MAT 126: Calculus B, Lecture 2, Fall 20

Lecture 2 Instructor

Prof. Nguyen-Bac Dang
email : Nguyen-Bac.Dang(at)
My homepage
Office Hours: M 3:00pm-4:00pm;M 4:00pm-5:00pm;by appointment
MLC Hours: W 9:00am-10:00am

Course summary

This a second course in calculus covering methods and applications of integration; enrolled students should have already passed MAT 125 or had an appropriate score on the Mathematics Department placement exam. We will cover the definitions of definite and indefinite integrals, the fundamental theorem of calculus, methods of explicitly evaluating integrals, methods of numerically estimating integrals, applications to computing areas, volumes, arclengths and other applications, parametric equations and calculus with polar coordinates.

A description of MAT 125 and links to webpages from previous semesters can be found here . If you need to review limits and derivatives, look at Chapters 1-4 of Volume 1 of our current textbook, that can be downloaded from Open Stax Calculus Vol I A Lumen OHM course giving review problems of MAT 125 material can be found here with course ID 44639 and enrollment key 'MAT 125 review'. This is not required and is only made available in case you want to review any MAT 125 topics on your own.


The textbook is Volume 2 of Calculus by Open Stax at Rice University. This is a free online textbook that can be downloaded from the link on this page .

If there is a problem with the above link, two alternatives are: Calculus, Volume 2 and here.

If you prefer smaller files, here are the individual chapters we plan to cover: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 7 . Links to individual sections of the text are given below in the lecture schedule.

In-person versus online recitation sections

In order to accomodate students who cannot come to campus regularly, MAT 126 is taught in two lectures, one with in-person recitations and one with online recitations. All Lecture 1 recitations are in-person and taught by Prof. Bishop; students who may attend these regularly have the possibility enroll in the other lecture and one of its recitations. Lecture 2 of MAT 126 is entirely taught online for lectures and recitations. The two MAT 126 lectures will have similar schedules and exams, and we will try to make it possible for students to view both lectures if they wish, but for grading will be important to regularly attend the lecture and recitation that you are enrolled in.

As per current university requirements for large classes, the twice-a-week lectures will be online via Zoom, but the once-a-week recitation sections led by teaching assistants (TAs), will meet in-person for Lecture 1, online for Lecture 2. Midterms and weekly quizzes will be administered in recitation for Lecture 1, but they will be done during lecture for Lecture 2. Times are locations are listed below, as well as contact information for the TAs.

Technical requirements

Since all lectures are presented via Zoom, all students will need a device with this software installed. Links to the Zoom lectures are provided in Blackboard.
We will use Lumen OHM for homework, so you will need a device with a web browser that can connect to the Stony Brook Blackboard site to access homework. You will also need to access your Stony Brook Google email to receive occasional emailed announcements (these will also appear in the Blackboard announcements for the course).

Special situations regarding online issues

With the online course, sometimes not everything can go right everytime when it comes to electronics and internet based issues. Here is what can happen if something shuts down.
-If my connection drops, I will try to reconnect and two cases happen. If I can reconnect, then I will try to resume where I left. Otherwise, if it fails for 15 minutes, then the class is canceled, and I will send an email with the remaining prerecorded remaining of the lecture and will reconvene a special zoom office hour where I go through the missing content.
-If it happens that your connection dropped, then the course (which is automatically recorded) is always available online on Blackboard and I am available by appointment to discuss the content you missed.


Grades will be based on 5 types of evaluation:
        Lumen OHM problems sets (20%): Lumen provides a free (to the student) Online Homework Management system that generates random variations of problems selected by the instructor and grades them automatically. You do NOT need to sign up for an Lumen OHM account; the assignments should be visible to you through Blackboard (in fact, if you access the homework from an individually set up Lumen OHM account, and not through Blackboard, your homework grades may not recorded in Blackboard correctly). We will drop the two lowest homework grades.
Assignments in Lumen OHM are automatically graded by the system, so you will see the results right away. You will be allowed multiple attempts to do each problem without a penalty, and to ask for an alternate version of the problem instead. The due dates of these will be the same for everyone in MAT 126, regardless of section, usually on Friday of the week following the week when the relevant material is presented in lecture (but you are encouraged to do it earlier, and even try to do them as soon as we covered the material in class). In general, the Lumen OHM problems only give credit for a correct answer in the correct form; no partial credit.
        Class participation (5%): There will be assignments in Lumen OHM to be done during lectures: many of these problems I will do as examples and you simply have to enter my answer into the assignment. A few I will leave for you to try during lecture, to ask me questions about and complete after class, if necessary. You will have 24 hours to complete these problems.
        Weekly quizzes on Monday (20%, drop worst 2 of 9): I will give short (about 20 minutes) quizzes at the end of most Monday lectures on non-exam weeks. Quizzes will be given using Lumen OHM. Details will be provided at the beginning of the semester. We will accomodate students who cannot attend the quiz on Monday. The worst two quiz grades will be dropped and missed quizzes will count among these.
There are no Monday quizzes in weeks 5, 9, and during Week 13, there will be a quiz on Monday and an Exam on Wednesday.
        Exams in Lecture (3 Online exams, 15% each, 45% total): There will be three exams taking up an entire lecture in weeks 5, 9 and 13 on Wednesday. These will cover roughly Chapters 1, 2 and 3 respectively; the exact sections covered on each exam are given in the lecture schedule below.
        Online final exam (10%): There will be a cumulative online final exam on all the sections of textbook covered in the class. It will be given in the Lumen OHM system, the same system used for the online homework. Some form of online proctoring will be used.


        Blackboard is the Stony Brook University class management system. Your homework, quiz and exam grades will be posted here. Letter grades for the course are posted in the Solar System. I will occasionally post announcements in Blackboard; you should receive email notifications whenever this occurs. Homework assignments and the online final can be accessed through your Blackboard account. Also links to the lectures via Zoom.

Solar System

        Solar System is the Stony Brook University administrative management system (registration, bills,...). It is not used for classes, except to post letter grades at the end of the semester..

Stony Brook Gmail

        Check your email here.

Stony Brook Virtual SINC Site

        Late in the course I expect to demonstrate software from the Virtual Sinc Site. This gives you access to various software packages on a university license, such as Mathematica and Matlab. These systems, among others, are can be used to compute some difficult integrals symbolically (Section 3.5 of the text) and most numerically (Section 3.6). I plan to demonstrate how they are used in lecture, but I won't require their use on assessments. Using the virtual Sinc Site requires downloading the Citrix receiver software (you will be prompted). Even though we won't need to use the Virtual Sinc Site much in this class, it is good idea to make sure you can access it for future classes.

Math Learning Center (MLC)

MLC webpage.

Normally, this is a room in the basement (SL level) of the Math Tower where you can go for face-to-face help with teaching assistants and faculty (not necessarily your own instructors). However, for Fall 2020 the MLC will be entirely online. To use the MLC click this link for MLC webpage. When there are tutors online, there is a zoom link to the session for that tutor. The zoom sessions are set up so that the student needs to be authenticated, usually with SBU netid, and the tutor is supposed to use the waiting room so that they get admitted "on demand" -- typically one student at a time. Each MAT 126 TA is supposed to hold three office hours each week, two of which take place in MLC. You may either seek out your own TA, or get help from whoever is available at the moment (however, TAs from other classes might not have access to MAT 126 textbook or assignments, so you will have to describe the problem to them, or show it to them with the share-screen feature).


        You can download Zoom here, if you do not already have it installed on your computer. Access to Zoom lectures and recitations will be provided through your Blackboard account.

Changes to the original lecture and recitation days-times-places

If you registered for MAT 126 in the Spring, then your original section choice may have been canceled or moved, so please make sure you know the new place and time of your lecture and recitation. For your convenience, all MAT 126 recitation times, places and TAs are listed below. Although both lectures and all recitations should cover the same material, attending the correct meetings is important to make sure your participation and assessments are recorded accurately.

Lecture 1 (lecturer is Prof. Bishop): TuTh 9:45am-11:05am. online lectures - access through Blackboard. All recitations for Lecture 1 are in-person.

    Recitations for Lecture 1:
    R01 F 10:30am-11:25am Javits Lectr 110, Jiasheng Teh, Math Tower 2-122
    R02 Tu 1:15pm- 2:10pm Engineering 143, Paul Frigge, Math Tower 2-107
    R03 Th 4:45pm- 5:40pm Engineering 143, Vinicius Canto Costa office TBA,
    R04 W 6:05pm- 7:00pm Engineering 143, Luke Kiernan office TBA,
    R05 W 4:25pm- 5:20pm Engineering 143, Mingming Lang, office TBA,
    R20 M 1:00pm- 1:55pm Engineering 143, Jiasheng Teh, Math Tower 2-122
    R32 Th 3:00pm- 3:55pm Engineering 143, Blythe Davis office TBA,

Lecture 2: Originally scheduled for MWF 10:00am-10:53am Simons Center 103. this lecture was cancelled and three of its sections (R20, R21, R22) were moved to one of the other two lectures. The other recitations were canceled.

Lecture 3 (Prof. Dang): Originally scheduled for TuTh 5:30pm- 6:50pm in Engineering 143, this lecture is now online with lecturers at MW 6:30pm-7:50pm. All recitations for Lecture 3 will be online.
    Recitations for Lecture 3:
    R21 Th 9:45am- 10:40am online, Conghan Dong
    R22 Tu 4:45pm- 5:40pm online, Yu Xiao
    R31 M 4:25pm- 5:20pm online, Mark Lombardi
    R33 Th 8:15pm- 9:10pm online, Mark Lombardi
    R34 W 4:25pm- 5:20pm online, Yu Xiao
    R35 Tu 4:45pm- 5:40pm online, Mingming Lang
    R36 Tu 6:30pm- 7:25pm online, Mingming Lang

Important University Dates

    Link to university academic calendars, including final exam calendars.

    First day of classes: Monday August 24, 2020.
    Last day to move-up/drop-down: Friday October 2, 2020.
    Fall break: Canceled. Instead of a short break on Oct 12 and 13, we will get all of Thanksgiving week off instead.
    Last day to withdraw or choose Grade/Pass/NoCredit: Friday October 23, 2020
    Last day for in-person classes: Friday, November 20. All classes meet online after Thanksgiving break.
    Thanksgiving break: Saturday November 21 to Sunday November 29, 2020.
    Last day of classes: Monday December 7, 2020.
    Reading day: Tuesday December 8, 2020.
    Finals: Wednesday December 9 to Thursday December 17, 2020.
    MAT 126 Common Final Exam: 2:15pm-5:00pm, Thursday December 10, 2020.
    Commencement: Friday December 18, 2020

Lecture Schedule

For each week I list sections of the text we plan to cover that week. When two sections are listed, we will generally do one per lecture. When there are three listed, the middle topic will often straddle both lectures.

Online homework on each week's sections will be assigned in Lumen OHM and due for everyone at the end of the following week. However, it is very highly recommended that you to complete the assignment by the time of your recitation class. Every Monday, the lecture will end with a short 10-15 minute quiz on the material from the previous week, so it is to your advantage to have done all the problems and ask for help during the recitation, before the quiz.

Lumen OHM MAT 126 Fall 2020 Lec 2 This is a link to Lumen OHM where you can find homework and other assigments and resources.

Week 1, Aug 24 - Aug 28
        Topics covered:
        Course administration, class webpage, Blackboard, Lumen OHM
        Very quick review of limits and derivative (MAT 125)
        Lumen OHM tutorial This a short assignment of very easy questions to illustrate how to do an assessment in Lumen OHM. We will go over this in the first lecture this week. Please check ahead of time that you can access this webpage, but you dont' need to do it ahead of time.
        Table of derivatives. You should know most of these already. We will go over some of these and other material from MAT 125 in the second lecture this week.
        Problems for Aug 27 lecture Some problems we will do in class.

Week 2, Aug 31 - Sept 4
        Topics covered:
        Section 1.1 Approximating areas
        Section 1.2 Integration

Week 3, Sept 7 - Sept 11, Quiz 1
        Section 1.3 The Fundamental Theorem of Calculus
        Section 1.4 Integration Formulas and the Net Change Theorem
        Section 1.5 Substitution

Week 4, Sept 14 - Sept 18, Quiz 2
        Topics covered:
        Section 1.6 Integrals involving Exponentials and Logarithms
        Section 1.7 Integrals Resulting in Inverse Trigonometric Functions

Week 5, Sept 21- Sept 25: Exam 1 on Sections 1.1 to 1.7. Exams given in lecture Wednesday.
        Topics covered:
        Exam 1 review
        Section 2.1 Areas between curves

Week 6, Sept 28 - Oct 2, Quiz 3
        Topics covered:
        Section 2.2 Determining Volumes by Slicing
        Section 2.3 Volumes of Revolution: Cylindrical Shells

Week 7, Oct 5 - Oct 9, Quiz 4 on Section 2.1
        Topics covered:
        Section 2.4 Arc Length of a Curve and Surface Area
        Section 2.5 Physical Applications

Week 8, Oct 12 - Oct 16, Quiz 5 on Section 2.2,2.3
        Topics covered:
        Section 2.6 Moments and Centers of Mass
        Section 2.7 Integrals, Exponential Functions and Logarithms

Week 9, Oct 19 - Oct 23: Exam 2 on Sections 1.6 to 2.5. Exam given in lecture on Wednesday
        Topics covered:
        Exam 2 Review
        Section 2.8 Exponential Growth and Decay

Week 10, Oct 26 - Oct 30, Quiz 6 on Section 2.6,2.7
        Topics covered:
        Section 3.1 Integration by Parts
        Section 3.2 Trigonometric Integrals

Week 11, Nov 2 - Nov 6, Quiz 7 on Section 2.8
        Topics covered:
        Section 3.3 Trigonometric Substitution
        Section 3.4 Partial Fractions
        Section 3.7 Improper integrals

        Wikipedia page on Heavyside method for computing partial fractions.

Week 12, Nov 9 - Now 13, Quiz 8 on Section 3.1,3.2.
        Topics covered:
        Section 3.5 Other Strategies for Integration (tables of integrals, computer systems)
        Section 3.6 Numerical Integration
        Section 7.1 Parametric Equations

Week 13, Nov 16 - Nov 20: Quiz 9 on Monday in lecture on Section 3.3,3.4,3.7.
Exam 3 on Sections 2.6 to 3.4, and 3.7 in lecture on Wednesday

        Topics covered:
        Review for Exam 3
        Section 7.2 Calculus of Parametric Equations

Week 14, Nov 23 - Nov 27
        Thanksgiving break, no classes Mon-Fri.

Week 15, Nov 30 - Dec 4 All university classes online this week. Last week for Lecture 1. Recitations meet online. No quiz this week.
        Topics covered:
        Section 7.3 Polar Coordinates
        Section 7.4 Area and Arc Length in Polar Coordinates
        Course review

Week 16, Dec 7 Classes on Monday only. Last meeting for Prof. Dang's lecture.
        Final Exam on Thursday Dec 10, 2:15pm-5:00pm.
        Final is online via Lumen OHM and is open book.
        It will be cumulative over all sections covered in MAT 126.

Helpful websites

Links to external websites if you need some additional review of any concepts.

Topics in the history of Calculus

Below are some reading about the history of calculus that maybe of interest.
        Wikipedia page on calculus.
        Wikipedia page on Issac Newton.
        Wikipedia page on Newton-Leibniz controversy.
        Wikipedia page on the discovery of the planet Neptune (using only mathematics).
The translated version of Leibniz paper entitled: Nova Methodus pro Maximis et Minimis (A new method for finding maxima and minima)

Office Hours

I will hold office hours via Zoom. Once the semester begins links will be provided in Blackboard. You may also use email to make appointments for other times.

Technology Support:

Student Technology Services. TLT provides academic technology support to all students. If you require assistance with Blackboard or other academic technologies, please contact TLT at:; Phone: 631.632.9602; Chat; or visit a SINC Site.

Students who need assistance with their personal devices can contact DoIT's service desk at: 631.632.9800, submit an online request, or visit the Walk In Center on the 5th floor of the Melville Library (West Campus), Room S-5410. For more information, visit:

Required Syllabus Statements

The University Senate Undergraduate and Graduate Councils have authorized that the following required statements appear in all teaching syllabi (graduate and undergraduate courses) on the Stony Brook Campus.

Student Accessibility Support Center Statement

If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, 128 ECC Building, (631) 632-6748, or at They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: and search Fire Safety and Evacuation and Disabilities.

Academic Integrity Statement

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website at

Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Schedule, and the Faculty-Employee Handbook.

Email instructors

Email Lecture 1 instructor Prof. Bishop

Email Lecture 2 instructor Prof. Dang

Email all MAT 126 TAs Costa, Davis, Dong, Frigge, Kierman, Lang, Lombardi, Teh

Email Lecture 1 MAT 126 TAs Costa, Davis, Frigge, Kierman, Lang, Teh

Email Lecture 2 MAT 126 TAs Dong, Lombardi