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!


Textbook and Worksheet bundle

You will need a MyMathLab access code for the textbook, and a worksheet bundle .

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


A custom UIC edition of the textbook is available at the bookstore.

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.

The worksheet bundle will be used in the problem solving sessions on Tuesdays and Thursdays. You can obtain a copy from the UIC bookstore, or print your own bundle under Review.

A pdf source for the matrix and linear map materials at the end of the semester will be made available towards week 10.

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 5.2, 5.3, 5.4 Discussion of course policies (including Crowdmark), review of definite integrals, the Fundamental Theorem of Calculus and working with integrals
2 5.5, 6.1, 6.2, 6.3 Substitution, Velocity, Regions between curves, and Volume by slicing and shells
3 Labor Day, 6.5, 6.7 Length of curves, physical applications
4 7.2, 7.5 Integration by parts, Partial Fractions
5 7.7, 7.8 Numerical integration, Improper integrals
6 8.1, 8.2 Review (on Wednesday) for Midterm 1 (given on Wednesday from 6-7:30pm), Introduction to sequences and series
7 8.3, 8.4, 8.5 Infinite series, Divergence and p-test, Ratio test
8 8.6, 9.1 , 9.2 Alternating series, Power series
9 9.2, 9.3, 9.4 Taylor series, Working with Taylor series
10 10.1 Review (on Wednesday) for Midterm 2 (given on Wednesday from 6-7:30pm), Parametric equations
11 10.2, 10.3 Polar coordinates and calculus in polar coordinates
12 10.3 NH 9.1 Polar coordinates (cont.), linear systems
13 NH 9.2 Matrices
14 NH 9.3 Linear Maps
15 Review 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.


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
Written Homework 12+4 points
MyMathLab Homework 13 points
Media 1 point
Midterm 1 20 points
Midterm 2 20 points
Final Exam 30 points


85 -- 100 A
70 -- 84 B
55 -- 69 C
40 -- 54 D
0 -- 39 F

We guarantee an A to students with a combined final course percentage of 85% or higher, a B to students with a percentage of 70% or higher, a C to students with a percentage of 55% 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.


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

Media - One course component will consist of watching videos or other media files prior to class. These videos will be posted on Blackboard. Watching the videos will be important in understanding the course materials.

MyMathLab Homework - MyMathLab is a tool to provide instant feedback to problems that cover the basic material of the course. You can access MyMathLab through the Blackboard link. Late MyMathLab homework is accepted with a one time 30% penalty and has to be completed before the next test.

Written Homework - After each class, 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 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. Written homework will be not be accepted late.

Homework will be due on the specified date (listed on the homework itself) by 11:59pm. 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 begin 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.

To accommodate for occasional illness and occasional technical glitches the lowest three scores for MyMathLab, the lowest three scores for Written Homework, the lowest 3 scores for Media Assignments, and the lowest score for the Written Homework on Linear Algebra topics will be dropped. Note that there will be no extensions on homework for any reason!

Midterms Exams

The midterm exams are scheduled in the evenings from 6-7:30pm. Check under the Exam tab above for the exam dates.

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

MyMathLab Homework 20%
Written Homework 20%
Midterm 1 60%

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: