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!



The required textbook for Math 181 is Calculus, Early Transcendentals, by W. Briggs and L. Cochran. The updated textbook is a custom UIC edition that is an unbound, looseleaf, 3-ring binder design.

We will only go through Chapters 6 through 10. This textbook has been in our use since 2011. Your instructor is not required to follow the text line­-by-­line or to use the same problems, so please be sure to take notes in class and use them as your primary source. A brief description of the material covered each week is given in the weekly schedule below.

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 Discussion of course policies, diagnostic test, review of Calc I
2 Labor Day, 6.2, 6.3 Regions between curves, Volume by slicing
3 6.3, 6.4, 6.5 Volume by slicing (cont.), Volume by shells, length of curves
4 7.1, 7.2 Basic integration techniques, Integration by parts
5 Review, 7.3 Review (on Monday) for Midterm 1 (given on Tuesday), Trigonometric integrals
6 7.4, 7.5 Trigonometric substitutions, Partial fractions
7 7.7, 7.8 Numerical integration, Improper integrals
8 8.1, 8.2 Introduction to sequences and series, Sequences
9 Review, 8.3, 8.4 Review (on Monday) for Midterm 2 (given on Tuesday), Series, Divergence and Integral tests
10 8.4, 8.5 Divergence and Integral tests (cont.), Ratio, Root, and Comparison tests
11 8.5, 8.6, 9.1 Ratio, Root, and Comparison tests (cont.), Alternating series, Introduction to power series
12 9.2, 9.3, 9.4 Properties of power series, 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


Attendance policy

As explained in the course description, your active involvement in learning is essential in order to successfully complete the course! A basic requirement of the course is therefore a serious commitment on your part to attend both the lectures and the problem sections. Attendance in the course will be taken as follows:

In lectures: Attendance in lectures will be taken by means of random spot quizzes. A minimum of 15 short quizzes will be given during the semester. The quizzes will be unannounced, and given at random times during lecture, on randomly chosen days. It is mandatory to take at least 80% of these quizzes, and failure to do so without official excuse will lead to a grade of F for the course.

In problem sessions: Your TA will take attendance in each problem session. 80% attendance is mandatory, and failure to achieve this without official excuse will lead to a grade of F for the course.

Excused absence policy

In order to be excused from attendance, students must inform the instructor and/or TA (as appropriate) in advance (except in cases of emergency), and must provide documentation (for example, a letter from a doctor).


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


Your final grade in Math 181 will be determined by the number of points you have earned at the end of the semester, on the following scale:

Number of points Grade
80 -- 100 A
65 -- 79 B
50 -- 64 C
40 -- 49 D
0 -- 39 F

Please note that there will be no curve for the final grade!

You can earn points as follows:
Up to 20 points on Midterm 1;
Up to 20 points on Midterm 2;
Up to 30 points on the Final exam;
Up to 20 points on the Homework;
Up to 5 points on the Quizzes given in lecture;
Up to 5 points on attendance and participation in the Problem Sessions.

It is MSCS policy to assign midterm grades to all students in Math 181. The grades will be assigned on March 13. They will follow the same cut-offs as for the final course grades (please see the table above), but with the following contributions:

20% Homework
5% Quizzes
5% Attendance and participation in Problem Sessions
35% Midterm 1
35% Midterm 2.

Tips on interpreting your midterm grade can be found at


Diagnostic test

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. That is why your instructor will administer a 50-minute diagnostic test on Wednesday of the first week of classes. This test will consist of up to ten problems based on topics from basic algebra to the material of Math 180, all of which are needed for Math 181.

The diagnostic test will be graded based on a simple Satisfactory/Unsatisfactory system. Its result will not effect or in any way be counted towards your final grade for the course; rather it is supposed to inform you, your instructor and your TA of possible background areas of weakness. The grade of U means that your current skills may not be sufficient to continue in Math 181 without substantial difficulties, and so you may be in danger of failing the course, unless you take steps to improve. Since the test is intended for your own evaluation, you are not required to do anything in case of a U grade. However, you are encouraged to talk to your instructor/advisor to discuss possible options. Those may include (re)taking Math 180, enrolling in additional ESP-sections, using the MLC, seeking tutoring help, etc. All these options are subject to availability, so you have to act quickly!


The quizzes will be graded by the instructor, and returned in lecture. There will be no make-up quizzes given, but only the largest 80% of quiz grades will be considered when computing the points corresponding to the Quizzes on the final grade.

The quizzes will be very short, and each will cover very recent material. The scores obtained on the quizzes count relatively little toward your final course score; their role is rather as a source of information. We realize that you are all very busy and taking many courses, and so it is easy to fall behind. The quizzes are here to keep you engaged in the lecture, and to let you know if you have not understood certain basic concepts, while they are still fresh from being presented in lecture. While it is natural to prioritize certain courses over others at times, we urge you to not ignore your quiz scores, and to make the time to catch up and to follow the material, should you find yourself falling behind! At the same time, quizzes will inform your instructor whether or not certain concepts have been well understood by the class at large -- and if not, (s)he can quickly work to correct this -- for example, by going back and explaining the concepts again, or by having the TAs spend more time on related problems.


Homework for the course is assigned every week (on Thursdays) by the course coordinator, and is the same for all sections. Assignments will be posted on Blackboard, on this page under Homework and distributed by instructors via e-mail. You are very strongly encouraged to work together with a group of colleagues on the homework problems, but you must write up the solutions by yourself!

Each homework will be due in the Thursday problem sessions, a week after it has been assigned. No late homework will be accepted, regardless of the reason, though a scanned homework can be sent by email, before the deadline, to the TA. There will be 14 homeworks assigned during the semester. The first homework (due during week 2) will not be counted towards the final homework grade, and the three worst homework scores from among homeworks 2 to 14 will be dropped at the end of the semester.

One or two problems chosen at random from each homework will be graded by the TAs. It is very important to note that the solutions to the 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 in each graded homework, since the midterms and the final exam will be graded in a very similar way. Shortly after the due date solution keys will be posted as well.

In addition to these mandatory assignments, optional sets of problems can be found under the Homework link. The same list will be available for use in you MyMathLab account. These problems are designed to build your basic problem solving skills and solidify understanding of the core course material. We recommend that you do them before taking on the more involved problems from the required homework.

Midterms and final exam

Two 2-hour midterm exams will be given on Tuesdays of weeks 5 and 9 of the semester, and one final exam on the Thursday of exam week. The final exam is cumulative and includes material from the entire course. Updates on time schedules, room assignments and preparation materials can be found under the Exams link. Make-ups can be given to students that comply with the Excused Absence Policy above for the day of the exam. The schedule of the make-ups will be announced at least one week before the corresponding exam.


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: