Math 121 section 2: Calculus II

Prof. Andrew M. Ross

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"


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: see

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
(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.
  1:30- 2:00 Office Hours
  2:00- 2:50 Math 121, PH 321 (CRN 20933)
  3:00- 3:30 Office Hours
 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)
	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.

    Supplementary Materials

    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


    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:

    Grading Policies


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


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


    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.

    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.

    Your overall score will be computed as follows: 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:

    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:

    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

    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.

    Standard University Policies

    In addition to the articulated course specific policies and expectations, students are responsible for understanding all applicable University guidelines, policies, and procedures. The EMU Student Handbook is the primary resource provided to students to ensure that they have access to all university policies, support resources, and student's rights and responsibilities. Changes may be made to the EMU Student Handbook whenever necessary, and shall be effective immediately, and/or as of the date on which a policy is formally adopted, and/or on the date specified in the amendment. Please note: Electing not to access the link provided below does not absolve a student of responsibility. For questions about any university policy, procedure, practice, or resource, please contact the Office of the Ombuds: 248 Student Center, 734.487.0074,, or visit the website: CLICK HERE to access the University Course Policies Student Handbook Link: Graduate School Policies:

    Food Pantry

    Swoop's Pantry (104 Pierce Hall,, 734 487 4173) offers food assistance to all EMU students who could benefit. Students are able to visit twice per month to receive perishable and non-perishable food items, personal hygiene items, baby items, and more. Students can visit our website for hours of operation and more information. If you are in a position to donate to Swoop's, I encourage you to do so!