework. This dishonest practice occurs when you seek to gain for yourself or another an academic advantage by deception or other dishonest means. You have a responsibility to understand the requirements that apply to particular assessments and to be aware of acceptable academic practice regarding the use of material prepared by others. Therefore, it is your responsibility to be familiar with the policies surrounding academic dishonesty as these may differ from other institutions.

## Acceptable use of AI in coursework

Any use of technology that misleads a reviewer in assessing the student's mastery of a specific set of skills or knowledge is a type of intellectual dishonesty, that is, a type of cheating. Students who are unsure about the appropriateness of using an artificial intelligence tool (or “AI”) should check with the instructor before using it. This includes the use of tools that generate text, images, video, code, and other works. If you are permitted by your instructor to use one or more AI tools in producing your work, you should disclose the use of that tool. You should say which tool you used and how you used it. Then if you use specific AI generated content (text, images, videos, audio, code, and so on) you should cite it in the style (APA, MLA, and so on) specified by your instructor.

## Access and accommodations

Your experience in this class is important to me. If you have already established accommodations with Disability Support Services (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 are 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 the Dean of Students – Ms. Melanie Richardson, Associate VP of Human Resources – Ms. Cynthia Johnson, Public Safety – Ms. Sharon Schnebly, or the Office of the Provost – Dr. Tanya Smith-Brice, unless you request that they make a report. 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 you are absent from class due to university-sanctioned activities, such as sports, it is your 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 your responsibility to turn in the assignments on time (prior to class). Assignments may be submitted as an attachment to email.

## Counseling and Wellness Center

There may be times, as a college student, when personal stressors interfere with your academic performance and your daily life. The Counseling and Wellness Center supports students by addressing mental and emotional well-being with FREE and confidential services. To schedule an appointment, call 360-412-6123 or email counselingcwc@stmartin.edu or stop by the CWC (1st floor St. Raphael Center).

If you would rather not go to the CWC or need support in the evenings and weekends, please consider using the TimelyCare app (timelycare.com/smusaints) to speak with a mental health provider, free, 24/7, from your phone or computer.

## Religious Accommodation

Saint Martin's University, in honor of the sacredness of the individual, and being deeply rooted in the Catholic Benedictine tradition of higher education, values the many religious and spiritual practices of our campus community. Saint Martin's University supports our students in their ongoing journey of becoming. In compliance with Washington State Law RCW 28B.137.010, Saint Martin's University reasonably accommodates students for reasons of religious observances.

## 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