Math 2720

Vectors and geometry in two and three dimensions, matrix algebra, determinants, vector differentiation, functions of several variables, partial differentiation, linear transformations, multiple integration, and change of variables. The computer algebra system Maple will be used to explore some of these topics.

Note: A graphing calculator is required.

Prerequisites and Corequisites: Prerequisite: MATH 1230. A grade of “C” or better is required to satisfy any course prerequisite.

• Students should have enough understanding of and facility using the course topics in vectors, vector valued functions, scalar valued functions, and the calculus of vector valued and scalar valued functions to apply those topics in the future and to learn more about those topics in the future.
• Students should have enough understanding of and facility using the course topics in linear algebra, matrix operations and linear transformations, to apply them in the future and to learn more about linear algebra in the future.
• Students should have a basic understanding of the computer algebra system Maple and how to use some of Maple for multivariate calculus problems.
• Students should have seen that many real world applications involve multivariate calculus.
• Students should have improved their skills in algebra, in differential and integral calculus of one variable, and in communicating mathematics both in symbolic formats and in English.

This class is an in-person class from 12:00 to 12:50 PM on MTuThF. Even though roll will not be taken, all students are expected to attend class every day.

Notes from lectures and videos of the class sessions will be posted after the class sessions on e-learning. The files containing the writing will be in the format for Xournal++, a free cross platform writing program that can be downloaded at Xournal++ downloads. These recordings are only for the use of students in this class. Do not share them.

The prerequisite for this class is Calculus II, Math 1230 at WMU. It will also be helpful for this section if you have some science background. We will try to include applications from science and engineering in this class.

You are responsible for all material in the text and all material presented in the class sessions. This includes any material not in the text presented in the class sessions and all material in the text that was not presented in the class sessions. A list of topics is available. This course will mostly follow the order of the material in the draft text.

It is expected that you will spend at least 3 to 4 hours working on Math 2720 outside the class sessions for every credit hour for class. Most students who do not spend enough time on this class do not pass.

A list of expectations for students and the instructor is available.

You are expected to follow all university conduct policies. This includes giving credit on any assignment you turn in for any help you receive and referencing any resources you use that are not from the text or the lectures.

There are some other university policies. you should be aware of.

The last day to withdraw is November 2, 2026. A tentative schedule is available.

There are many places on campus where tutoring is available. Do not hesitate to get help if you are lost. Among the places where tutoring for Math 2720 is available are the mathematics tutoring lab and the Bronco Study Zone.

When working with a tutor, please remember that you are restricted to the notation for this class. It is also necessary to learn the techniques in this class since some exam and/or quiz problems will restrict the techniques you can use to solve the problems. Any work you turn in must include the name and location of a tutor who helped you. This will not reduce your grade on a problem.

All cameras, cell phones, wireless devices, mp3/mp4 type media players, and similar devices are to be turned off and put away while you are in the classroom. If you ask, you may get an exception for note taking. This means taking written notes, not recording the class. Since the lectures will be posted, you should never take a picture of the screen. Use of one of these devices during a quiz/exam is forbidden and will be considered cheating.

A TI CAS graphing calculator is highly recommended. You can use many of the extra features of these calculators, including their symbolic computation abilities. As an instructor I will be using Maple for illustrations and computations during class. The TI calculators will be allowed during some quizzes and exams if they do not have wifi capabilities.

Although artificial intelligence can do many things for people, the goal of this class is not to teach you how to use AI. The goal is for you to increase your understanding of, ability to do, and ability to use mathematics. Since those are the goals of this class and I have seen students using inappropriate tools on assignments without giving appropriate references, most of your grade is from proctored exams and quizzes. For those portions of your grade that are not proctored but graded by a human, you should not use an AI. In other words you can use the text, other students, tutors, other texts, web videos, and your professor to get help on assignments. You cannot use an AI. If you use any resource besides the class text or your professor, it is an academic violation to not include the information of where you got help for the assignment. Waiting until the last few hours before an assignment is due is not a reason to use an AI.

A portion of your grade will come from homework and quizzes. A list of problems to work will be on this web site. Assignments to be turned in will be posted in the dropbox section of elearning. Although some of this homework may be collected, you are responsible for all of the problems on the list. If you have any questions about homework problems, please ask them in class, in office hours, via e-mail, or by making an appointment for a personal session.

All written homework will be submitted as a PDF file through a dropbox in e-learning. Submit all written assignments as a single PDF file containing the solutions to all of the assigned problems. The problems must be legible and in order of section and the numerical order, e.g. section 2.1 problem 1, section 2.1 problem 5, section 2.2 problem 2,... All pages in your PDF must be the same size. If a signed statement is required for the assignment, it is to be the first page of your submission with a written, not typed, signature. Do not submit a zip file. Your name must be in the name of the file. Make certain that you have clicked the submit button for the dropbox in e-learning.

If I cannot read the assignment or there are other problems with it, I reserve the right to not grade the assignment. For those using a cell phone to scan your assignments, I recommend using either Adobe Scan or Microsoft Lens.

If you get help from a tutor or someone else on a written assignment, that must be noted on your submission. You will not lose points for getting help, but I want to know if a tutor is using methods or notation that are not appropriate.

There will be on-line homework. Access to the on-line homework will be through elearning. For many of the problem Maple syntax is required/usable for the on-line homework. Unless otherwise requested, give exact answers for all problems in Mobius. Last minute questions about formatting or what is going wrong may be left unanswered. Professors also need to sleep.

Please do the on-line homework. Most people who do not pass this class do not do the on-line homework. Please do not spend too much time on the on-line homework. The problems may require a lot of computation, but they are only the basics of what you should learn. Using Maple or a calculator for complex computations is allowed for the Mobius homework. On exams you are required to show your work, so not working many of the problems by hand could cause you difficulties.

After the assignments are due you should have access to your old assignments along with answers using the Mobius gradebook link in the content section of elearning. If I forget to change the access to the answers for an assignment, please remind me.

There will be assignments using Maple, a computer algebra system. You must use the techniques illustrated in the Maple worksheets for each assignment. Using other techniques is not worth any points. Using an AI will be considered an academic violation. These assignments will be in drop boxes on WMU's e-learning system. All assignments must be turned in as a single Maple worksheet through e-learning. Do not submit a zip file. More details will be available later.

Three exams will be given. The dates are on the tentative schedule. Information about the format of the exams will come later.

A final exam will be given. The final exam will be given on Wednesday, December 16, 2026 at 2:45 to 4:45 p.m. The final exam will be comprehensive. Some people make plans to leave early and request an early final exam. Those requests will be turned down.

All exams will follow this outline: 50% of the questions are things you must be able to do, 25-30% of the problems are things you should be able to do, and 20-25% of the questions are more difficult. It is not uncommon for averages to be around 60% or lower.

To pass this class with a "C" you must demonstrate that you can do all of the required material. A starting scale is: A 85%+; BA 78+; B 72+; CB 66+; C 58+; DC 52+; and D 46+. This scale will probably change as the term progresses. Often the bottom C grade is around 50%. The lowest C grade will not go below 50%.

The distribution of points for calculating grades is as follows. The final exam is worth 30%, each of the other exams is worth 15%, and the quizzes, homework, and other assignments are worth a total of 25% of your grade. The on-line homework is worth 5% of your grade.