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Syllabus for Math 226/227, Spring 2021

Contact Information

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

Course Coordinator:

  • Prof. L. William Kazmierczak, Director of Calculus

Class Meeting Schedule - All Sections

Math 226: Integration Techniques and Applications, Feb 12 - March 29.

Math 227: Infinite Series, April 2 - May 18.

(227 Final Exam Date TBA)


A grade of C- or better in both MATH 224 and 225 is required to take MATH 226, but a grade of C or better is HIGHLY RECOMMENDED. Historical data shows that students with just C- in Calculus I (224/225) usually had serious trouble in Calculus II (226/227). You have been warned! A grade of a C- or better in MATH 226 is required to take MATH 227.

Office Hours

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


``Calculus Single Variable'' by James Stewart, Ninth Edition (with WebAssign Access Code), Cengage Learning, 20 Channel Center Street, Boston, MA.

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

There is free tutoring offered though University Tutoring Services. All information regarding tutoring can be found here:

If you have test anxiety, the Discovery Program has helpful information regarding test-taking strategies, found here:

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 2% of your total score based on attendance or classroom participation, 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.

Homework and WebAssign

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 have a multi-term access code from when taking 224/225, then you do not need to purchase another one. (Exception: if you only purchased one-semester access, then you'll need to buy it again.) If you bought the book through the Binghamton University Bookstore then it comes with an access code. This is a Multi-term Access Code and can be used for multiple semesters including Calculus III. This is the most affordable package with textbook that you'll find. If you did not buy the textbook package through the Bookstore, then you'll need to purchase ($119.99) “Cengage Unlimited”, 1 term -4 months. This is a multi-term access code and comes with the ebook. It can also be purchased through our Bookstore. You will have temporary free access to WebAssign for two weeks into the semester without an access code. All information regarding how to login with Class Key and purchase an access code can be found here WebAssign Student Quick Start Guide

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

WebAssign Login Page

Exams and Grading

In each half-semester course, Math 226 and Math 227, there will be the following grade distribution:

WebAssign Homework/Quizzes 20% (WebAssign HW will count for 10% of your course grade)
Skills Test 10%
Exam 1 35%
Exam 2 35%

A detailed description of the Skills Test, and how it will be administered, is given below. The above distribution is not used for online courses.

Instructor adjustments to your grade may include: written assignments, group 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. 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.

One final, extremely important, note about grading: instructors do not “give grades.” Instructors simply award points based on the work the student produces. Each student's point total will correspond to a letter grade decided at semester's end, and it will be the same for all sections. Very little subjectivity is involved in the grading process. The following is a typical letter grade distribution given for past semesters. This distribution could change due to exam scores.

Your Percentage Grade
92% - 100% A
89% - 91% A-
86% - 88% B+
81% - 85% B
78% - 80% B-
73% - 77% C+
69% - 72% C
63% - 68% C-
60% - 62% D
< 60% F

Exams with Solutions

Academic Honesty

Cheating is considered a very serious offense. 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.

Exams: According to the University Bulletin, cheating consists of: “Giving or receiving unauthorized help before, during or after an examination”.

Homework: Please keep in mind that plagiarism on HW is also considered cheating. You are encouraged to work with others when doing your HW, but you still need to submit your own work. In regards to WebAssign, under NO CIRCUMSTANCE are you permitted to submit an answer from Wolfram Alpha into WebAssign.

The shift to remote and hybrid teaching due to the COVID-19 pandemic has required that both instructors and students make changes to their normal working protocols for courses. Students are asked to practice extra care and attention in regard to academic honesty, with the understanding that all cases of plagiarism, cheating, multiple submission, and unauthorized collaboration are subject to penalty. Students may not collaborate on exams or assignments, directly or through virtual consultation, unless the instructor gives specific permission to do so. Posting an exam, assignment, or answers to them on an online forum (before, during, or after the due date), in addition to consulting posted materials, constitutes a violation of the university’s Honesty policy. Likewise, unauthorized use of live assistance websites, including seeking “expert” help for specific questions during an exam, can be construed as a violation of the honesty policy. All students should be familiar with the University’s Student Academic Honesty Code.

Basic Skills Test

Math 226 and 227 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 226/227 as a prerequisite. There will be one Basic Skills Test for 226 and one Basic Skills Test for 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.

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.

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.

Administration of Exams

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

The dates and times are given in the weekly schedule below and will be confirmed or modified before each exam.

The Exam 2 (Final Exam) for Math 227 for all sections will be administered on a common exam date.

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, 7.3, 7.4, 7.8, 8.1, 8.2, 10.1, 10.2

Math 227 Basic Skills Test: Sec. 10.3, 11.1, 11.2

Math 227 Exam 1: 10.3 - 10.4, 11.1 - 11.4.

Math 227 Exam 2 (Final Exam): Will cover 11.2 - 11.11 with a focus on 11.5 - 11.11.

Students may need to know and use results from the Chapter 11 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).

Schedule for Math 226/227 (Beginning Feb 12)

Next to certain sections below you'll see “Video Required”. These videos are located at the beginning of that section's assignment in WebAssign. You are required to watch these videos before that section is covered in class.

Week Dates Sections Topics Basic Skills Tests
1 Feb 12 6.1 (Video Required)Functions and their InversesNone
2 Feb 15-19 (Add Deadline is Wed Feb 17)6.2*The Natural Logarithmic Function
6.3*The Natural Exponential Function
6.4* General Logarithmic & Exponential Functions
3 Feb 22-26 (Drop Deadline Wed Feb 24) 6.5 (Video Required) Exponential Growth and Decay
6.6Inverses of Trigonometric Functions
6.8Indeterminate Forms & L'Hospital's Rule
4 Mar 1-5 7.1Integration by Parts The Basic Skills Test begins Monday March 1 at 5:00 PM, it covers sections 6.1-6.4 & 6.6. You have until Tuesday March 2 at 11:59 PM to finish both attempts.
7.2Trigonometric Integrals
Review None
5 Mar 8-12Exam 1 Topics cover sections 6.1-7.1Exam will take place in person during regular class time, either in your regular classroom or the Events Center
7.3 (Video Required) Inverse Trig Substitution
7.3 (Video Required) Inverse Trig Substitution
6 Mar 15-19 (Withdraw Deadline is Oct 2) 7.4 (Video required) Integration of Rational Functions
No ClassRejuvenation Day
7.8 (Video Required)Improper Integrals
7 Mar 22-26 8.1 (Video Required) & 10.1Arc Length & Parametric Curves
10.2 (Video Required)Calculus with Parametric Curves
ReviewFinal Exam covers all topics from the course but with focus on sections 7.2-10.2
8 Mar 29-31 (Withdraw Deadline is Mon. March 29) Final ExamExam will take place in person during regular class time, either in your regular classroom or the Events Center
No class(Math 226 is over)

Math 227 Begins Friday, April 2

Week Dates Sections Topics Basic Skills Tests
9 Apr 2 10.3Polar CoordinatesNone
10 Apr 5-9 (Add Deadline Thursday, Apr 8)10.4Calculus Using Polar Coordinates
10.4More Calculus Using Polar Coordinates
11.1 (Video)Sequences
11 Apr 12-16 (Drop Deadline Thursday, Apr 15)11.1 & 11.2Sequences & Infinite Series
11.2Infinite Series
11.3 (Video)Integral Test
12 Apr 19-23 11.4Comparison TestsThe Basic Skills Test begins Monday April 19 at 5:00 PM, it covers sections 10.3, 11.1-11.2. You have until Tuesday April 20 at 11:59 PM to finish both attempts.
ReviewExam covers sections 10.3, 10.4, 11.1-11.4None
Exam 1Exam will take place in person during regular class time, either in your regular classroom or the Events Center
13 Apr 26-3011.5Alternating Series
11.6Absolute Convergence, Ratio & Root Tests
11.8Power Series
14 May 3-7 11.8 & 11.9 (Video)Representing Functions as a Power Series
11.9 (video)Differentiation & Integration of a Power Series
11.10 Taylor Series
15 May 10-14 11.10 More Taylor Series
11.11Taylor Polynomials
11.11Taylor Polynomials
16 May 17 (Withdraw Deadline Monday, May 17)Review for final Final covers sects. 11.2 - 11.11 with a focus on sects. 11.6 - 11.11
17 May 19-21 Final Exam PeriodFinal exam date and location TBA

Math 226 Weekly Schedule Beginning on April 2

Week Dates Sections Topics Basic Skills Tests
1 Apr 2 (Add deadline October 26)6.1Functions and their InversesNone
2 Apr 5-9 (Drop Deadline is Thursday Apr 8) 6.2*The Logarithm Function
6.3*The Exponential Function
6.4*Arbitrary Bases
3 Apr 12 - 16 (Drop Deadline is Thursday Apr 15 6.5Exponential Growth and Decay
6.6Inverses of Trigonometric Functions
6.8Indeterminate Forms & L'Hospital's Rule
4 Apr 19 - 237.1Integration by PartsThe Basic Skills Test begins Monday April 19 at 5:00 PM, it covers sections 6.1-6.4 & 6.6. You have until Tuesday April 20 at 11:59 PM to finish both attempts.
ReviewExam covers sections 6.1-6.6, 6.8, 7.1None
Exam 1Exam 1 will take place in person during regular class time, either in your regular classroom or the Event Center
5 Apr 26 - 307.2Trigonometric Integrals
7.3Inverse Trig Substitution Trigonometric Integrals
7.3Inverse Trig Substitution Trigonometric Integrals
6 May 3 - 7 7.4Integration of Rational Functions by Partial Fractions
7.8Improper Integrals
7.8 & 8.1More Improper Integrals & Arc Length
7 May 10-14 10.1Parametric Equations (Curves)
10.2Calculus Using Parametric Curves
10.2Calculus Using Parametric Curves
7 May 17 (Withdraw Deadline is Monday, May 17) ReviewReview for Final Exam
May 19-21 226 Final ExamExam will take place in person at time and place to be announced

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.

Polynomial Long Division (Useful for Partial Fractions)

Factorization of polynomials (Useful for Partial Fractions)

Useful Limits to Know

Guide to Checking Convergence/Divergence of Series (from Prof. Kazmierczak)

Another Guide to Checking Convergence/Divergence of Series

A flowchart 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: 2021/04/05 17:24 by kaz