MATH 181: Calculus II




Math 181 is the second semester of our standard three-semester calculus sequence. As such, its goal is to continue the study of calculus on the real line, which you started in Math 180 (Calculus I), with a focus on integration, the basics of sequences and series, as well as parametric descriptions for sets in the plane.

Calculus is a beautiful and venerable subject, whose main aim is to understand the properties of functions, and how they can be used to describe and predict the behavior of various physical systems. The prominence and importance of such study reaches far beyond the pure mathematical endeavor into numerous applications, among others in engineering, natural sciences, and economics.

Students enter Math 181 from a variety of backgrounds: many of you have taken Calculus I at UIC, some have transferred from other schools, or placed directly into Calculus II following your calculus studies in high school. Regardless of your background coming in, our goal is to help every one of you succeed, and enjoy yourselves as much as possible in the process!

However, calculus is often a subtle and challenging subject, and experience has taught us (both as students once ourselves, and as educators) that success in Math 181 requires a lot of work, many hours of study and problem solving, and your active involvement in learning, both inside and outside the classroom. We have designed our course with the aim of helping you stay constantly involved with the course and the material, and within easy reach of some of your best resources: your instructor, your teaching assistants, and your colleagues! Working (quite hard!) together, you will find that at the end of the semester you have not only learned the basics of the course, but mastered the concepts, their connections, and many of their possible applications!



You will need the MyMathLab access code. The access code comes with an electronic version of the book, however you are welcome to also purchase the hard copy of the textbook. You can purchase the textbook and access code separately or together.

The textbook is Calculus: Early Transcendentals by William Briggs and Lyle Cochran, published by Addison-Wesley.

cover3 cover1 cover2

A custom UIC edition of the textbook is available in an unbound, looseleaf, 3-ring binder design.

We will cover chapters 6 through 10 in Math 181. A brief description of the material covered each week is given in the weekly schedule below.

You are expected to read the textbook before the lecture of each topic, as indicated on the schedule of homework and reading assignments.

Course structure

The class contains three hours of lectures on MWF, and two hours of problem solving session on TR. Please see your class schedule for specific times and classrooms. In addition, your instructor and TA will be available during their office hours. Specific information can be found under Sections.


The prerequisite for Math 181 is a grade of C or better in MATH 180. The prerequisite is enforced throughout all sections of the course without exceptions! Students that have not met the prerequisite will not be allowed to take the course.

Weekly schedule

Here is a brief overview of the material we will cover each week. (See also: detailed schedule and homework list)

1 5.3, 5.5, 6.2 Discussion of course policies (including Crowdmark) diagnostic test, review of Calc I
2 6.3, 6.4 Volume by slicing and shells
3 Labor Day, 6.5, 7.1 Length of curves, Integration by parts
4 7.1, 7.2, 7.3 Integration by parts, Trigonometric integrals, Trigonometric substitutions
5 Review, 7.3, 7.4 Review (on Monday) for Midterm 1 (given on Tuesday from 6-8pm), Trigonometric substitutions, Partial fractions
6 7.4, 7.7 Partial fractions, Improper integrals
7 8.1, 8.2 Introduction to sequences and series
8 8.3, 8.4 Infinite series, Divergence and Integral tests
9 Review, 8.4, 8.5 Review (on Monday) for Midterm 1 (given on Tuesday from 6-8pm), Divergence and Integral tests, Ratio, Root and Comparison tests
10 8.5, 8.6, 9.1 Ratio, Root, and Comparison tests, Alternating series, Power series
11 9.1, 9.2, 9.3 Power series, Properties of power series, Taylor series
12 9.3, 9.4 Taylor series, Working with Taylor series
13 10.1, 10.2 Parametric equations, Polar coordinates
14 10.2, 10.3 Polar coordinates (cont.)
15 10.3, Review Calculus in polar coordinates (cont.), Review for Final Exam


Cell Phones

You may not use your phone during lecture or discussion/problem solving sessions for any reason other than class participation. We ask that you stay focused on the material while attending class. If this becomes a problem, your instructor or teaching assistant will ask you to leave the room.


The use of any electronic devices with computing capabilities is prohibited during all exams and quizzes.


Given the variety of students taking the course, it is important to ensure that every one of you has the necessary mathematical background which allows you to fully focus on the wealth of new material which you must learn in Math 181. There will be a short diagnostic exam administered online (through MyMathLab) during the first week of classes. This exam will consist of problems based on topics from basic algebra, pre-calculus, and Math 180 material that are required for Math 181. The results of the diagnostic exam will not affect or in any way be counted towards your final grade for the course. If you receive a low score on the diagnostic exam, you are encouraged to talk to your instructor/advisor to discuss your options. Those may include (re)taking Math 180, enrolling in additional ESP-sections, seeking tutoring help, etc. All these options are subject to availability, so you have to act quickly.


The course grade is based on the following categories with the point values associated to each. Students are expected to be present for all exams. Makeup exams will only be given in case of a verifiable emergency or a formal request by the UIC athletic department. Do not schedule travel on an exam date.

Attendance see attendance policy
Quizzes (in lecture) 5 points
Written Homework 15 points
MyMathLab Homework 10 points
Midterm 1 20 points
Midterm 2 20 points
Final Exam 30 points


83 -- 100 A
65 -- 82 B
50 -- 64 C
40 -- 49 D
0 -- 39 F

We guarantee an A to students with a combined final course percentage of 83% or higher, a B to students with a percentage of 65% or higher, a C to students with a percentage of 50% or higher, and a D to students with a percentage of 40% or higher. Final grades in general are not curved, however, the department reserves the right to be more lenient than this.



Lectures and discussion/problem sessions: As explained in the course description, in order to successfully complete the course, your active involvement in learning is essential. Therefore, a serious commitment on your part to attend both the lectures and the discussion/problem sessions is a basic requirement of that. Attendance in the course will be taken both in lecture and in discussion sections starting with week 3.

A percentage below 75% in lecture or a percentage below 75% in discussion will result in a drop of one letter grade for the course as a consequence. Below 50% attendance in either one of these categories will result in an automatic F for the course.

Appeals: Students that know ahead of time that they have an existing or potential conflict with the class must inform their instructor in the first two weeks of the semester using the absence appeals form.

Furthermore, students can appeal during week 9 and 10, as well as week 14 and 15 to their instructor using the appeals form provided below. Note: no appeals will be accepted after the last day of class or at any other time!

In cases when the instructor cannot determine whether or not the reason is compelling, the instructor will forward the appeal to the director of undergraduate studies, who will decide.


The pop quizzes will be given by the instructor during class time. There will be no make-up quizzes given, but the lowest two scores will be dropped. The pop quizzes will be 5-10 minutes in length and will be problems chosen by your instructor. The instructor reserves the right to not accept a quiz from a student who was not present during a significant portion of lecture on that day; in other words, a student cannot walk in for the last 10 minutes and take the quiz and count that as attending class that day.


Homework for the course is assigned in two ways, both of which will count towards your grade.

MyMathLab Homework - MyMathLab is a wonderful tool to provide instant feedback to problems that cover the basic material of the course. You can access MyMathLab through the Blackboard link.

After a section is completed (according to the schedule on the Homework link above), the MyMathLab homework for that section will be due by midnight the night before the next lecture (with the exception of the material covered in the first two weeks). In the first two weeks, all sections completed will have due dates of Tuesday of Week 3.

Written Homework - Each week, the MATH 181 coordinator will publish a set of homework problems that are to be turned in during discussion/problem solving sessions. These written problems will (generally) be more challenging than the MyMathLab homework problems and will require you to show your full work. You are strongly encouraged to work together with a group of colleagues on these (and any) homework problems, but you must write up the solutions by yourself! The written homework will be submitted to you via email through the Crowdmark system. Solutions will be posted under the Homework link above.

Written homework problems will be graded in full, and just an answer will not earn any credit. You should pay a lot of attention to the comments made by your TA on each graded homework, since the midterms and the final exam will be graded in a very similar way.

Homework will be due on the specified date (listed on the homework itself) by 8pm. Late homework is accepted with a 25% penalty per day it is late. Note that if you resubmit your homework after the deadline (even if it was turned in on time), it will be counted as late. Your last submission is the one Crowdmark uses for your grade, so please make any submissions BEFORE the due date. You are also encouraged to being the submission process early to account for any technical issues; technical issues will not be grounds for a penalty waiver.

The goal of these written problems is to help you learn how to write mathematics as you will need to do on the midterms and final exam. Solutions to the written homework will be posted online.

Midterms Exams

The midterm exams are scheduled for the evenings of Tuesday, February 9 and Tuesday, March 8, both being from 6-7:30pm.

Final Exam

The final exam will take place on Thursday of finals week from 3:30-5:30pm and will be a cumulative exam.

Models of midterm and final exams can be found by clicking the Exams link above.

With all exams, make-ups will not be given except under extreme circumstances.


It is MSCS policy to assign midterm grades to all students in MATH 181. Midterm grades will follow the same cut-offs as for the final course grade, but with the following contributions

Quizzes 10%
MyMathLab Homework 20%
Written Homework 30%
Midterm 1 40%

Tips on interpreting your midterm grade can be found at


Academic integrity policy

As an academic community, UIC is committed to providing an environment in which research, learning, and scholarship can flourish and in which all endeavors are guided by academic and professional integrity. All members of the campus community - students, staff, faculty, and administrators - share the responsibility of insuring that these standards are upheld so that such an environment exists. Instances of academic misconduct by students will be handled pursuant to the Student Disciplinary Policy:

Academic deadlines

The current academic calendar, as well as the list of academic deadlines can be found at

Disability policy

The University of Illinois at Chicago is committed to maintaining a barrier-free environment so that students with disabilities can fully access programs, courses, services, and activities at UIC. Students with disabilities who require accommodations for access to and/or participation in this course are welcome, but must be registered with the Disability Resource Center (DRC). You may contact DRC at 312-413-2183 (v) or 312-413-0123 (TTY) and consult the following:

Religious holidays

Students who wish to observe their religious holidays shall notify the faculty member by the tenth day of the semester of the date when they will be absent unless the religious holiday is observed on or before the tenth day of the semester. In such cases, the student shall notify the faculty member at least five days in advance of the date when he/she will be absent. The faculty member shall make every reasonable effort to honor the request, not penalize the student for missing the class, and if an examination or project is due during the absence, give the student an exam or assignment equivalent to the one completed by those students in attendance. If the student feels aggrieved, he/she may request remedy through the campus grievance procedure. For a calendar of this year's religious holidays, please see:

Grievance procedures

UIC is committed to the most fundamental principles of academic freedom, equality of opportunity, and human dignity involving students and employees. Freedom from discrimination is a foundation for all decision making at UIC. Students are encouraged to study the University's "Nondiscrimination Statement". Students are also urged to read the document "Public Formal Grievance Procedures". Information on these policies and procedures is available on the University web pages of the Office of Access and Equity: