Eastern Michigan University Creed

Basic Information

Official Course Catalog Entry

Calculus of functions of a single variable; differential calculus, including limits, derivatives, techniques of differentiation, the mean value theorem and applications of differentiation to graphing, optimization and rates. Integral calculus, including indefinite integrals, the definite integral, the fundamental theorem of integral calculus, and applications of integration to area and volume.

General Education rationale

Very important notice

Prerequisites

Related Courses

Class 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 synchronous video session, or email me for an appointment for a video chat if the scheduled synchronous session doesn't work for you. The synchronous 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 120 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

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.

The Mathematics Student Services Center (or "Math Lab") is operating via email this semester.

During an in-person semester, The Mathematics Student Services Center (or "Math Lab") is also here to help you, in Pray-Harrold 411. Their hours are posted here. Please give them a call at 734-487-0983 or just drop by.

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, or at least formulas that are related to 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.

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.

Our required text is APEX Calculus Version 4.0, Volume 1 (chapters 1-6), which is freely available online at APEX Calculus. I recommend that you have a hard copy, whether you print it from a PDF or buy the cheap (about $20 total) printed copy online.

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

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 and my youtube channel. 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.
• 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
• Some of my favorite videos from my childhood: 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, 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! Previously-free PDFs in the Canvas course shell
• other online textbooks, like Strang or Boelkins.
• Integration by Lego: Planimeter and video 1 and video 2
• SOHCAHTOA

Course Content

QR outcomes

1. Build an appropriate model.
2. Use the model to solve the problem.
3. Communicate the results of their analysis.
4. Evaluate the model.

1. Build an appropriate model.
   1. Estimate an answer to the problem.
   2. Identify important components of the model.
   3. Collect or generate appropriate data.
   4. Analyze the situation using arithmetic, geometric, algebraic, and/or probabilistic or statistical methods.
2. Use the model to solve the problem.
   1. Propose a solution.
   2. Evaluate the reasonableness of the solution.
3. Communicate the results of their analysis.
   1. Share the findings in oral or written reports using appropriate mathematical language.
   2. Write summaries to explain how they reached their conclusions.
   3. Communicate quantitative relationships using symbols, equations, graphs, and tables.
4. Evaluate the model.
   1. Draw other inferences from the model.
   2. Identify the assumptions of the model.
   3. Discuss the limitations of the model.

Math 120 Student Learning outcomes

1. Master the functions from precalculus, using numerical, graphical, algebraic representations, while recognizing and explaining functions in context
2. Use the derivative of a function to determine the properties of the graph of the function and use the graph of a function to estimate its derivative
3. Solve problems in a range of mathematical applications using the derivative or the integral, including optimization, related rates, in-depth graphing problems, linearizations as approximations, and simple differential equations
4. Explain and apply the Mean Value Theorem and the Fundamental Theorem of Calculus
5. Determine the continuity and differentiability of a function at a point and on a set
6. Use appropriate modern technology to explore calculus concepts
7. (From precalculus): construct, interpret, and critique mathematical models of data obtained from applied scenarios
8. Compute limits and derivatives of algebraic, trigonometric, transcendental, implicit, and piecewise defined functions, both algebraically and graphically
9. Compute definite and indefinite integrals of algebraic and trigonometric functions using formulas and substitution

Course Topic Outline

Differential Equations in Spreadsheets
Modeling: building, using, communicating, evaluating.
An introduction to Limits
Finding Limits Analytically
One-Sided Limits
Continuity
Limits Involving Infinity
Computer methods; forward, backward, and central difference quotient
Modeling with Graphs and Functions
Instantaneous Rates of Change: The Derivative
Interpretations of the Derivative
Basic Differentiation Rules
The Product and Quotient Rules
The Chain Rule
Implicit Differentiation
Extreme Values
The Mean Value Theorem
Increasing and Decreasing Functions
Concavity and the Second Derivative
Curve Sketching
Related Rates
Optimization
Differentials (and linear approx)
Antiderivatives and Indefinite Integration
The Definite Integral
Riemann Sums
The Fundamental Theorem of Calculus
Numerical Integration
u-Substitution for integrals
Fourier Methods (bonus)
preview of Taylor series (bonus)

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 excuse (possibly with evidence) is given. In the unfortunate event of a need, the appropriate grade or grades might 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, standard projects, possible online discussions
• 30 percent total: small structured interviews (1 per week, a total of 6 or 7 of them, TBD)
• 20 percent: proposal, final project, and its interview

• 12 points: project proposal
• 100 points: project report (usually a Word file, or similar; see below)
• 50 points: presentation and interview

From:	To:	Grade:
-infinity 56 F
56	59.33333333	D-
59.33333333	62.66666667	D
62.66666667	66	D+
66	69.33333333	C-
69.33333333	72.66666667	C
72.66666667	76	C+
76	79.33333333	B-
79.33333333	82.66666667	B
82.66666667	86	B+
86	89.33333333	A-
89.33333333	infinity	A

Notice that there are about 40 homeworks (not including the projects), so each is worth about 1 percentage point on your grade. This means that missing one homework can easily move you from an A to an A-, or a B to a B-, etc, and missing two will almost DEFINITELY knock you down!

General Caveat

Advice from Other Calculus 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 might 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 day before assignments are due.
• 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 50 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!

Growth Mindset Statements

Instead of I'm not good at this,
try: what am I missing?

Instead of I'm awesome at this,
try: I'm on the right track.

Instead of I give up,
try: I'll use some of the strategies we've learned (or email the professor!)

Instead of This is too hard,
try: This may take more time and effort

Instead of I can't make this any better,
try: I can always improve so I'll keep trying.

Instead of I just can't do calc,
try: I'm going to train my brain in calculus

Instead of I made a mistake,
try: Mistakes (and spotting them) help me to learn better

Instead of She's so smart. I will never be that smart,
try: I'm going to figure out how she does it.

Instead of It's good enough,
try: Is it really my best work (in the time available)?

Instead of Plan "A" didn't work,
try: Good thing the alphabet has 25 more letters!

Standard University Policies and Resources

Resources

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.

University Writing Center

Land Acknowledgement

Standard University Policies

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