Eastern Michigan University Creed

Basic Information

Official Course Catalog Entry

Calculus of functions of a single variable continued; additional applications of definite integration to moments, centroids, arc length, surface area and work. Transcendental functions, infinite series, methods of integration, review of conic sections.

Prerequisites

Related Courses

Many students who take Math 121 also take Physics 223 (Mechanics and Sound). Also, a fair number of questions on the Math Subject GRE and various math PhD qualifying exams are based on Calc 2: see https://www.math.umass.edu/graduate/sample-qualifying-exams , http://www.ets.org/s/gre/pdf/practice_book_math.pdf , http://www.ets.org/gre/subject/about/content/mathematics/ (if a link goes dead, go to archive.org and paste the link into their WayBack machine--maybe it has a copy of the page)

Class Format and Meetings

For each new topic (section of the textbook), I will post a few short videos for you to watch, then try some straightforward practice problems (some that are on the homework, some that are not). Then as you try the more challenging problems on the homework, you can email me for help, or drop by the video-chat session, or email me for an appointment for a video chat if the scheduled session doesn't work for you. Those sessions will include some groupwork on the harder problems.

If we take the point of view of an in-person class: To succeed in Math 121 it usually takes 12 hours per week outside of class during a regular (Fall or Winter) semester, or twice that (24 hours/week) during a double-pace Summer semester. The federal standard for what a credit-hour means is a _minimum_ of 2-hours-outside-class for every credit hour, and our class is 4 credit hours, so that's at least 8 hours/week outside class.

For an asynchronous online class, add 4 hours/week for a regular semester (total of 20 hours/week) or 8 hours/week for a fast summer semester (total of 32 hours/week) for most people to succeed.

Instructor information

Office Hours and other help

M/T/W/Th 11:00-11:45am
M/T/W/Th  2:00- 2:45pm

I am also happy to make appointments if you cannot come to the general office hours. Please send me e-mail to arrange an appointment. It can even be in the evening or on a weekend.

The Mathematics Student Services Center (or "Math Lab") is operating all virtually in Fall 2020. You can find the details here.

During an in-person semester: A good place to study, if the Math Lab doesn't suit you, is the Math Den, Pray-Harrold room 501.

Teaching philosophy, interests

I am a very applied mathematician. Applied, applied, applied. Not pure. Impure. I try to focus on real-world problems, rather than artificial drill problems (though I do recognize the need for some drill). My classes spend much more time on formulating problems (going from the real world to math notation and back) than on proving theorems. If you want the theoretical basis for anything we are discussing, please ask!

My general math interests are in Industrial Engineering and Operations Research (IEOR). In particular, I do research in applied probability and queueing theory, the mathematics of predicting how long it takes to wait in line for service. You can learn more about this in Math 319 and 419 when I teach them. I also enjoy teaching about cost-minimizing/profit-maximizing methods called Non-Linear Programming (NLP) in Math 319 and Math 560.

I was a licensed amateur radio operator, and enjoy bringing aspects of electronics and the physics of sound/music into the classroom. You will see lots of sines and cosines in my classes, and exponentials/logarithms, but not much in the way of tangent, secant, etc.

I am also one of the leaders of the Data Science and Analytics (DSA) major at EMU--a combination of statistics, computer science, and business. One of the important function shapes in that field is the s-shape, like Logistic functions, so we'll use those a fair bit.

Required materials

A webcam or cell phone video camera capability is required for identity verification and the video structured interviews. Similarly, some way to take photos of your by-hand work so you can upload it is required.

We will use Excel and/or Google Sheets fairly often. This is often difficult to do on a tablet without a keyboard, and very difficult on a phone, so try to have a laptop/desktop handy.

Chapters 5-9 of "APEX Calculus Version 4.0", available via a free download as follows: Chapters 5-8 are at

• In color, with 3-dimensional content, 13 Mb
• In color, without 3-dimensional content, 6 Mb
• In black/white, without 3-dimensional content, best for printing on a black/white printer

Reading a math textbook takes certain skills! Here are some guides:

• Various study skills
• How to Read A Math Textbook
• Reading a Math Textbook
• search for: how to read a math textbook

You basically need either a laptop so you can use Desmos.com, or a TI-83/84 graphing calculator. While it's possible to uses Desmos on a cell phone, it's not nearly as easy to use as when it's on a laptop. A TI-83/84 is allowed, but is not ideal, since there are many problems in the world that can't be solved by a graphing calculator. I would advise you to learn more professional technology tools than just a TI. A TI-89 or TI-Nspire is not required, but is allowed just as much as a TI-84 sort of calculator.

Course Web Page

I will post data files, homework assignment files, etc. in Canvas, and possibly also at my home page. A record of all homework assignments is at this Google Doc (or, this link in case the bitly link fails)

We will use the Canvas system to record scores. You are expected to keep an eye on your scores using the system, and get extra help if your scores indicate the need.

Supplementary Materials

• a free online precalculus textbook if you need some review.
• APEX Calculus I
• Khan Academy: Calculus
• Schaum's Outline of calculus
• The Cartoon Guide to Calculus
• The Manga Guide to Calculus
• any book with a depressing, insulting title like Calculus for Dummies or Complete Idiots
• The Mechanical Universe videos, like derivatives (starts around 6.5 minutes), integration, potential energy, harmonic motion.
• A Companion to Calculus, 2nd Edition by Ebersole, Schattschneider, Sevilla, and Somers; ISBN-10: 049501124X
• Calculus: Single Variable, any edition, by Hughes-Hallett, Gleason, McCallum, et al.
• Calculus Problems for a New Century: Resources for Calculus Collection
• Calculus for the Life Sciences: A Modeling Approach, a free online bio-oriented calc textbook!
• other online textbooks, like Strang or Boelkins.
• Integration by Lego: Planimeter and video 1 and video 2
• Univ. of Michigan old Calc 1 and 2 exams (Calc 2= Math 116 there): https://dhsp.math.lsa.umich.edu/examshops.html

Course Content

Math 121 Student Learning outcomes

1. Explore more fully the meaning and uses of the Second Fundamental Theorem of Calculus
2. Examine various techniques of integration (including substitution and integration by parts, etc.) and apply them to definite and improper integrals,
3. Approximate definite integrals using numerical integration techniques with appropriate technology and solve related problems,
4. Apply integration to problems (including volumes by slicing, etc.)
5. Model physical phenomena using differential equations,
6. Define, graph, compute limits of, differentiate, integrate and solve related problems involving functions represented parametrically or in polar coordinates,
7. Distinguish between the concepts of sequence and series, and determine limits of sequences and convergence (including p-series, ratio, alternating, integral, comparison, and limit comparison tests) and approximate sums of series,
8. Define, differentiate, and integrate functions represented using power series expansions (including radius of convergence), Taylor series, and solve related problems.

Schedule

Related Course Goals

Students should be able to:

• work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations.
• understand the meaning of the derivative in terms of a rate of change and local linear approximation and they should be able to use derivatives to solve a variety of problems.
• understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.
• understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
• communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.
• model a written description of a physical situation with a function, a differential equation, or an integral.
• use technology to help solve problems, experiment, interpret results, and verify conclusions.
• determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
• develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

Grading Policies

Attendance

Since this is an asynchronous online class, there is no real concept of "attendance". There are some things that are like attendance: any online discussions within Canvas, and the optional synchronous sessions.

Homework

Homework will be assigned just about every day, often 2 new homeworks a day in a fast summer semester. We might be using a free on-line homework system like WeBWoRK, but probably not.

In general, you should write out your homework by hand, take pictures of it (and possibly turn them into a PDF using something like GeniusScan), and upload it to Canvas.

I encourage you to work together in study groups, but each person must work out and write out their own homework (no copying from each other). As in any academic work, you should "cite your sources": write down who you received help from (including tutors, but not including me) on any particular problem, or at the top of the homework paper if it's more efficient.

Overall Grades

No scores will be dropped by default, unless a valid medical excuse with evidence is given. In the unfortunate event of a medical need, the appropriate grade or grades may be dropped entirely (at the professor's discretion), rather than giving a make-up. You are highly encouraged to still complete the relevant assignments and consult with me during office hours to ensure you know the material.

• 50 percent: homeworks, a possible standard project, possible online discussions
• 15 percent: cumulative review assignments
• 10 percent total: 2 small structured technical interviews
• 25 percent: final assessment (exact format TBD)

From:	To:	Grade:
-infinity 59 F
59 62 D-
62 65 D
65 68 D+
68 71 C-
71 74 C
74 77 C+
77 80 B-
80 83 B
83 86 B+
86 89 A-
89 infinity A

I am open to doing contract honors for this class for students in the Honors College. Please contact me if you are interested in doing so.

Academic Honesty

Academic dishonesty, including all forms of cheating, falsification, and/or plagiarism, will not be tolerated in this course. Penalties for an act of academic dishonesty may range from receiving a failing grade for a particular assignment to receiving a failing grade for the entire course. In addition, you might be referred to the Office of Student Conduct and Community Standards for discipline that can result in either a suspension or permanent dismissal. The Student Conduct Code contains detailed definitions of what constitutes academic dishonesty but if you are not sure about whether something you are doing would be considered academic dishonesty, consult with the course instructor. You may access the Code online at: www.emich.edu/responsibility/

Classroom Behavior

For in-person classes: Those who use laptops during class other than when everyone is using them should sit in the back row or sides if possible, to avoid distracting others with what is on their screens.

For online classes: To avoid distracting others with random noises from your environment and/or echoes, please keep yourself muted when possible. In many video chat apps, you can hold down the space bar to temporarily unmute, and then when you let up on the space bar, you're muted again, so you don't have to remember to re-mute. For the most part, please keep your video on if you can, to promote personal relations. Students who deliberately disrupt group video chats will lose the privilege of doing group video chats. Please be considerate about what appears behind you in video chats, mainly about things that would likely offend or unfairly distract other people.

General Caveat

Advice from Other Math 121 Students

• Do ALL the homework.
• Always ask questions, he will answer everything. Do homework and study properly, his tests cover material he covers in class.
• Go to class, do the homework, ask questions.
• This professor is very much on the applied side, not theoretical.
• Ask for help
• Try to complete homework early and have questions prepared for next class.
• Spend some time making your note sheet.
• Start your homework early and show all your work.
• Office hours are very helpful, make sure you make use of them. Also, the practice tests may not be graded, but still do them. GRAPH EVERYTHING!
• Start the homework when it's assigned. When in doubt, graph it.
• Make sure you do all the homework.... Also make sure you have at least tried all of the problems and ask questions ....
• The practice exams can be very helpful if you take it like an exam (no book, with your note sheet, and set a time limit).
• Graph everything! Even if you don't think you need to. Take some time to review trig and log functions.
• Graphing the problems a lot of the time can show an obvious answer.
• Use e-mail, Prof. Ross is good about getting back to you in about an hour, depending.
• Use office hours.
• Do the homework and do it well; it's [a big] percent of your grade. Not doing one assignment can really hurt. Passing the tests is not good enough to do well in this class.
• This is not a blow-off class by any means; homework needs to be done every night just to stay on top of the material.
• Be sure to speak up if you don't understand something, otherwise you'll get snowballed (gains momentum while rolling down hill). He enjoys participation in class, so don't be shy, speak up.
• do ALL the homework, because that's a huge part of your grade.
• It often confused me the emphasis put on guessing solutions at the beginning of the semester. After years of concentrating on getting the right answer it seemed weird. I just didn't really understand the importance of doing that until it was way too late.

Advice from Research on How Students Learn

From the book "Learning and Motivation in the Postsecondary Classroom" by Marilla D. Svinicki: "researchers have demonstrated that students who are initially allowed to generate their own ideas about a problem before they receive a lecture on it better understand the concepts behind the problem than students who are simply told what those concepts are." What does this mean for you in this class? Most of the time, after the first class meeting about a new section of the book, it's best to do the homework that night and ask questions during the next class meeting, then turn it in that day to get the most rapid feedback from me. There is a temptation to not try it the first night, and just sit and try to absorb information about the problems from the discussion the next day. The research cited above says this is not good for your learning.

Also, "students who learn to monitor their own understanding and take steps to modify their thinking in light of that monitoring become much better problem solvers in the long run." I almost always want you to check your work by comparing to sensible upper and lower bounds, guesses, etc., or by taking a derivative to check an integral formula you just found. This way, you are monitoring how well you can do the problems in real-time, without having to wait for feedback from me grading your paper. The research I just mentioned shows that this makes you a better problem solver. AND, you get more credit because you can fix the problems you find you got wrong, even before turning it in!

Land Acknowledgement

University Writing Center

Standard University Policies

Health Screening

Physical Distancing

Face coverings

Hygiene

Wellness & Community Responsibility

Mental Health Support

Food Pantry