# Winter Semester 2017

## Eastern Michigan University Creed

We believe the INTEGRITY of our work and the RESPECT we show for our fellow students, faculty, alumni and staff are an integral part of our ongoing EDUCATION.

We believe that the RELATIONSHIPS we have and those we continue to develop will support us as we learn and grow together as a community.

INTEGRITY adds value to our educational experience.

RESPECT promotes unity and understanding through individual differences within our community.

EDUCATION allows us to develop socially, intellectually, and emotionally.

RELATIONSHIPS are the foundation of our growth.

## Basic Information

Note: this syllabus is temporary, and may change up to the first day of class.
This version posted on: 2017-01-02

### 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.

Unofficial Better Title: "Integrals as the Mathematics of Unification, Used to Handle Wholeness"

### Prerequisites

At least a C in Math 120.

### 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: seehttps://www.math.umass.edu/graduate/sample-qualifying-exams 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/

For math majors and physics majors (but not math-education majors), I recommend that you take Computer Science (COSC) 120: Matlab Programming as soon as you can. Calc isn't even a prerequisite--you could take them together if they are offered the same semester. Let your friends know too! For those who are going farther in the calculus sequence, I STRONGLY recommend that you sign up for Linear Algebra (Math 122) this semester (right now!) and then Calc III the semester after that. Calculus is sort of like a language, and if you skip it for a semester, your skills will decay. Let your friends know too! Follow-up courses: Math 223 (Multivariable Calc a.k.a. Calc III), other math and physics courses.

### Class Format and Meetings

In-person, not hybrid or online.
```Section 2 CRN 20933: Mon, Tue, Wed, Thu  2:00pm-2:50pm; Pray-Harrold 321
```
4 credit hours.

Class meetings will be mostly interactive lectures, with some time to work on problems in class, and some time to go over problems from the homework. For some class sessions I'll ask you to bring a laptop, or buddy up with someone who has one, to use spreadsheets. Exams will also be held during class meetings.

I expect that you will work on Math 121 for 8 to 12 hours per week outside of class. 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.

### Instructor information

Professor Andrew Ross
Office: Pray-Harrold 515m
andrew.ross@emich.edu
http://people.emich.edu/aross15/
(734) 487-1658, but I strongly prefer e-mail instead of phone contact.
Math department main office: Pray-Harrold 515, (734) 487-1444

### Office Hours and other help

Here is my complete schedule.
```Mon/Wed
1:30- 2:00 Office Hours
2:00- 2:50 Math 121, PH 321 (CRN 20933)
3:00- 3:30 Office Hours
Tue/Thu
10:00-11:00 Office Hours
11:00-12:15 Stat 360-0, PH 405
12:15- 1:00 Office Hours, lunch
1:15- 1:45 faculty research meeting (Thursdays only)
1:30- 2:00 Office Hours
2:00- 2:50 Math 121, PH 321 (CRN 20933)
3:00- 3:30 Office Hours
5:00- 5:30 Office Hours
5:30- 6:45 Math 419W/519, PH 324 (CRN 26352/26362)
Fri:
no schedule--I'm often on campus, though.
I have various meetings to go to.
Send e-mail to make an appointment.
```

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. However, I am not available when I am teaching other classes (see above).

The Mathematics Student Services Center (or "Math Lab") is also here to help you, in Pray-Harrold 411. Their hours are posted here.

A good place to study, if the Math Lab doesn't suit you, is the Math Den, Pray-Harrold room 501.

Another resource on campus is the Holman Success Center, formerly the Holman Learning Center.

### 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 push for Data Science and Analytics 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

Our required text is chapters 5 through 11 of "Calculus, Early Transcendentals", mostly the 7th edition but 8th is okay too. by James Stewart published by Thomson--Brooks/Cole. There are three ways to get it: (These are 7th-edition links)

• Single Variable Calculus: Early Transcendentals, Volume 2 (just Calc II) (chapters 4-11) Amazon link ,
• Single Variable Calculus: Early Transcendentals (Calc I and II) (chapters 1-11) Amazon link
• The entire book (Calc I, II, and III)(Ch. 1-17), Amazon link (Vol 1,2,3)
• If you already have the 8th edition, that's okay too.

The textbook should be available at all the usual bookstores on and around campus.

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

A TI-83/84 calculator is strongly recommended. A TI-89 or TI-Nspire is not required, but is allowed just as much as a TI-84 sort of calculator. I'd have a hard time helping you with it, though. Some exams might have a section with no calculator allowed.

#### Course Web Page

I will post data files, homework assignment files, etc. on my home page.

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.

## Course Content

Chapters and Topics: Almost all of these sections will have a homework assignment.
Chapter Topic
5.4 Integrals: Review, Net Change
5.5 Integrals: the substitution rule
6.1 Areas between curves
6.2 Volumes
6.3 Volumes by cylindrical shells
6.4 Work
6.5 Average Value of a Function
7.1 Integration by Parts
7.2 Trigonometric integrals
7.3 Trigonometric substitution
7.4 Integration of rational functions by partial fractions
7.5 Strategy for integration
7.7 Approximate integration
7.8 Improper Integrals
8.1 Arc Length
8.2 Area of a surface of revolution
8.3 Applications to physics and engineering (pressure, centroids)
10.1 Parametric curves in the plane
10.2 Calculus of Parametric curves
10.3 Polar curves
10.4 Calculus of Polar curves
11.1 Sequences
11.2 Series
11.3 The integral test and estimates of sums
11.4 The comparison test
11.5 Alternating Series
11.6 Absolute convergence and the ratio and root tests
11.7 Strategy for testing series
11.8 Power series
11.9 Representations of functions as power series
11.10 Taylor and Maclaurin series
11.11 Applications of Taylor Polynomials

### Schedule

```1	1/4/2017	Wed	Introductions; Syllabus, etc.
2	1/5/2017	Thu	5.4  Integrals: Review, Net Change
3	1/9/2017	Mon	continued
4	1/10/2017	Tue	5.5  Integrals: the substitution rule
5	1/11/2017	Wed	continued
6	1/12/2017	Thu	7.7  Approximate integration
7	1/16/2017	Mon	MLK day
8	1/17/2017	Tue	6.1  Areas between curves
9	1/18/2017	Wed	6.2  Volumes
10	1/19/2017	Thu	continued
11	1/23/2017	Mon	6.3  Volumes by cylindrical shells
12	1/24/2017	Tue	6.4  Work
13	1/25/2017	Wed	6.5  Average Value of a Function
14	1/26/2017	Thu	continued
15	1/30/2017	Mon	review day
16	1/31/2017	Tue	exam 1
17	2/1/2017	Wed	7.1  Integration by Parts
18	2/2/2017	Thu	continued
19	2/6/2017	Mon	7.2  Trigonometric integrals
20	2/7/2017	Tue	continued
21	2/8/2017	Wed	7.3  Trigonometric substitution
22	2/9/2017	Thu	7.4  Partial fractions
23	2/13/2017	Mon	7.5  Strategy for integration; 7.8 warmup
24	2/14/2017	Tue	7.8  Improper Integrals
25	2/15/2017	Wed	continued
26	2/16/2017	Thu	review day; last day before Break Week
27	2/27/2017	Mon	first day after Break Week; 8.1 Arc Length
28	2/28/2017	Tue	exam 2
29	3/1/2017	Wed	8.2  Area of a surface of revolution
30	3/2/2017	Thu	8.3 Physics & Engr (pressure, centroids)
31	3/6/2017	Mon	continued
32	3/7/2017	Tue	10.1,2 Parametrics & calculus
33	3/8/2017	Wed	10.3,4 Polar & calculus
34	3/9/2017	Thu	11.1  Sequences
35	3/13/2017	Mon	continued
36	3/14/2017	Tue	11.2  Series
37	3/15/2017	Wed	continued
38	3/16/2017	Thu	11.3  Integral test; estimates of sums
39	3/20/2017	Mon	continued
40	3/21/2017	Tue	11.4  The comparison test
41	3/22/2017	Wed	continued
42	3/23/2017	Thu	11.5  Alternating Series
43	3/27/2017	Mon	11.6  Absolute convergence; ratio & root tests
44	3/28/2017	Tue	11.7  Strategy for testing series
45	3/29/2017	Wed	review day
46	3/30/2017	Thu	exam 3; start 11.8 pre-lab exercise
47	4/3/2017	Mon	11.8  Power series
48	4/4/2017	Tue	continued
49	4/5/2017	Wed	11.9  Representations of functions as power series
50	4/6/2017	Thu	continued
51	4/10/2017	Mon	11.10  Taylor and Maclaurin series
52	4/11/2017	Tue	continued
53	4/12/2017	Wed	11.11  Applications of Taylor Polynomials
54	4/13/2017	Thu	continued
55	4/17/2017	Mon	Bonus topics: Fourier? Filtering? DiffEq?
56	4/18/2017	Tue	review day; last day of classes
4/19/2017	Wed	other classes having finals
4/20/2017	Thu	other classes having finals
4/24/2017	Mon	other classes having finals
4/25/2017	Tue	Final exam 1:30-3:00---a HALF-HOUR EARLY
```

### Related Course Goals

Here are the goals that the AP Calculus AB course has (that's more like Calc I rather than Calc II, but they're still important!)

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.

#### Attendance

Regular attendance is strongly recommended. There will be material presented in class that is not in the textbook, yet will be very useful. Similarly, there are things in the textbook that are might not be covered in class, but are still very useful. If you must miss a class, arrange to get a copy of the notes from someone, and arrange for someone to ask your questions for you. If you are stuck on occasion without your usual child care, you may bring your child to class, and need not even get advanced permission (this is my personal policy--I don't know if EMU has a policy). Please be considerate to your classmates if your child becomes disruptive.

My lectures and discussions mostly use the document camera, along with demonstrations in Excel and other mathematical software. I do not usually have PowerPoint-like presentations, and thus cannot hand out copies of slides.

#### Homework

Homework will be assigned for most class periods. Ideally, you'd complete it in advance of the next class session.

#### Quizzes

We might have short quizzes. Some of these might be announced; others might be unannounced.

#### Exams

The dates of mid-semester exams shown above are temporary, but will be fixed during the first week of class. The final exam will be cumulative.

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.

Your overall score will be computed as follows:
• 30 percent: homeworks and quizzes
• 45 percent: mid-term exams (3 exams at 15 percent each)
• 25 percent: final exam.
The following scale will be used: 89 and above is an A; [86,89) is an A-; [83,86) is a B+, etc. This scale is based on student performance from last year.

Most homeworks and worksheets will be graded as credit/no credit instead of graded in detail. These homeworks might then be counted with less weight than the occasional graded-in-detail homework. If a student falls hopelessly behind in the homeworks, they may request a grand make-up assignment (which might be done at home or in the math testing room, at the instructor's discretion). This request might or might not be granted, at the instructor's discretion.

An important part of getting into graduate school is showing the ability to do research. Research doesn't just mean looking stuff up online or in the library--it means asking interesting questions and solving problems that nobody has solved before, or solving in new ways. Most of my classes (even Calculus 1) involve a mandatory project to get you thinking about research. While my Calc 2 class doesn't have a mandatory project, I encourage you to do a project for extra credit. Email me or come talk to me if you're interested.

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.

### General Caveat

The instructor reserves the right to make changes to this syllabus throughout the semester. Notification will be given in class or by e-mail or both. If you miss class, it is your responsibility to find out about syllabus and schedule changes, especially the due dates and times of various work.

### Advice from Other Math 121 Students

In the last few years, I've asked my Math 121 students to give advice to you, future Math 121 students, based on their experiences in my course. Here are some of the highlights:
• 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.
• Try to complete homework early and have questions prepared for next class.
• Spend some time making your note sheet.
• 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, not just the evens. 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 [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.
• Even though the odd problems are not required, do them, it helps you understand the concepts better (but do them last, that way you don't get stuck on a problem you don't need to do).
• 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, I will want you to try the homework that night and ask questions during the next class meeting, then you have the night after that to finish up the homework and turn it in at the start of the next class meeting. 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!

### University Writing Center

The University Writing Center (115 Halle Library; 487-0694) offers one-to-one writing consulting for both undergraduate and graduate students. Students can make appointments or drop in between the hours of 10 a.m. and 6 p.m. Mondays through Thursdays and from 11 a.m. to 4 p.m. on Fridays. The UWC opens for the Winter 2017 semester on Monday, January 9, and will close on Thursday, April 20. Students are encouraged to come to the UWC at any stage of the writing process.

The UWC also has several satellite locations across campus (in Owen, Sill, Marshall, Porter, Pray-Harrold, and Mark Jefferson). These satellites provide drop-in writing support to students in various colleges and programs. The Pray-Harrold UWC satellite (rm. 211) is open Mondays through Thursdays from 11 a.m. to 4 p.m. The locations and hours for the other satellites can be found on the UWC web site: http://www.emich.edu/uwc.

UWC writing consultants also work in the Academic Projects Center (116 Halle Library), which offers drop-in consulting for students on writing, research, and technology-related issues. The APC is open 10 a.m. to 5 p.m. Mondays through Thursdays. Additional information about the APC can be found at http://www.emich.edu/apc.

Students seeking writing support at any location of the University Writing Center should bring a draft of their writing (along with any relevant instructions or rubrics) to work on during the consultation.