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Syllabus for Math 226/227, Spring 2016

General Information About All Sections

Contact Information

The instructor for your section will provide you with contact information.

General Administration of Course: Prof. Alex Feingold

Class Meeting Schedule - All Sections

Math 226: Integration Techniques and Applications, Jan. 25 - Mar. 15, 2016.

Math 227: Infinite Series, Mar. 18 - May 11, 2016.

Section Instructor Days Times Room
20 Ting Su MWF 8:00-9:30 WH G002
21 Richard Behr MWF 8:00-9:30 OR 100D
22 Ruiqi Liu MWF 8:00-9:30 LN 1406
23 Thomas Kilcoyne MWF 8:00-9:30 FA 209
24 Micah Loverro MWF 8:00-9:30 LN 2447
25 John Brown MWF 8:00-9:30 AP G15
28 William Kazmierczak MWF 9:40-11:10 OR 100D
29 Nan Bi MWF 9:40-11:10 LN 1406
30 Alex Feingold MWF 9:40-11:10 WH G002
31 Wiktor Mogilski MWF 11:20-12:50 WH G002
32 Nan Bi MWF 11:20-12:50 OR 100D
33 Xiaojie Du MWF 11:20-12:50 LN 1406
34 Kunal Sharma MWF 11:20-12:50 FA 209

Note that Walter Carlip will be the coordinator responsible for the following sections of

Math 226: Integration Techniques and Applications, Mar. 18 - May 11, 2016.

Section Instructor Days Times Room
01 MWF 8:00-9:30 EB N25
02 Walter Carlip MWF 8:00-9:30 LH 11
03 MWF 8:00-9:30 Canceled
04 Charles Evans MWF 9:40-11:10 EB N25
05 Amelia Mattern MWF 9:40-11:10 LH 11
50 Xin Qi MWF 8:00-9:30 SW 329

Click here for a weekly schedule of topics and tests for Math 225/226 sequence.

Solutions to 226 Exam 1 April 20, Spring 2016

226 Practice Final with Solutions Spring 2016


A grade of C- or better in Calculus I is required, but a grade of C or better is HIGHLY RECOMMENDED. Historical data shows that students with just C- in Calculus I usually had serious trouble in Calculus II. You have been warned!

Office Hours

Each instructor will inform you of office hours or scheduled problem sessions outside of class times.


``Calculus Single Variable'' by James Stewart, Eighth Edition (with WebAssign Access Code), Cengage Learning, 20 Channel Center Street, Boston, MA 02210, USA, ISBN: 978-1-305-26663-6.

Objectives and Course Contents

Calculus II is being taught in two half-semester courses; Math 226: Integration Techniques and Applications, and Math 227: Infinite Series.

The main goal of Calculus II is to continue the development of differential and integral calculus started in Calculus I, including specific topics which have been found to be valuable for applications in many other fields. Students will be introduced to new classes of functions including the exponential functions, logarithm functions, and inverse trig functions. Students will then learn how to apply the techniques of Calculus (differentiation and integration) to those functions. The method of L'Hospital's Rule will be taught for dealing with certain limits. Various techniques for integration will be taught (integration by parts, trig integrals, trig substitutions, partial fractions, and improper integrals). We will study several applications of integration, including: finding the length of arc of a curve, finding the area of a surface of revolution (even when the equations are given in parametric form, in rectangular or polar coordinates).

Infinite sequences and series will be studied, and methods for investigation of their convergence will be taught (the integral test, the comparison tests, the ratio and root tests, alternating series, absolute convergence and power series). Methods of representing functions as power series with a radius of convergence will be taught, as well as the Taylor series representations of a given function.

The course material is vital to the study of Calculus III and Differential Equations, and is very useful in many other courses in the Department of Mathematical Sciences and in other departments (e.g., Physics, Chemistry, Biology, and Economics).

Help Outside of Class

The Calculus 2 Help Room room, located in Whitney Hall (WH-235), is staffed by some of the instructors and will be open starting Sept. 8, 2015, during most business hours. Students can walk in with no appointment and can ask questions of any available instructor. The exact schedule for this semester will be posted here soon. Click here for the Help Room schedule.

People learn in many different ways: through reading, listening, practicing and working with others. Students may wish to work with others while doing the practice problems or preparing for an exam. That is acceptable and even encouraged. However, unethical behavior in this class will not be tolerated. Cheating on an examination, or any other ethics violation, will result in a serious penalty. See the section below on Academic Honesty.

General Comments

Regular class attendance is required for success in this course. Lack of attendance will most likely result in a lower grade. When a student does not come to class, it is a clear message to the instructor that the student does not think he/she can teach them. The instructor may assign 15 points of your total score based on attendance, classroom participation or additional quizzes, and will decide borderline cases. The material is a combination of theory and calculation, and it is necessary to understand the theory in order to do sensible calculations and interpret them correctly. Lectures can be interrupted at any time for questions. At the start of each class be ready to ask questions about homework problems or about the previous lecture. A grade of C or better in Calculus I is strongly recommended for this course. If you do not meet that condition, see the instructor immediately for advice.

Student use of cell phones and other electronic devices is becoming increasingly disruptive in class and is actually insulting to the instructor. Holding the cell phone in your lap and looking down to text does not make you invisible! All electronics should be turned off and put away before the beginning of class. Students found using such devices may be asked to leave the class.

University Attendance Policy

Students are expected to attend all scheduled classes, laboratories and discussions. Instructors may establish their own attendance criteria for a course. They may establish both the number of absences permitted to receive credit for the course and the number of absences after which the final grade may be adjusted downward. In such cases it is expected that the instructor stipulate such requirements in the syllabus and that the syllabus be made available to students at or near the beginning of classes. In the absence of such statements, instructors have the right to deny a student the privilege of taking the final examination or of receiving credit for the course, or may prescribe other academic penalties if the student misses more than 25 percent of the total class sessions. Excessive tardiness may count as absence.

If you are seriously ill (running a fever, upset stomach) you should not come to class. Documented illness of this sort is an excused absence and will not be counted against your attendance grade. Absence for more than one or two days needs to be documented by health services. If you are going to be ill for an extended period of time (a week or more) be sure to contact your instructor as soon as you can so that plans can be made for you to make up the work you will be missing.


For each section of material covered there will be an assignment of problems on WebAssign. Your WebAssign homework counts towards your grade. Study groups are encouraged, but students should not become too dependent on others. Watching the instructor, or other students, do the problems will not be enough to learn the material. It will be necessary for you to do many exercises yourself in order to be successful on the exams. Attempts to solve homework problems provide the best way to learn the material and to prepare for exams.

WebAssign is an online homework system which includes an e-book version of our text. If you buy the textbook through the University bookstore it comes with an access code for WebAssign. If you do not buy the textbook from the bookstore then you will need to purchase an access code on the WebAssign website. You will have temporary free access to WebAssign for 2 weeks into the semester without an access code. If you bought a WebAssign access code from a previous semester, you do not have to buy it again. (Exception: if you only purchased one-semester access, you'll need to buy it again.) When logging into WebAssign for the first time you will need to self-enroll with a “Class Key”. The “Class Key” will be provided to you by your instructor. All info for getting started with WebAssign can be found here WebAssign Student Quick Start Guide

Your username is your Binghamton University username and the institution code is “binghamton”.

Exams, Grading and Cheating

In each half-semester course, Math 226 and Math 227, there will be a total of 300 possible points, distributed in the following way for Math 226:

WebAssign Homework 20 Points
Instructor Adjustments 15 Points
Quizzes 15 points (for example, five 3-point quizzes)
Skills Test 50 points
Exam 1 100 points
Exam 2 100 points

but for Math 227 points will be distributed this way:

WebAssign Homework 20 Points
Instructor Adjustments 15 Points
Quizzes 15 points (for example, five 3-point quizzes)
Exam 1 125 points
Exam 2 125 points

A detailed description of the Skills Test in Math 226, and how it will be administered, is given below.

Instructor adjustments to your grade may include: additional quizzes, attendance and classroom participation. Your grade will be determined primarily by your numerical scores on the quizzes, WebAssign homework, the skills test and the exams. The numerical score of each exam will be given a letter grade interpretation in order to give you some idea of how you stand in relation to all other students in the course. Your Total of all points at the end of the course will also be given a letter grade interpretation, which will be your course grade, but borderline cases can be adjusted up or down based on your instructor's judgment.

We may post some practice exams and their solutions here to help you prepare. They have the questions first, which you should try to answer without looking at the solutions. After each exam is graded and returned, a set of solutions will be posted here on this webpage. You should compare your exam to the solutions, and understand your mistakes so you will be able to do such problems correctly in the future. That would be a very good way to prepare for the final exam. If you do not understand your mistakes, or think your exam was not correctly graded, you should immediately (at most within two days) bring the test to your instructor for re-evaluation. If you are not satisfied with the re-evaluation of your test, you can appeal to the course coordinator, Prof. Feingold, whose decision will be final. DO NOT MAKE ANY CHANGES OR WRITE NEW MATERIAL ON YOUR GRADED EXAM!! Turning in a modified exam for extra points is CHEATING. Instructors may be making copies of random exams before they are returned, so if a student changes a graded exam, it will be clearly shown by comparison with the copy.

Any cases of cheating will be subject to investigation by the Academic Honesty Committee of Harpur College.

Practice Exams and Solutions

In addition to the review done by your instructor in class, there will be a review done by UTS for the Math 227 Exam 1. Jason is running it in SL-212 on Sunday, April 17, 2:30-6:30. The exam will be given on Wednesday, April 20.

A practice Exam 1 for Math 227 is available from the following link: Math 227 Practice Exam 1 and its solutions

A practice Exam 2 for Math 227 is available from the following link: Math 227 Practice Exam 2 and its solutions

There are links to three pdf files below (Supplementary Materials and Links) to help guide your strategy understanding series. Two are new guides made by Bill Kazmierczak.

Solution guides to the two versions of Exam 1 for Math 227 are available from the following two links:

Math 227 Exam 1V1 Solutions

Math 227 Exam 1V2 Solutions

The letter-grade interpretation of the Math 227 Exam 1 scores are in the following table. The average over all sections was 95.87 = 76.696%.

Letter Grade Exam 1 Score Percentage Cutoff
A 115 - 125 92%
A- 110 - 114 88%
B+ 105 - 109 84%
B 100 - 104 80%
B- 95 - 99 76%
C+ 90 - 94 72%
C 80 - 89 64%
C- 75 - 79 60%
D 65 - 74 52%
F 0 - 64 0%

The letter-grade interpretation of the Math 227 Exam 2 scores are in the following table. The average over all sections was 104.56 = 83.648%.

Letter Grade Exam 1 Score Percentage Cutoff
A 115 - 125 92%
A- 110 - 114 88%
B+ 105 - 109 84%
B 100 - 104 80%
B- 95 - 99 76%
C+ 90 - 94 72%
C 85 - 89 64%
C- 78 - 84 60%
D 70 - 77 52%
F 0 - 69 0%

The letter-grade interpretation of Total Course scores for Math 227 are in the following table. The average over all sections was 237.5 = 79.166%.

Letter Grade Total Course Score
A 270 - 300
A- 255 - 269
B+ 240 - 254
B 225 - 239
B- 215 - 224
C+ 200 - 214
C 175 - 199
C- 165 - 174
D 150 - 164
F 0 - 149

Academic Honesty

Cheating is considered a very serious offense. According to the University Catalog, cheating consists of: “Giving or receiving unauthorized help before, during or after an examination”. The full strength of Binghamton Academic Honesty Policy will be applied to anyone caught cheating. This may include failing the course, and further disciplinary action.

Basic Skills Test

Math 226 will have a Basic Skills Test which will cover basic computational skills that you absolutely must be able to do for any class that has Math 226 as a prerequisite. There will be one Basic Skills Test for 226 in Spring 2016, but in future semesters we may also have one in 227. The Basic Skills test will be administered and evaluated by computer, with no partial credit, but you may take it twice. A Practice Basic Skills Test will be available on WebAssign containing all the possible problems you could be asked on the actual Basic Skills Test.

The Basic Skills Test will be administered by computer in Whitney Hall, Room G18, using the same software as the WebAssign homework, so you must have a WebAssign key before you take the test. For security reasons, you must use the computers provided. You are not assigned a particular time to take the test – you will reserve a time for your test via the following link: Calculus Testing Center Reservation System.

You have a window of two weeks to try it, and you may take the test twice, but only once per week. If you wait until the second week the test is offered, you will only get one try. The time window is weeks 3 and 4, that is, Feb. 8 - 19.

Only exact answers are accepted in WebAssign. For example, 1/3 cannot be written as .33 and pi cannot be written as 3.14. No electronic devices are allowed and none may be taken during a lavatory break.

If you try the Basic Skills test more than once, only your highest score is counted. Your best strategy is to take the test during the first week it's offered, so if it doesn't go well, you can make another attempt to improve your score in the second week.

To take into account the lack of partial credit, scores on the Skills Test will be rounded up, so that scores between 70% and 79% will count as a 79%, scores between 80% and 89% will be recorded as 89%, and scores 90% to 100% will receive 100%. If a student's highest score is lower than 70%, their highest percentage among the attempts will be recorded and will not be rounded up. Since the Skills Test counts for 50 points toward the final grade, the rounded percentage will be multiplied by 50 to determine the point total.

Administration of Exams

Exams for all sections will be administered at your normal meeting time in your normal meeting room, except for the Math 227 Exam 2.

The dates, times and places given below for Exams will be confirmed or modified before each exam.

The Exam 2 for Math 227 for all sections will be administered in a common exam during May 13-19.

The schedule of exams is as follows:

Math 226 Basic Skills Test: Feb. 8 - 19, 2016.

Math 226 Exam 1: Feb. 22 2016.

Math 226 Exam 2: Mar. 14, 2016.

Math 227 Exam 1: Apr. 20, 2016.

Math 227 Exam 2: May 16, 2016, 8:00 - 10:00 AM, GW-69 (West Gym) for all sections.

Note that the Math 226 mini-course Add Deadline is Jan. 29, 2016, the Drop Deadline is Feb. 5, 2016, and the Withdrawal Deadline is Feb. 26, 2016.

The Math 227 mini-course Add Deadline is Mar. 23, 2016, the Drop Deadline is April 4, 2016, and the Withdrawal Deadline is Apr. 26, 2016.

A detailed contents of each exam will be determined one week before the exam, but we expect it to be as follows:

Math 226 Basic Skills Test: Sec. 6.2*, 6.3*, 6.4*, 6.6.

Math 226 Exam 1: Sec. 6.1, 6.2*, 6.3*, 6.4*, 6.5, 6.6, 6.8, 7.1.

Math 226 Exam 2: Sec. 7.2 - 7.4, 7.8, 8.1, 8.2, 10.1, 10.2.

Math 227 Exam 1: 10.3, 10.4, 11.1 - 11.6.

Math 227 Exam 2: 11.7 - 11.11.

Students may need to know and use results from sections covered on Exam 1 in order to answer questions on each Exam 2, so you should treat Exam 2 as if it were a Final Exam for that course.

Important Note: No use of calculators, cellphones or laptop computers will be allowed during exams.

Students are not allowed to take a cellphone to the lavatory during any exam.

Scientific calculators may be needed for some homework.


Note: Students who miss an exam because of illness must contact the instructor ahead of the exam (or as soon afterwards as possible) and provide proof of the illness (doctor's note or call from health service).



Week 1: Jan. 25, 27, 29 6.1, 6.2*, 6.3*
Week 2: Feb. 1, 3, 5 6.4*, 6.5
Week 3: Feb. 8, 10, 12 6.6, 6.8, (Window for Basic Skills Test)
Week 4: Feb. 15, 17, 19 7.1, 7.2, Review, (Window for Basic Skills Test)
Week 5: Feb. 22, 24, 26 Math 226 Exam 1, 7.3, 7.4
Week 6: Feb. 29, Mar. 2, 4 7.8, 8.1, 8.2
Week 7: Mar. 7, 9, 11 10.1, 10.2, Review
Week 8: Mar. 14, 16, 18 Math 226 Exam 2, No Class, 10.3
Week 9: Mar. 21, 23, 25 10.4, 11.1
Week 10: Mar. 28, 30, Apr. 1 Spring Break
Week 11: Apr. 4, 6, 8 11.2, 11.3, 11.4
Week 12: Apr. 11, 13, 15 11.5, 11.6, 11.7
Week 13: Apr. 18, 20, 22 Review, Math 227 Exam 1, 11.8
Week 14: Apr. 25, 27, 29 11.8, 11.9
Week 15: May 2, 4, 6 11.9, 11.10
Week 16: May 9, 11 11.11, Review
Week 17: May 16 Math 227 Exam 2, 8-10 AM, GW-69

Here we provide links to documents and websites you may find useful throughout the semester. They do not constitute an official part of the course, nor are they endorsed by the Department of Mathematical Sciences. Use them at your own discretion.

Factorization of polynomials (Useful for working with Partial Fractions)

Useful Limits to Know

Guide to Checking Convergence/Divergence of Series

Another Guide (by Bill Kazmierczak) to Checking Convergence/Divergence of Series

A flowchart (by Bill Kazmierczak) to help you check Convergence/Divergence of Series

The following are pdf files with a polar coordinates grid (in radians or degrees) on which you can conveniently make graphs of functions given in polar coordinates.

Polar Coordinates Graph (radians)

Polar Coordinates Graph (degrees)

Visual Calculus - Step by step tutorial on the topics of our course.

For Calc II see:

An excellent source for math videos

Another excellent source for math videos

Integration: Techniques of Integration, Numerical Integration, Improper Integrals

Sequences, Series, Power Series



Visual Calculus has guided tutorials on almost all the subjects we're doing. You see a question posted and work on it. If you click on the link, it will do one step of the solution. If that helps you, fine. If not, click again and it will show the next step. Thus, if you get stuck, you can get one hint at a time. It won't give away the answer all at once, so you can practice each step for yourself. Try it!

Calculus On the Web an online tutorial.

The math forum - various math resources. Check out the topics on calculus

MathWorld - more math resources.

Mathnerds - get hints on your math questions.

calculus/math_226_227/start.txt · Last modified: 2016/05/18 14:37 by alex