Department of Mathematics and Statistics, Binghamton University

people:mckenzie:math223

2022-12-09T18:46:58-04:00

WELCOME TO MATH 223/224 INTRODUCTION TO CALCULUS/DIFFERENTIAL CALCULUS

See Math 223/224 Director's page for syllabus with grade policy and distribution of points to tests, quizzes/take-home assignments, participation, and WebAssign.

To create your WebAssign account, go to Cengage log in and register. Our class key is BINGHAMTON07007209

The e-book for Stewart's Precalculus 7e and Calculus 9e are found on the main student page in Cengage. Readings from both will be assigned; most problem sets will come from Calculus.

Exercises in Precalculus, Stewart, 7th ed. are to do in addition to the WebAssign. If they are listed it's because they focus on the skills you should have. Ask in class about any you have difficulty with.

Each week I'll desk check and sometimes collect a selection of these exercises. I'll let you know in the preceding class when I do this.

WEEK 1 AUG 24-26

Summary of assignments for first week – if an exercise gives you trouble, rest assured we'll cover them in class. These early exercises give me a broad idea of how familiar you are with fundamentals.

Exercises are to be done in a separate part of your notes. It's up to you to do them, and to have questions ready to ask in class. I will tell you ahead of time when I plan to collect a set.

Wednesday

Watch Real numbers
Read Appendix A in Calculus
In Appendix A, do #1, 5, 8, 10, 11, 25, 31, 43, 45, 49, 51
Do WebAssign warmup (you have free access until Sept 7)

Friday to Sunday

View Dr Kazmierczak's required videos and read the corresponding sections in Precalulus e-book:

Inequalities Sec 1.8

Lines Sec 1.10 Coordinate plane; graphs of equations; circles Sec 1.9

Helpful internet mini-videos on solving inequalities:

Video 1 Video 2 Video 3 Video 4

In Precalculus e-book, do Exercises Sec 1.8 #16, 18, 22, 32, 38, 47, 52, 60, 65, 79, 81, 97, 99, 113, 119 (Monday desk check only)
Lecture Notes Week 1

Go to Cengage unlimited for info on purchasing and renting the book

WEEK 2 Aug 29-Sept 2

WA schedule with some extensions to help those just getting into WA:

By Tuesday night, Appendix A and Warm-up Appendix C
By Wednesday, class time, Appendix B and Warm-up Sec 1.1
By Friday, class time, Warm-up Sec 1.2
By Friday before midnight, App C

—-

Monday-Tuesday

Do in Precalulus: Sec 1.10 (lines): #3-8 (short answer), 25, 29, 35, 37, 47, 59, 67, 77
View Graphing a circle in standard form and Completing the square to find circle equation
Do in Precalulus: Sec 1.9 (coordinate plane, circles) #7, 15, 16, 25, 85, 89, 91, 95* (we can do it in class), 99, 103

View Dr Kaz's videos, read corresponding sections in Precalulus e-book:

Rational expressions & domain Sec 1.4

Graphs of functions Sec 2.2

Getting information from a graph Sec 2.3

Transformations of functions Sec 2.6

Wednesday-Thursday

Read in Calculus e-book, Secs 1.1 & 1.2
Kazmierczak videos Equations, Quadratic fcns & models & Polynomial fcns & their graphs
Do in Calculus: Sec 1.1 (Four ways to represent functions) #39, 41, 47, 51, 53, 56 (important piecewise function), 65, 70, 81, 83, 85
Read Sec 1.2 (Mathematical models/essential fcns) #1, 4, 17, 21, 27, 28
Study Table 3: Essential fcns & their graphs (know how to sketch from memory by midterm)
Here are my own Essential fcn sketches with domains & short video to accompany it: Domain & range of 9 basic fcns
Summary of Stewart exercises so far: Precalulus Secs 1.8, 1.0, 1.10, & Calculus Secs 1.1, 1.2

Without fail, on Friday I'll do a desk check of these

Lecture notes Week 2

LABOR DAY WEEKEND

Before Tues lecture

If you need more on domain, view Domain of rational and root functions
Everyone view Odd and even functions
Read in Calculus, Sec 1.3 On fcn transformations
View Kazmierczak videos Fcn transformations (shifts) & Fcn transformations (reflections, stretches, and compressions)

WEEK 3 SEPT 6-9

WebAssigns due this week:

Class warmup Sec 1.3, due Tuesday night 9/6
Sec 1.1, due Wednesday night 9/7
Class warmup Dividing polynomials and factoring, due Thursday morning 9/8
Sec 1.2, due Thursday night 9/8
Class warmup App D, due Friday 9/9 before class, Sec 1.3, due Friday night

Tuesday

The second half of lecture today kind of fell short, in that I didn't take the time to do more combined transformations. So … I'll be adding some notes to the lecture notes and inserting them as before. And I will embellish the intro to polynomials.

Polynomial hw has been moved to Thursday night. Catch up on WebAssign.

* On the last page of Lecture notes Week 2 I've described the domains of the four composite functions. Express these in interval notation and hand in tomorrow. It's not an involved exercise!

Kazmierczak videos Dividing polynomials & Real zeros of polynomials

Wednesday-Thursday

Do exercises in Precalculus Sec 2.6 #7-51 odd (mainly short answer), 59, 63, 65, 69, 83-89 odd
Do exercises in Precalculus Sec 3.3 (dividing polynomials): #4 (can't do it with synthetic in the form it's in) 13, 17, 23, 27, 31, 39, 57, 63
Kazmierczak videos for Friday: Trigonometry of right angles, Unit circle
Division algorithm office hour video

Friday First trigonometry lecture

WEEKEND SEPT 10-11

Read App D in Calculus and for greater detail see Precalulus Secs. 5.1-2, 6.1-3
Do Exercises in Precalculus Sec 3.4 (real zeros of polynomials): #1, 5, 9, 11, 17, 31, 55, 61
Kaz video Trig fcns of real numbers
Trig exercises to start: Sec 5.1: #1, 5, 13, 17, 19, 25, 29, 47, 51 and Sec 5.2: 5-21 odd, 27-35 odd

WebAssigns due next (I've been generous with extensions of older function material, get them done)

CLASS WARMUP: Section 1.1 due Saturday night
Dividing Polynomials and Factoring due Monday night
Section 1.3 (Part 2) due Monday night Appendix D (Trigonometry)
Math 223 Midterm Review (not graded) Definitely do it by Wed class time

Lecture notes Week 3

WEEK 4 Sept 12-16

Monday New trig and review for Friday's midterm

Watch Unit circle video
UNIT CIRCLE ART HW GRADE! Create a unit circle to bring to class on Wednesday. Use a jar lid or compass to make an accurate circle and use a straight edge to make the lines. Prefer blank or copy paper to lined.
Short trig quiz on Wednesday (using unit circle you create)
Finish up Sec 5.1 and 5.2 exercises

Trigonometry exercises for the rest of the week

Textbook exercises in Calculus App. D #1, 5-11 odd, 19, 23-33 odd, 65-71 odd, 83-87 odd
Nutley H.S. solving trig eqns worksheet #1-10 (focus on sine, cosine, tangent)

Graphs are not on the quiz tomorrow, but an ability to render a graph is needed to both understand inverse functions next week and to draw trig transformations on the final).

Some of the questions here on the Previous midterm Fall 2015 and Solutions are not in our list, some are. Do the WebAssign midterm review and of course see exercises I have listed.

Midterm topics: Absolute value inequalities, quadratic or rational inequalities; write parabola or circle in standard (h,k) form to determine features and be able to graph result; transformations of essential functions and intercepts; polynomial stuff; trigonometry part 1 (anything we have done, including solving a simple trig eqn (Nutley HS).

Watch the Office hour video!. You can see some of the more recent midterm questions here, the one I can't post but did cover many items from in class and a couple here.

Friday Midterm, no lecture

—- WEEKEND SEPT 17-18

View Arc length and area of a sector of a circle
In Precalculus do Sec 6.1 Exercises #53-69 odd with arc length s = theta x r; sector area = (r²)(theta/2)
In Precalculus read Sec 2.8 (inverse fcns), Sec 5.5 (graphs of inverse trigonometric functions), and Sec 6.4 (evaluating inverse trig fcns)
View Kaz videos:

WEEK 5 Sept 19-23

Monday

First go back and do the weekend viewing; then do the arc length and sector area problems – I will post my own short video on this, as I never got a chance to talk about it in class
In Calculus read Sec 6.1 up to p 415 (skip the end of this section on derivatives!)
Sec 6.1 #17-29 odd, #37, 39
In Calculus read Sec 6.6 to p 489 (skip limits!)
View Inverse trig fcns and triangles
Try these inverse trig evaluations in Sec 6.6 #1-9 odd

Here’s my Arc length and sector area video

Wednesday

View Kazmierczak mini-videos (total viewing time is under 9 minutes!):

To hand in by email by Friday 3 pm from Nutley High School worksheet, #13, 15, and 16; be sure to show your complete work!

FRIDAY WE WILL MEET REMOTELY AT THE ZOOM LINK

Friday's quiz moved to Wednesday when we return. 5 questions total, 3 topics:

1. Determine if a fcn is even, odd, or neither using definitions 2. Find inverse of non-trigonometric fcn and graph the two fcns on one plane 3. Do three inverse trig function calculations, including a composition

WEEKEND SEPT 25

Friday Sept 23 lecture

Office hour questions on inverse trig fcns with Rui

Do these Calculus textbook exercises for Wednesday:

Trigonometry: Sec 6.6, #1-13 odd Inverse fcns: Sec 6.1 #7-13 odd, 25-29 odd Log and exp fcns: Sec. 6.2 #7, 9, 17; Sec. 6.3 #3-7 odd, 15, 17, 21, 23

WEEK 6 SEPT 28-30

Wednesday

Do these Calculus textbook exercises for Friday: Sec 6.2* #1, 3, 7, 9; Sec 6.3* #3, 5 (leave in e or ln form), 17, 21, 23; Sec 6.4* #1, 3, 7, 9

Friday-Sunday

Read in Calculus Secs 1.5 and 1.6; for more detail see Precalculus Secs 13.1 and 13.2

View Finding limits numerically and graphically and Finding limits algebraically

—- WEEK 7 OCT 3-7

Monday-Thursday All readings and exercises are in the Calculus text:

Sec 1.5, p 60, in addition to #1-18 ALL, do #27-35 odd

Read again Sec 1.6

view these: Lots of limits part 1 (with overview of techniques)

and Lots of limits part 2 (skip over the limits at infinity for now; you'll see them in 24)

Sec 1.6, p 70, do #1-31 odd (do as many as you can using the reading and video help); for class discussion, #44

By next week, getting ready for final, in Sec 6.3, p 438 do #3-11 all; #21-31 odd; 43, 47, 49-53

WEEKEND OCT 7-9

Friday-Sunday

I meant to give you this definition of vertical asymptote, which formally ties VA limit:

x = a is a vertical asymptote of f(x) is the limit as x goes to a from either direction is + or - infinity

The below video gives the same definition with several examples similar to what we did in class:

Vertical asymptotes

Lecture Notes: I re-uploaded above any that disappeared; here are the latest:

Lecture notes week 5 Lecture notes week 7 part 1 and Lecture notes week 7 part 2

Complete the WebAssignments by tonight, please. Continue working out the limit exercises. If WA asks for limits at infinity, you may omit those, but let me know.

Start working on Math 223 Fall 2015 Final and Math 223 Fall 2016 Final for practice

Read Sec 1.8, continuity

WEEK 8

Wednesday class will be at this Zoom link

View Limits and continuity

In Sec 1.6, p 70, do these further limit exercises #33, 44*, 45, 51, 54*

In Sec 1.8, do continuity exercises #3, 7-27 odd, 39-48 all, #54-58 all

You may like a complete overview of limits, view Intro to limits, Properties of limits (kind of tedious, but some good examples), and Determinng limits

On Friday you’ll have a Math 223 skills quiz. Today, Wednesday, is the zoom class.

Wednesday Here is Today's zoom lecture recording

Besides studying for the final exam, prepare for the Math 223 skills quiz on Friday, which will be these topics:

Domain of function
Essential graphs, including graphing an absolute value transformation (like we did today)
Factoring, including special factors
Evaluating trig expressions
Evaluating log and exponential expressions
Finding intercepts of circles and parabolas
Basic limits

Practice quiz page 1

Practice quiz page 2

Key to practice skills quiz page 1

Key page 2

Key graphs

Lecture Notes (recent) from Rui

Sunday Oct 16

Solutions to Fall 2015 final

Solutions to Fall 2016 final

WEEK 9 HERE IS WHERE MATH 224 BEGINS

Monday Review limits and continuity homework, readings and videos. For the new folks, here was the WEEK 8 homework. For the continuing students, this is a good time to go back and do the text exercises you might have 'missed'

Read in Calculus Secs 1.5 and 1.6; for more detail see Precalculus Secs 13.1 and 13.2

View Finding limits numerically and graphically and Finding limits algebraically

Do Sec 1.5 p 60, #1-18 ALL, do #27-35 odd and Sec 1.6, p 70, do #1-31 odd, #33, 44*, 45, 51, 54*

View these: Lots of limits part 1 (with overview of techniques)

and Lots of limits part 2 (skip over the limits at infinity for now; you'll see them in 24)

Lecture Notes: I re-uploaded above any that disappeared; here are the latest:

Lecture notes week 5 Lecture notes week 7 part 1 and Lecture notes week 7 part 2

Read Sec 1.8, continuity

Do Sec 1.8 exercises #3, 7-27 odd, 39-48 all, #54-58 all

NEW Link to Warm-up and flip videos for Math 224 which I will explain in class tomorrow how to navigate.

Wednesday Reminder: All readings and exercises are in Stewart Calculus, 9th ed. e-book on the Cengage site

1. View rest of Limit of a function, started in class, and Detail of limit of sin(x)/x as x --> 0

2. If you are not on solid ground with inequalities and absolute values, read Appendix A in Calculus e-book

3. Read Sec 1.4 and view Tangent and velocity problem

4. Write up to hand in:

Find the instantaneous rate of change (IROC) of f(x) = sq rt x at x = 1. (This is the a value.) Do this by using the detailed formula for finding IROC at x = a and showing all the work that gets you to the numerical answer. It's a limit problem.

Draw an accurate sketch of this function, and indicate with two secant lines arbitrary through the curve at a = 1 and a + h = 1 + h

Write a sentence about the most interesting thing you learned or were reminded of today in class (about mathematics, I mean, though feel free to share other new things you'd like to share)

Friday

Do exercises in Sec 1.4 and do exercises #3, 5, 7 (video and reading in Wednesday homework)

View Derivatives as rates of change

Read Sec 2.1

Do exercises #15, 17, 19, 23, 27

View these important Kazmierczak videos. They are largely review of limits, but without this understanding, the development of derivative has no framework (the first and last I have posted before).

And finally, something we looked at on Friday, but take another look! It will help you soon: Trigonometric limits

First set of WebAssignments, due next week; please do before the due date so you don't miss 8 a.m. posted time:

CLASS WARM-UP: Section 1.4 Monday Oct 31, 8 a.m. (before class)

WEEK 10

CLASS WARM-UP for Section 2.1 Wednesday Nov 2, 8 a.m. (before class)

Monday-Tuesday

Read Sec 2.2 and view the videos therein as well as:

Sec 2.2 Differentiation formulas

Wednesday I moved WebAssign Warmup Sec.2.3 to Saturday night Nov 5; you have Sec 2.4 Warmup on Monday.

Here are Mon and Wed lecture notes from Rui

From p 125 of Sec 2.2, “How can a function fail to be differentiable?” We looked a bit at this. The graph of function fails to be differentiable at points where either we can't establish a tangent line (corners and cusps – think absolute value function at x = 0); at points of discontinuity (kind of obvious); and at a point where the tangent line is vertical, hence its derivative undefined (e.g. cube root function).

Friday: 2-question quiz: something like #15 and #17 (interpreting a graph); something like #27-30 (equation of line tangent to polynomial curve at a given x, use power rule to determine derivative)

To hand in Friday with the quiz: Sec 2.2, #26 use definition of derivative (NO SHORTCUTS–an LCD will be needed)

Continue reading in Calculus, Sec 2.2; do Exercises #3, 7, 11, 13, 15

View these: Position, velocity, acceleration--nice! and Sec 2.3 Power rule

WEEKEND NOV 5-6

See the SKILLS TEST NEWS from the Director, Professor Kazmiercak

Do Sec 2.3 Derivative rule exercises #1-49 every other odd (#1, 5, 9, 13, etc.) #59, 63, 67, 83, 87

* Read App D and Sec 2.4, trigonometry review and trigonometric function derivatives

View Derivatives of trigonometric functions

Next WebAssigns I gave you a bit more time for Sec 2.3 Warmup. Moved the Practice Skills Test 1 to where you can see it in the WA current list.

CLASS WARMUP Sec 2.3 due 11-6-22 Sunday night

CLASS WARMUP Sec 2.4 due 11-7-22 Monday morning

WEEK 11

Monday

WebAssignments: Sec 2.2 due Nov 8 Tuesday night

CLASS WARMUP Sec 2.5 due Nov 9 Wednesday morning

For practice: WebAssign Skills Test 1. We've covered all the material. Have questions to ask in class!

Do Sec 2.4 trig derivatives p 154 #3, 7, 8, 13, 16, 23, 25, 39, 35, 37, 41, 45 (try also #47, 51)

Wednesday

TWO ANNOUNCEMENTS:

NO LIVE LECTURE TODAY, WEDNESDAY. Lecture will be recorded and posted this evening for your required viewing.

Ms Debra Levy at Cengage asks me to have you write to her directly debra.levy@cengage.com, if you have enrollment problems or other technical issue. She fixes things efficiently.

ASSIGNMENT

Thursday

View my recorded lectures:

Nov 10 part 1

Nov 10 part 2

Read (already assigned Monday night) Sec 2.5 and view Chain rule

Do Sec 2.5 chain rule p 162 #1, 3, 5, 9, 16, 18, 21, 34, 37, 45, 53, 51, 67

Friday to Sunday

MIDTERM IS WEDNESDAY! Do the Fall 2016 midterm and have questions ready for Monday. Skip the question on intermediate value theorem. If you have no questions, I will proceed with the lecture on new material, except for…

… Rui's question on trig limits in class. She was referring to lim as x goes to 0 of sin(ax)/bx. Or, sin(ax)/sin(bx). Thanks, Rui, for asking! She does the exercises. Which translates into high test marks, as I draw from them for the exams I write. We'll discuss both these types of limits.

I did prove the chain rule on my video with f(u(x)) notation! WATCH MY 2 RECORDED VIDEOS (required for Wed attendance) and Prof Mosely on chain rule. The real world scenario is motivating!

On Sunday I'll check Panopto for your viewing time and ask a sneaky question to see if you didn't just leave it running and go to the kitchen.

We start implicit differentiation on Monday (not on midterm). Read Sec 2.6 and see Dr Kazmierczak explain Implicit differentiation

WEEK 12

Monday The old exam I posted is actually the Fall 2016. Here it is again as well as solutions. And below it, the Spring 2016 midterm and solutions.

Fall 2016 midterm and Solutions

Spring 2016 midterm and Solutions

Tuesday I reserved the big room down the hall from my office, WH Room 227, for office hours, 1:30-3:30. That was the window I could get, so be sure you come sometime in that window with questions.

Wednesday-Thursday View Implicit differentiation and read Sec 2.6

WebAssign CLASS WARMUP for Section 2.6 due by class time Friday

WebAssign CLASS WARMUP for Section 2.7 due by class time Monday

Weekend homework in text will be posted Friday

Friday-Sunday

Implicit differentiation (ID) lets us find dy/dx even when y cannot be expressed as an explicit function of x (or other relevant IROC, such as a related rate)

View helpful ID video 1 and ID video 2

* Do Sec 2.6 exercises #3, 4 7, 11, 17, 21, 25, 29, 31, 39, 41

In-class quiz on Monday (inspired by above exercises)

Read Sec 2.7 and view motion videos (rates of change in science, and with deeper focus on motion):

Do Sec 2.7 exercises #1, 3, 9, 17, 21

WEBASSIGN CLASS WARMUP Section 2.6 due Sunday night

WEEK 13 THANKSGIVING WEEK

Mon-Fri The following work is not to be ignored over the break!

Read Sec 2.8 Related Rates and view:

Do Exercises #9, 13 (these are practically the same as the sliding ladder problem) and #2 (circle, see last video)

WEBASSIGN CLASS WARMUPS have been extended. PLEASE do them before the time runs out.

Friday-Sunday

Recent lecture notes (mine)

Here 20221209172236112.pdfis a Brief lecture on rates of change in science, but at the start I do an exercise from Stewart on implicit diff'n as well.

The final sections we will cover are Secs. 3.1, 3.3, 3.4, 3.5 (Sec 3.2 is covered in Math 225)

View Finding critical numbers of a function and local max and min

Finding absolute max and min of a fcn on a closed interval

Read Sec 3.1 and try textbook exercises: Sec. 3.1 #1, 3, 9, 11, 17, 18, 31, 35, 41, 45, 51, 59

NOTE: Skills Test 2 begins Nov 28. It covers trigonometric derivatives, chain rule, and implicit differentiation. You have until Dec 9, to take all 3 attempts.

WEEK 14

Monday-Tuesday

Read 3.3

Continue Sec 3.1 exercises.

(I didn’t do absolute extremes today, only local, of which there is more to say about the first derivative test for local maxima and minima, as demonstrated in class today, but not named as such. Much more on this soon.)

Webassign 3.1 warmup due Wed morning

Webassign 3.3 warmup due Wed night

View First derivative add shape of a graph and Second derivative and shape of a graph

Wednesday-Friday

Webassign 3.4 warmup due Friday morning

Do Sec. 3.3 #1, 4, 11-14, 15, 17, 20, 21, 27, 43, 49, 62, 63

My handout summary (used in class today) of Curve sketching with calculus

Today's recorded remote class

Thursday note I was looking at the exercises I mentioned in lecture yesterday, and I meant to assign #18 in obht Sec 2.7 and 2.8. The first #18 is interesting because its derivative is linear, but it will be good to see how it relates to absolute max and min!

Hold off on Sec 3.3 till I decide on two good ones.

Weekend assignment

View How to sketch a curve

In place of Dr Kazmiercazk paper assignment, you are doing this one, to hand in Monday: HW Quiz 5*.

* I forgot to add identify any vertical and horizontal asymptotes. Please do so by using the limit definitions if they apply.

We will use Dr. Kazmaierczak’s for curve sketching review this week.

WEEK 15

Monday

I was looking at Stewart solutions manual, and I notice it has slightly different problems (actually, the same, but different numbering, some of them). They are from an earlier edition. So after my class tonight I will match them up and post pics of many I like including the ones you did.

For homework, be sure you have read through Sec 3.5 (but skip Sec 3.2)

On Wednesday I will go over the Kazmierczak problems (not to hand in) and we will do a selection of Stewart problems on limits at infinity, from Sec 3.4 (no hw on those tonight, but catch up if you need to on WebAssign).

Wednesday-Friday

Sec 3.4 exercises #7, 8, 13, 17/18 (limits at infinity)

Recent notes through Friday part 1 and part 2

Previous exam (2016) with solutions

Math 226/227 (Calculus 2; formerly Math 222)

2026-04-05T19:18:42-04:00

Syllabus for Math 226/227, Spring 2026

Contact Information

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

Course Coordinator:

Dr. L. William Kazmierczak, Director of Calculus [226/227]

Class Meeting Schedule - All Sections

The drop deadline is February 2 and the withdrawal deadline is February 25

Math 226: Integration Techniques and Applications, January 21 - March 11.

The drop deadline is March 27 and the Withdrawal deadline is April 23

Math 227: Infinite Series, March 16 - May 6.

(227 Final Exam Date TBA)

The drop deadline is February 2 and the withdrawal deadline is February 25

Math 227: Infinite Series, January 21 - March 11.

The drop deadline is March 27 and the Withdrawal deadline is April 23

Math 226: Integration Techniques and Applications, March 16 - May 6.

(226 Final Exam Date TBA)

Prerequisites

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.

Textbook

``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.

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 Help Rooms, located on the 2nd floor of Whitney Hall, are 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 ask questions of any available instructor. Click here for the Help Room schedule. There are no Help Room or office hours after the final exam during the week of midsemester grading.

There is free tutoring offered though University Tutoring Services. All information regarding tutoring can be found here: http://www.binghamton.edu/clt/tutoring-services/index.html

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. 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.

Students are expected to attend all scheduled calculus classes. It is important to attend class in order to learn the material and successfully complete the course. University policy states that if a student misses more than 25 percent of the total class sessions, then the instructor has the option to fail that student. University policy states that if a student misses more than 25 percent of the total class sessions, then the instructor has the option to fail that student and not allow them to take the final exam. So, if a student has more than 5 unexcused absences for our half semester course and they fail the midterm exam, then they will not be permitted to take the final exam and will receive a course grade of “F” if they do not withdraw from the course.

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 purchased the textbook/WebAssign or Cengage Unlimited (1 semester) from our bookstore when taking 224/225, then you do not need to purchase it again. If you bought the book through the Binghamton University Bookstore then it comes with an access code. This Access Code works 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 “Cengage Unlimited” (1 semester, 4 months). This comes with the ebook and also gives you access through Calculus III. 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.

To gain access to your WebAssign HW section you need to self-enroll by submitting the “Class Key” supplied to you by your instructor. All information regarding how to login with Class Key and purchase an access code can be found here Binghamton University WebAssign Registration

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

Just submit your section's “Class Key” here 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	10%
Quizzes (in-class), Attendance, Other	15%
Skills Test (at Math Testing Center)	13%
Exam 1	31%
Exam 2	31%

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.

The Midterm and Final will cover higher-level problems. These are paper tests, graded by the instructors, (and you will not be allowed to re-take these). They will not focus on the sort of basic computational problems covered by the Basic Skills Tests, although of course you may be required to do some basic computations as part of a bigger problem. Your average on both exams (Midterm and Final) must be at least a 50% to pass Math 227 and a 50% to pass Math 226, regardless of what your other course scores are.

The grade category of “Quizzes” may include written assignments, group quizzes, attendance, or in-class work at the discretion of your instructor. But most or all of your score/grade for Quizzes will be determined by the numerical scores from the 15–20 minute quizzes that you take in class. 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. If you do not understand your mistakes after receiving your graded exam back, 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

226 Exam 1 with solutions, Spring 2017

226 Exam 1 with solutions, Spring 2016 A

226 Exam 1 with solutions, Spring 2016 B

226 Final with solutions, Spring 2016 v1

226 Final with solutions, Spring 2016 v2

226 Final with solutions, Fall 2017 v1

……………………………….

227 Exam 1 Spring 2016 with solutions

227 Exam 1 Fall 2017 _:_ Solutions Here

227 Final Spring 2016 with solutions

227 Practice Finals (three) The solutions for these are located here: solutions

There are links to three pdf files below (Supplementary Materials and Links) to help guide your strategy understanding series.

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.

The Basic Skills Test will be administered by computer in Whitney Hall, Rooms G12 & 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'll receive an email once the Reservation System is ready.

You have a window of about 10 weekdays to take it twice. You cannot take it twice in one day.

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 calculators or electronic devices are permitted during the test. No calculators or electronic devices are permitted during the test. You cannot use your cell phone for any reason while taking the test. If a proctor catches a student looking at their cell phone while taking the test then that student will receive a score of “0” and their instructor will be notified.

If you take 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: Sects 6.2*, 6.3*, 6.4*, 6.6.

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

Math 226 Exam 2: Sects 7.2, 7.3, 7.4, 7.8, 10.1, 10.2

Math 227 Basic Skills Test: Sects 10.3, 11.1, 11.2

Math 227 Exam 1: Sects 10.3 - 10.4, 11.1 - 11.5.

Math 227 Exam 2 (Final Exam): Will cover sects 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.

ANYONE UNABLE TO TAKE AN EXAM SHOULD CONTACT THEIR INSTRUCTOR AHEAD OF TIME TO EXPLAIN THE REASON.

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 Wednesday, January 21)

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 - 23	6.1 (Video Required)	Functions and their Inverses	None
1	Jan 21 - 23	6.2*	The Natural Logarithmic Function
2	Jan 26 - 30 (Add Deadline - Monday, Jan 26)	6.3*	The Natural Exponential Function
		6.4*	General Logarithmic & Exponential Functions
		6.5 (Video Required)	Exponential Growth and Decay (No Newton's Law of Cooling)
3	Feb 2 - 6 (Drop Deadline is Monday, Feb 2)	6.6	Inverses of Trigonometric Functions
		6.6 & 6.8	Inverses of Trigonometric Functions & “Indeterminate Forms” & L'Hospital's Rule
		6.8	“Indeterminate Forms” & L'Hospital's Rule
4	Feb 9 - 13	7.1 (Video Required)	Integration by Parts	The Basic Skills Test begins on Monday Feb 9 and you have until Feb 13 to take at least your first attempt. Last day to take your last (2nd) attempt is Feb 24.
		7.2	Trigonometric Integrals
		7.2 & Review	More Trig Integrals
5	Feb 16 - 20	Exam 1 Topics cover Sections 6.1-7.1	Exam will take place in class during normal class time
		7.3 (Video Required)	Inverse Trig Substitution
		7.3 & 7.4 (Video required)	More Inverse Trig Subst. & Integration of Rational Functions
6	Feb 23 - 27 (Withdraw Deadline - Wednesday, Feb 25)	7.4 (Video required)	Integration of Rational Functions	Feb 24 is the last day to take your last (2nd) attempt of the Basic Skills Test
		7.8 (Video Required)	Improper Integrals	None
		No Class	Rejuvenation Day
7	March 2 - 6	7.8 & 10.1	More Improper Integrals & Parametric Curves
		10.1/10.2 (Video Required)	Calculus with Parametric Curves
		10.2 (Video Required)	Calculus with Parametric Curves (No Surface Area, No Area Under Curve)
8	March 9 - 11	Catch up & Review
8	March 9 - 11	Final Exam	The exam is during normal class time on Wed March 11 and covers all topics from the course but with a focus on Sections 7.2-10.2
9	March 13	No Class on Fri March 13	Math 226 has ended

Math 227 Begins Monday, March 16

Week	Dates	Sections	Topics	Basic Skills Tests
9	Mar 16 - 20 (Add Deadline - Friday, March 20)	10.3	Polar Coordinates	None
		10.4	Calculus Using Polar Coordinates
		10.4	More Calculus Using Polar Coordinates
10	Mar 23 - 27 (Drop Deadline - Friday, March 27)	11.1 (Video)	Sequences
		11.1 & 11.2	More Sequences & Infinite Series
		11.2	More Infinite Series
11	Mar 30 - April 3	No Class	Spring Break
		No Class	Spring Break
		No Class	Spring Break
12	April 7 - 10 (Monday Classes Meet on Tuesday April 7)	11.3 (Video)	Integral Test (No estimating the sum)	Skills Test 1 Begins on Tuesday, April 7 and covers sections 10.3, 11.1, & 11.2. Last day to take your last attempt is Tuesday, April 21
		11.4	Comparison Tests (No Estimating sums)
		11.5	Alternating Series & Alternating Series Estimation Thm
13	April 13 - 17	Review Problems
		Exam 1 Topics cover Sections 10.3 - 11.5	Exam will take place in person during class time
		11.5 & 11.6	Absolute Convergence, Ratio & Root Tests
14	April 20 - 24 (Withdraw and P/F Grade Option Deadline - Thursday, April 23)	11.8	Power Series	Last day to take your last attempt is Tuesday, April 21
		11.8	More Power Series	None
		11.9 (Video)	Representing Functions as a Power Series	None
15	April 27 - May 1	11.9 (Video)	More Representing Functions as a Power Series	None
		11.10	Taylor Series (No binomial coefficients, No Binomial Series Formula, No Multiplication/Division of Power Series)
		11.10	More Taylor Series
16	May 4 - 8	11.11	Taylor Polynomials (No Application to Physics)
		Review Problems	11.5 - 11.11
		No Class	Reading Day
17	May 9 - 14	Final Exam on Date and Time Assigned by Registrar, View Final Exam schedule here	Final Exam covers all topics from the course but with a focus on Sections 11.5 - 11.11

Schedule for Math 227 (Beginning Wednesday, January 21)

Week	Dates	Sections	Topics	Basic Skills Tests
1	Jan 21 - 23	10.3	Polar Coordinates	None
1	Jan 21 - 23	10.4	Calculus Using Polar Coordinates
2	Jan 26 - 30 (Add Deadline - Monday, January 26)	10.4	More Calculus Using Polar Coordinates
		11.1 (Video)	Sequences
		11.1 & 11.2	More Sequences & Infinite Series
3	Feb 2 - 6 (Drop Deadline is Monday, Feb 2)	11.2	More Infinite Series
		11.3 (Video)	Integral Test
		11.4	Comparison Tests
4	Feb 9 - 13	11.5	Alternating Series	The Basic Skills Test begins on Monday Feb 9 and you have until Feb 13 to take at least your first attempt. Last day to take your last (2nd) attempt is Feb 24.
		11.5	Absolute Convergence
		Review
5	Feb 16 - 20	Exam 1 Topics cover Sections 10.3-11.5	Exam will take place during normal class time
		11.6 & 11.8	Ratio & Root Tests and Power Series
		11.8	Power Series
6	Feb 23 - 27 (Withdraw Deadline - Wednesday, February 25)	11.9 (Video)	Representing Functions as a Power Series	Last day to take your last (2nd) attempt is Tuesday Feb 24.
		11.9 (Video)	More Representing Functions as a Power Series	None
		No Class	Rejuvenation Day
7	March 2 - 6	11.10	Taylor Series
		11.10	More Taylor Series
		11.11	Taylor Polynomials & Taylor's Inequality
8	March 9 - 11	Review & 11.11	More Taylor's Inequality
8	March 9 - 11	Final Exam	The Final Exam is during normal class time on Wed March 11 and covers all topics from the course but with a focus on Sections 11.6 - 11.11
9	March 13	No Class	Math 227 has ended

Schedule for Math 226 (Beginning Wednesday, March 16)

Week	Dates	Sections	Topics	Basic Skills Tests
9	March 16 - 20 (Add Deadline - Friday, March 20)	6.1 (Video Required)	Functions and their Inverses	None
		6.2*	The Natural Logarithmic Function
		6.3*	The Natural Exponential Function
10	March 23 - 27 (Drop Deadline - Friday, March 27)	6.4*	General Logarithmic & Exponential Functions
		6.5 (Video Required)	Exponential Growth and Decay (No Newton's Law of Cooling)
		6.6	Inverse of Trigonometric Functions
11	March 30 - April 3	No Class	Spring Break
		No Class	Spring Break
		No Class	Spring Break
12	April 7 - 10 (Monday classes meet on Tues April 7)	6.8	“Indeterminate Forms” & L'Hospital's Rule	Skills Test 1 Begins on Tuesday, April 7 and covers sections 6.1-6.4* & 6.6. Last day to take your last attempt is Tuesday, April 21
		6.8 & 7.1	More L'Hospital's Rule & Integration by Parts
		7.1 (Video Required)	More Integration by Parts
13	April 13 - 17	Review
		Exam 1	Exam covers sections 6.1-7.1
		7.2	Trigonometric Integrals
14	April 20 - 24 (Withdraw and P/F Grade Option Deadline - Thursday, April 23)	7.3 (Video Required)	Inverse Trig Substitution	The last day to take your last attempt of the Skills Test is Tues, April 21
		7.3 (Video Required)	More Inverse Trig Substitution	None
		7.4 (Video Required)	Integration of Rational Functions
15	April 27 - May 1	7.4 & 7.8 (video required)	Improper Integrals
		7.8 (Video required)	More Improper Integrals
		10.1	Parametric Curves
16	May 4 - 8	10.2 (Video Required)	Calculus with Parametric Curves (No Surface Area, No Area Under the Curve)
		10.2 & Review for Final	More Calculus with Parametric Curves (No Surface Area, No Area Under the Curve) & Review
		No Class	Reading Day
17	May 9 - 14	Final Exam on Date and Time Assigned by Registrar, View Final Exam schedule here	Exam covers all topics from the course but with focus on Sections 7.2-10.2

Supplementary Materials and Links

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)

For Calc II see:

An excellent source for math videos

Another excellent source for math videos

MathWorld - more math resources.

Cycloid

Applications: Flipped Calculus at Binghamton SUNY

2015-08-28T22:35:15-04:00

Linearization and Differentials

Section 2.9 in Stewart's Calculus.

Preclass Learning Objectives:

Lines are functions, even tangent lines.
Linearization of a function f(x) approximates the values of f(x).
The change along the y-axis can be approximated with linearization.

Section	Instructor	Days	Times	Room
01	Binbin Huang	MWF	8:00-9:30	LN 2409
02	Simon Joyce	MWF	8:00-9:30	LN 2447
03	David Biddle	MWF	8:00-9:30	EB R15
04	Mathew Wolak	MWF	8:00-9:30	SL 302
05	Binbin Huang	MWF	9:40-11:10	LN 2409
06	Simon Joyce	MWF	9:40-11:10	LN 2447
07	Alex Feingold	MWF	9:40-11:10	WH G002
08	Jaiung Jun	MWF	11:20-12:50	LN 2409
09	Adam Allan	MWF	11:20-12:50	LN 2447
10	Matt Zaremsky	MWF	11:20-12:50	WH G002

WebAssign Homework	40 Points
Instructor Adjustments	30 Points
Quizzes	30 points (for example, ten 3-point quizzes)
Exam 1	100 points
Exam 2	100 points
Exam 3	100 points
Final Exam	200 points.

Letter Grade	Numerical Range
A	92 - 100
A-	88 - 91
B+	84 - 87
B	77 - 83
B-	72 - 76
C+	67 - 71
C	60 - 66
C-	55 - 59
D	50 - 54
F	0 - 49

Letter Grade	Numerical Range
A	90 - 100
A-	86 - 89
B+	82 - 85
B	75 - 81
B-	70 - 74
C+	64 - 69
C	56 - 63
C-	50 - 55
D	41 - 49
F	0 - 40

Letter Grade	Numerical Range
A	180 - 200
A-	170 - 179
B+	160 - 169
B	150 - 159
B-	140 - 149
C+	130 - 130
C	110 - 129
C-	95 - 109
D	80 - 94
F	0 - 49

Week 1: Aug. 31 - Sept. 4	6.1, 6.2, 6.3
Week 2: Sept. 7 - Sept. 11	6.4*, 6.5
Week 3: Sept. 14 - 18	6.6, 6.8
Week 4: Sept. 21 - 25	Review, Exam 1
Week 5: Sept. 28 - Oct. 2	7.1, 7.2, 7.3
Week 6: Oct. 5 - Oct. 9	7.4, 7.8
Week 7: Oct. 12 - 16	11.1, 11.2
Week 8: Oct. 19 - 23	Review, Exam 2, 11.2
Week 9: Oct. 26 - 30	11.3, 11.4
Week 10: Nov. 2 - 6	11.5, 11.6
Week 11: Nov. 9 - 13	11.8, 11.9
Week 12: Nov. 16 - 20	11.10, 11.11
Week 13: Nov. 23 - 27	8.1, 8.2
Week 14: Nov. 30 - Dec. 4	Review, Exam 3, 10.1
Week 15: Dec. 7 - 11	10.2, 10.3, 10.4
Week 16: Dec. 14 - 18	Review, Final Exam

Section	Instructor	Days	Times	Room
01	Alex Feingold	MWF T	10:50-11:50 10:05-11:30	AP G14 LN G208
02	Diego Penta	MWF R	9:40-10:40 8:30-9:55	AP G15 LN G332
03	Withanage De Mel	MWF R	10:50-11:50 10:05-11:30	AP G15 LN G208
04	Gangotryi Sorcar	MWF R	12:00-1:00 11:40-1:05	AP G14 AP G15
05	Patrick Milano	MWF T	12:00-1:00 11:40-1:05	AP G15 AP G15
06	Elizabeth Perry	MWF T	1:10-2:10 10:05-11:30	AP G14 LN G209
07	Kevin Klonoff	MWF R	1:10-2:10 10:05-11:30	OR 100D LN G209
08	Walter Carlip	MWF T	2:20-3:20 4:25-5:50	FA 209 S2 144
09	Andrew Kelley	MWF R	2:20-3:20 4:25-5:50	OR 100D S2 143
10	David Biddle	MWF R	3:30-4:30 4:25-5:50	AP G15 S2 260
11	Qiyi Lu	MWF T	3:30-4:30 4:25-5:50	LN 2403 S2 260
12	Laura Anderson	MWF	8:00-9:30 SL 206
13	Simon Joyce	MWF	8:00-9:30	SL 210
14	Simon Joyce	MWF T	9:40-10:40 8:30-9:55	LN G335 LN G335
15	William Kazmierczak	MWF	8:00-9:30	SL 306

Letter Grade Interpretation	Score Range
A	92 - 100
A-	88 - 91
B+	84 - 87
B	77 - 83
B-	72 - 76
C+	67 - 71
C	60 - 66
C-	55 - 59
D	50 - 54
F	0 - 49

Letter Grade Interpretation	Score Range
A	170 - 200
A-	160 - 169
B+	145 - 159
B	127 - 144
B-	116 - 126
C+	106 - 115
C	86 - 105
C-	78 - 85
D	65 - 77
F	0 - 64

Letter Grade Interpretation	Score Range
A	520 - 600
A-	500 - 519
B+	470 - 499
B	420 - 469
B-	400 - 419
C+	360 - 399
C	320 - 359
C-	280 - 319
D	240 - 279
F	0 - 239

Sections	Exam Room	Time
1 - 3	LH-2	7:00 - 8:30 PM
4 - 6	LH-8	7:00 - 8:30 PM
7 - 9	LH-14	7:00 - 8:30 PM
10 - 11	AA-G008	7:00 - 8:30 PM
12, 15	EB-110	7:30 - 9:00 PM
13, 14	S1-149	7:00 - 8:30 PM

Room	Sections
LH-1	1,4,5,6,7,9,15
LH-9	3,12
LH-10	8,11
LH-14	2,10,13,14

Week 1: Jan. 26 - 30	6.1, 6.2, 6.3
Week 2: Feb. 2 - Feb. 6	6.4*, 6.5
Week 3: Feb. 9 - 13	6.6, 6.8
Week 4: Feb. 16 - 20	7.1, 7.2, Exam 1
Week 5: Feb. 23 - 27	7.3, 7.4
Week 6: Mar. 2 - Mar. 6	7.8, 11.1
Week 7: Mar. 9 - 13	11.2, 11.3
Week 8: Mar. 16 - 20	11.4, Review, Exam 2
Week 9: Mar. 23 - 27	11.5, 11.6
Week 10: Mar. 30 - Apr. 2	11.8
Week 11: Apr. 6 - 10	Spring Break
Week 12: Apr. 13 - 17	11.9, 11.10
Week 13: Apr. 20 - 24	11.11, 8.1, 8.2
Week 14: Apr. 27 - May 1	10.1, 10.2, Exam 3
Week 15: May 4 - 8	10.3, 10.4, Review
Week 16: May 11, 8:05-10:05 PM	Final Exam

Department of Mathematics and Statistics, Binghamton University

people:mckenzie:math223

Math 226/227 (Calculus 2; formerly Math 222)

Syllabus for Math 226/227, Spring 2026

Contact Information

Class Meeting Schedule - All Sections

Prerequisites

Office Hours

Textbook

Objectives and Course Contents

Help Outside of Class

General Comments

University Attendance Policy

Homework and WebAssign

Exams and Grading

Exams with Solutions

Academic Honesty

Basic Skills Test

Administration of Exams

Schedule for Math 226/227 (Beginning Wednesday, January 21)

Schedule for Math 227 (Beginning Wednesday, January 21)

Schedule for Math 226 (Beginning Wednesday, March 16)

Supplementary Materials and Links

Applications: Flipped Calculus at Binghamton SUNY

Flipped Calculus 1 at Binghamton

Linearization and Differentials

Critical Points and the Closed Interval Method

The Mean Value Theorem

The Shape of a Graph

Horizontal Asymptotes

Curve Sketching

Optimization

Antiderivatives

Laura Anderson and Joseph Brennan

Integrals: Flipped Calculus at Binghamton SUNY

Flipped Calculus 1 at Binghamton

Definite Integrals

The Fundamental Theorem of Calculus

Indefinite Integrals

Integration with Substitution

Area

Volume

The Average Value of a Function

Laura Anderson and Joseph Brennan

Derivatives: Flipped Calculus at Binghamton SUNY

Flipped Calculus 1 at Binghamton

The Derivative as a Function

Differentiation Formulas

Trigonometric Derivatives

The Chain Rule

Implicit Differentiation

Rates of Change in the Sciences

Related Rates

Laura Anderson and Joseph Brennan

Limits: Flipped Calculus at Binghamton SUNY

Flipped Calculus 1 at Binghamton

The Limit of a Function

Tangents, Derivatives, and Rates of Change

Limit Laws

Continuity

Laura Anderson and Joseph Brennan

Chapter 3

Calculus Chapter 3

Critical Points and the Closed Interval Method

The Mean Value Theorem

The Shape of a Graph

Horizontal Asymptotes

Curve Sketching

Optimization

Antiderivatives

Chapter 1

Calculus Chapter 1

The Limit of a Function

Tangents, Derivatives, and Rates of Change

Limit Laws

Continuity

Math 222 (Calculus 2) Fall 2015

Syllabus for Math 222, Fall 2015

General Information About All Sections

Contact Information