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Course Description

Linear Algebra is a basis on which modern mathematics was built. Almost all solvable problems use the techniques developed in Linear Algebra. Throughout this course, you will learn how these techniques are used in a variety of fashions, from standard solving of system of equations to identifying functions that are useful in solving differential equations. It is appropriate we wrap up the course with an introduction to differential equations, because it is your understanding of linear algebra which will allow you to find or approximate the solutions you need in solving differential equations.

Course Information

● Introduction to Linear Algebra & Differential Equations

● MATH20580

● Credits: 3.5

Course Delivery and Format

This course is delivered in both an On-line and In-person format. Section 04 is On-line and the others are In-person. All tutorials will be In-person. Advance preparation and attendance in class are mandatory. Course content including learning resources and grades will be made available to students on the Sakai platform and this website. Delivery of information is going to be essentially the same between the sections to facilitate the dual delivery needed for the In-person section. Meaning ALL sections, both On-line and In-person sections will be required to go through content on Sakai and this website.

Learning Objectives/Goals

Upon successful completion of this course, students will be able to:

● Solve linear equations and identify the space in which the solutions live.

● Use basis to more effectively understand linear systems, vector spaces and corresponding subspaces.

● Utilize linear algebra in a way beyond what they learned in high school. Specifically, the ability to use diagonalization to simplify problems and its uses with abstract vector spaces.

● Identify types of differential equations and solve basic ODEs.

Course Content

The course is organized around the topics listed below.

1. Euclidean Spaces

2. Abstract Vector Spaces

3. Applications and Techniques

4. Introduction to Ordinary Differential Equations

Required Materials

We will use two textbooks, Poole: Linear Algebra: A Modern Introduction 4th Edition and Zill: A first course in differential equations with modeling applications, 11th edition. We will also be using the On-line homework system Enhanced Webassign (EWA) provided by the book publisher. For access to the 2 books in Webassign, we suggest that you buy the Cengage Unlimited option as that will give you access to Digital Versions of both books for roughly the cost of the one book. For more information on Cengage Unlimited and to purchase it go to this website. Buying a hard copy of these books for this course is optional. You may prefer to use just an e-book, or an e-book and a used (and possibly older edition of the book). It is advisable to register for On-line homework (see below) to preview the e-book and attached media files before you make your decision on what to purchase. Through Cengage Unlimited there is also an option to rent a hard copy of either book.

To register for the On-line homework system Enhanced WebAssign (EWA), follow the instructions given below. You will get a class key from your instructor. You can register any time after Tuesday, February 2nd. You will have a grace period of about 2 weeks to work on your homework and view the e-book. You will need to purchase an Enhanced WebAssign access code within that period in order to continue taking homework and have your work saved. 

Guidelines for Purchasing a Book/Access Code 

1. Purchase Cengage Unlimited from the Cengage website.

2. You may also purchase an access code On-line through webassign after you register for On-line homework.

3. When you sign up with WebAssign be sure to use the same username as you used in the past. If you have previously bought Cengage Unlimited your account may still be active through the summer.

On-line Homework Registration Information

The following guide and/or the steps given below will help you register:

(You may register anytime after Tuesday, February 2nd, 2020)

Step 1: Go to this Website.

Step 2: Click on Enter class key at the top right of the page. You can find your class key on the Sakai page for this course. It is the same for all sections.

Step 3: Enter the class key that you get from your instructor and click on Submit.

-Verify Information and click on Yes, this is my class.

-If you don't have a Webassign account click on Continue and follow to the next step. If you already have a WebAssign account check the appropriate button, click on Continue and you should be set.

Step 4: You will then be asked to fill out an Information Form. Choose your username. It needs to be unique to the webAssign system covering many schools.It is a good idea to use your Notre Dame email address for a username. Your institution code is nd. Choose a password and Re-enter the password. (If you forget this at some point throughout the semester, contact student support through the WebAssign Support Center as soon as possible to obtain a new password.) Enter your First Name and Last Name as they appear on

your Notre Dame ID. A student ID number is not required and I recommend you leave this field blank. See The example below:

Preferred Username: calciscool

Institution Name: nd

Password: iluvcalc1

Re-Enter Password: iluvcalc1

First Name : Melinda

Last Name: McNulty

E-mail Address: mcnultym@nd.edu

Student ID Number: Leave blank

Click on Create My Account. You may now log in to your account.

Step 5: A Greeting Notice will be displayed on your Homepage telling you that the grace period (for usage without an access code) ends about Feb. 17. Choose continue my trial period and click on the Continue Button at the bottom of the page.

You will now be able to view your Home Page, which will give you a list of Current assignments. You are now ready to start work on your current assignments. Your Home Page also offers a window with information on the e-book. You can preview the e-book and the attached media files if you click on this window.

If you experience technical issues with sign up or use of onlike homework, first make sure you are following the instructions exactly, and if the problem persists, contact Cengage technical support. Due to Covid it may take awhile to resolve issues.

Computing Equipment Requirements (for virtual participation)

In order to succeed in this course, students need a/an:

● Stable internet connection - a wired (ethernet) connection is recommended

● Link to the video conferencing software used for weekly live class meetings (Zoom). The same link is used for every class meeting but different for each section. The link is posted for the class on Sakai.

● Reliable webcam and microphone

Mobile devices (e.g., iPads, tablets, smartphones) should not be relied upon as the primary means of receiving and engaging with course content as course interactions will likely extend beyond the limitations of those devices and may not provide an optimal user experience.

It is the responsibility of students to ensure a consistent and dedicated connection when joining all weekly live meetings. While most phones, tablets, and laptops have built-in webcams that are completely acceptable to use for class, it is recommended that students get and use some sort of external microphone (like a headset or earbuds).

Either pen & paper or a tablet will help you record mathematical notation successfully.

If you are having problems with Sakai, Wi-Fi or other local computer issues, contact the OIT help desk. Technical support for computer issues ie Sakai is provided, not by your Instructor or TA, but by the OIT Help Desk and the Sakai Team. If you have a question or issue, please contact the Help Desk at oithelp@nd.edu or phone: 574-631-8111. You can also walk in; they’re located in 115 DeBartolo Hall. For this semester's walk-in hours, please check oit.nd.edu/help-desk.

Support Staff will contact your instructor or TA if they need to discuss the issue with us. Please tell them the web address to our Sakai site, your instructor/TA NetID and your NetID, and specifically name the assignment or task you need help with.

Technical Tips Before Contacting the OIT Help Desk:

Never login to Sakai or webAssign more than once at the same time, especially when taking a test. You may lose answers.

Course Policies

Due Dates and Time Zones

All due dates are all presented in the time at Notre Dame (Eastern Standard or Eastern Dayight depending). Students are responsible for every and all time zone conversion that might be required for submission of assignments and other class activities by the stated deadline.


Attendance is mandatory and thus essential for obtaining a passing grade in the class. If you need to miss a class, please contact your instructor ahead of the absence or as soon as possible after missing the class. See the following make-up policy section for more information on mitigating the impact of a class absence. Also please let your instructor & TA know when you enter and when you leave quarantine.

Health and Safety Protocols

In this class, as elsewhere on campus, students must comply with all University health and safety protocols, including:

● Face masks that completely cover the nose and mouth will be worn by all students and instructors;

● Physical distancing will be maintained in all instructional spaces;

● Students will sit in assigned seats throughout the semester, which will be documented by faculty for purposes of any needed contact tracing; and

● Protocols for staged entry to and exit from classrooms and instructional spaces will be followed.

We are part of a community of learning in which compassionate care for one another is part of our spiritual and social charter. Consequently, compliance with these protocols is an expectation for everyone enrolled in this course. If a student refuses to comply with the University’s healthand safety protocols, the student must leave the classroom and will earn an unexcused absence for the class period and any associated assignments/assessments for the day. Persistent deviation from expected health and safety guidelines may be considered a violation of the University’s “Standards of Conduct,” as articulated in du Lac: A Guide for Student Life, and will be referred accordingly.

Health Checks and Attendance

Every morning, members of the Notre Dame Community will be asked to complete a daily health check and submit their information via the Return to Campus Advisor application. The health check application will indicate one of the following:

1. Student is cleared for class and should attend class in person; or

2. Student is advised to stay home to monitor symptoms and should participate in class virtually and complete all assignments and assessments; or

3. Students must consult a healthcare provider and should contact University Health Services (UHS) for an assessment. In the meantime, the student should participate in class virtually and complete all assignments and assessments. Depending on the medical assessment, UHS will follow the University’s standard protocol for obtaining an excused absence for medical reasons.

Make-up Policy

The student is required to view the transcript of the missed class and complete all class assignments in a timely manner. Other required make-up work will be specified by the instructor.

The minimal consequence is that student will be assigned zero participation points for the missed class session. Other consequences capable of impacting course grade are at the discretion of the instructor.

Access to Grades

All grades for this course will be recorded and made visible to students in Sakai Gradebook. Students can expect your Sakai Gradebook will be updated after each quiz.

Course Communication

While much of the course conversations will take place during the weekly class meetings, students may have need to contact the instructor outside of the class meetings. The instructor for this course uses email as the primary mode of communication. Students should always keep the instructor informed of issues, questions, or (un)expected delays or outages that may occur.

Students can expect a reply to email within 36 hours IF the Subject heading of the email begins with Math20580 (to an instructor) or Math22580 (to a TA). If you are emailing both, either will suffice. Mail links on this website set the Subject correctly. Feel free to append additional information to the Subject line.

Assignments and Grading

Your course letter grade is determined by how many points you have earned during the semester. The ways to earn points are through performance on the three hour exams (100 points each), on the final (150 points), on the tutorial quizzes (50 points), on tutorial participation (25 points), on class participation (25 points) and on homework (50 points). The total number of points is 600. See the Earning Points page for more information.


The hour exams start at 7:30pm and end at 9:00. The final begins at 1:45pm and ends at 3:45. Current plans call for the exams to be on-line but this is subject to change. In particular, University policy states that students should be prepared to attend all final exams in-person. The three 90 minute exams are on-line BUT the final is in-person. Room information is here.


At start of the semester the cut-off for an A is 93.33% or 560 points. Cut-offs for all the letter grades can be found here.

During the semester we may feel the need to curve an exam. What this means is that the cut-offs for some of the letter grades may be lowered depending on class performance. This lowers the number of points you need to achieve a particular letter grade. The cut-offs will be updated after each exam. There has never been a need to curve homework grades, participation grades or quiz grades. Typically the gap from one letter grade to the next is about 25 points so you need to do well in ALL assessment areas.

Real-time assessment

If you want to know where you stand at any time during the semester add up your exam scores completed thus far from your class Sakai Gradebook. Add up your quiz scores and participation scores thus far from your Sakai tutorial page. Find your total score from webAssign and subtract your exam total if that is included and any scores for future homework you have done. Scale your homework and other scores to the appropriate amounts. Look at the running cut-offs here.

Day to day activities

This course works on a Friday to Thursday basis. Each Friday's class will start with a "goals" page listing concepts to understand, skills to acquire and references to the text relevant to these. The bulk of Friday's class will be devoted to discussing the material. Students should look at the link for that date before class and begin to think about the new material. Friday (and as many subsequent days as necessary) will be devoted to a more in-depth coverage of the material. Thursday's tutorial will test your mastery of the listed skills.

Most sections depend crucially on your mastery of previous sections in order to understand the new material. Furthermore, many sections repurpose old skills to solve new problems. This is great if you have mastered the old skills, disastrous if you have not.

Right of Revision

The university reserves the right to change any statements, policies or scheduling as necessary. Students will be informed promptly of any and all changes.

University Policies

Honor Code: As members of the Notre Dame community, students must abide by all Academic Honor Code policies. All cases of alleged academic dishonesty will be processed according to procedures described within this Honor Code document.

Copyright statement: The University of Notre Dame has adopted several policies related to the creation and use of copyrighted materials. These are outlined here.

ADA statement: “The University of Notre Dame will not tolerate discrimination or harassment on the basis of disability. Persons with disabilities (including students, faculty, staff, and job applicants) will be provided equal opportunities in accordance with the requirements of the Americans with Disabilities Act of 1990 (ADA), the Rehabilitation Act of 1973, and other applicable state and federal laws.”

Additional Support

On-campus resources for student support are listed below. Students taking this course from outside the South Bend area should contact the respective offices using the links below to explore if and how these resources are accessed by distance/remote students.

Title IX

Violence and harassment based on sex and gender are Civil Rights offenses. If you or someone that you know has been harassed or assaulted, you can find resources at the University’s Title IX website. 

Counseling Services

● The University Counseling Center (UCC) provides confidential short-term counseling and crisis intervention services to eligible Notre Dame students. More information available here.

Library - Research

LibGuides  are research, course, and how-to guides published by Hesburgh Librarians.

Curate ND: a collection of Notre Dame’s research and scholarship for study throughout time.

Academic Services & Collections 

Avoiding Plagiarism 

Library - Digital Media Creation

Remix - assembles a broad variety of tools in one place to help students find, mix, and create new digital media.

● The Center for Digital Scholarship (CDS)

Sound Studio - for recording audio-only

One Button Studio - for recording video and audio

Technology Support Service 

Disabilities Services

Sara Bea Disability Services: Registered students can request accommodations for reducing/eliminating the barriers that may be caused by the interaction of a disability and a traditional academic environment.

Last updated: 2021-01-21@07:51