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Syllabus for Math 226/227, Spring 2019

Contact Information

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

Course Coordinators:

  • Prof. L. William Kazmierczak and Carlos Vega [226/227]
  • Prof. Walter Carlip [226, Second Half]

Class Meeting Schedule - All Sections

Math 226: Integration Techniques and Applications, January 23 - March 13, 2019.

Math 227: Infinite Series, March 25 - May 10, 2019.

(227 Final Exam TBA: May 13-17)

Math 226: Integration Techniques and Applications, March 25 - May 10, 2019


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, 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-231, 233), is staffed by instructors who teach the course and will be open after the first week of classes. 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 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”.

Exams and Grading

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

WebAssign Homework 7%
Instructor Adjustments 2%
Quizzes 5%
Skills Test 16%
Exam 1 35%
Exam 2 35%

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

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 low 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.

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.

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 for the Skills Test section 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 take it twice, but only one attempt per week. If you wait until the second week the test is offered, you will only get one try.

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.

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 (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, 10.1, 10.2

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

Math 227 Exam 1: 10.1 - 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 January 23)

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 Jan 21–24 6.1 (Video Required)Functions and their Inversesnone
6.2*The Natural Logarithmic Function
2 Jan 28–Feb 1
(Add Deadline: Monday, Jan 28)
6.3*The Natural Exponential Function
6.4* Genral Logarithmic & Exponential Functions
6.5 (Video Required) Exponential Growth and Decay
3 Feb 4–8
(Drop Deadline:
Monday, Feb 4)
6.6Inverses of Trigonometric Functions
6.8Indeterminate Forms & L'Hospital's RuleSkills Test 1: First Attempt begins Wednesday, Feb 6. Last day to take first attempt is Wednesday, Feb 13
7.1 (Video Required)Integration by Parts
4 Feb 11–157.1More Integration by Parts
ReviewSkills Test 1: Second Attempt begins Thursday, Feb 14. Last day to take last attempt is Thursday, Feb 21
5 Feb 18–22Exam 1All exams in class
7.2Trigonometric Integrals
7.3 (Video Required)Inverse Trig Substitution None
6Feb 25–Mar 1
(Withdraw Deadline: Thursday, Feb 28)
7.3More Inverse Trig Substitution
7.4 (video required) Integration of Rational Functs. by Partial Fractions
7.8 (Video Required)Improper Integrals
7 Mar 4–88.1 (Videos Required)Arc Length
10.1Parametric Equations (Curves)
10.2 (Videos Required)Calculus with Parametric Curves
8 Mar 11–15Review
Final ExamIn class
Math 226 is over.No Class

Math 227 Begins Monday, March 25

Week Dates Sections Topics Basic Skills Tests
10 March 25–29
(Add Deadline: Friday, March 29)
10.3Polar Coordinates
10.4Calculus Using Polar Coordinates
10.4More Calculus Using Polar Coordinates
11 April 1–5
(Drop Deadline: Friday, April 5)
11.1 (Videos Required)More Sequences
11.1 & 11.2Sequences & Series
11.2 (Videos Required)Series
12 April 8-1211.2More SeriesSkills Test 1: First attempt window is Monday, April 8 through Friday, April 12.
11.3 (Video Required)Integral Test
11.4Comparison Test
13April 15–19 ReviewSkills Test 1: Second attempt begins Monday, April 15.
Exam 1All exams in class
Easter Break
14April 22–26 11.5Alternating Series Test & Estimation ThmSkills Test 1: Last day to take second attempt is Tuesday, April 23.
11.6, 11.7Absolute Convergence & Ratio and Root TestsNone
11.8Power Series
15April 29–May 3
(Withdraw Deadline: Monday, April 29)
11.9 (Video Required)Representing Functions as Power Series
11.9, 11.10Taylor and Maclaurin Series
11.10More Taylor and Maclaurin Series
16May 6–1011.11 (Video Required)Taylor Polynomials and their Applications
11.11Taylor Polynomials
17Wednesday May 14Final Exam: 5:40-7:40 in GW 69EX (West Gym)Final exam will cover sections 11.2-11.11 with a focus on sections 11.5 through 11.11.

Math 226 Weekly Schedule Beginning on March 25

9 March 25-29 (Add Deadline is Friday, 3/29)6.1 (video required)Inverses of Functions None
6.2*The Logarithm Function
6.2* and 6.3*More Logarithm Function; The Exponential Function
10 April 1-5 (Drop Deadline is Friday, 4/5)6.3*More Exponential Function
6.4*General Exponential and Logarithmic Functions
6.4* and 6.5General Exponential and Logarithmic Functions; Growth and Decay
11 April 8-126.5 (video required)Exponential Growth and Decay
6.6Inverses of Trigonometric FunctionsThe Basic Skills Test starts Thursday, April 11, covering 6.2-6.4 and 6.6. You have until Thursday April 18 to take 1st attempt.
6.8Indeterminate Forms & L'Hospital's Rule
12 April 15-197.1 (video required)Integration by Parts
7.2Trigonometric Integrals
Easter Break
13 April 22-26Review for Exam 1 on sections 6.1 through 7.12nd attempt for Basic Skills Test can be taken April 22 - April 26
Exam 1All Exams in Class
7.3 (video required)Inverse Trigonometric SubstitutionLast day for Basic Skills Test
14 April 29-May 3 (Withdrawal Deadline is Monday, 4/29)7.4 (video required)Integration of Rational Functions & Partial FractionsNone
7.3 & 7.4Review of Integration Techniques
7.8 (video required)Improper Integrals
15 May 6-108.1 (video required)Arc Length
10.1Curves Defined Parametrically
10.2 (video required)Calculus with Parametric Curves; Last Day of Class
15 May 13-17Final Exam Period; Mon. May 13, 2019 12:50–2:50 GW 68EX; Check BU Brain for confirmation; Final exam will cover all topics with a focus on sections 7.2, 7.3, 7.4, 7.8, 8.1, 10.1-10.2

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: 2019/05/08 23:53 by kaz