Final Exam Solutions

Submitted by Michael C. Ching on Tuesday, 12/20/2011, at 3:33 PM

Please let me know if you have any questions or corrections.

Solutions to Midterm III

Submitted by Michael C. Ching on Sunday, 12/4/2011, at 9:13 PM

Please let me know if you find any mistakes, or have any questions:

Midterm II: Friday 28 October

Submitted by Michael C. Ching on Wednesday, 10/26/2011, at 11:26 AM

The second midterm test will be at 9:00am in Seeley Mudd 206 (usual class time and room) on Friday 28 October. The test will last 50 minutes and you will not be allowed to use books, notes, calculators or any other aids. I'll be having extra office hours this week at the following times:

Monday: 2-4pm

Wednesday/Thursday: 2-6pm

Below are some practice materials to help you prepare for the test:

Any questions or mistakes, please let me know.

Midterm I: Friday 30 September

Submitted by Michael C. Ching on Wednesday, 9/28/2011, at 9:45 PM

The first midterm exam is on Friday 30 September at 9:00am in Seeley Mudd 206 (the usual class room and time). You will have 50 minutes and you will not be allowed to use notes, books or calculators.  The following materials should help you prepare:

Please let me know if you have any questions about these.

Help at the QCenter

Submitted by Michael C. Ching on Friday, 9/9/2011, at 8:48 PM

One source of help with the course is the Moss Quantitative Center (QCenter). This is in Room 202 Merrill Science.

They have drop-in hours for help with all calculus courses. This semester, the hours are:

Mon-Fri: 1-5pm

Sun-Thur: 7-9pm

You can also organize peer-tutoring through the QCenter.


Submitted by Michael C. Ching on Sunday, 9/4/2011, at 4:06 PM

Hello students for Math 111 Section 2. The first class is Wednesday September 7 at 9:00am in Seeley Mudd 206. Please look through the syllabus/policies below. If you have any questions, please email me at .


Submitted by Michael C. Ching on Tuesday, 9/6/2011, at 9:01 AM

Instructor Information:

  • Email:
  • Office: Seeley Mudd 305
  • Phone: (413) 542-5530
  • Office Hours: Mon (10-11), Wed/Thu/Fri (10-11, 2-3)
  • Web page:


Monday, Wednesday, Thursday, Friday at 9:00am in Seeley Mudd 206


(Single Variable) Calculus, by Stewart, 7th edition.

There are several versions of the textbook. Make sure yours is the 7th edition and contains chapters 1 - 6. If you are pretty sure you will go on to take Math 121 in the Spring, you might want to get a version with chapteres 1 - 11.

Course Objectives:

  • give you a firm understanding of the basic concepts of differential and integral calculus;
  • give you lots of practice at using these concepts to solve a variety of problems;
  • help you learn how to write clear and convincing explanations for the solutions to these types of problems.

Problem Sets:

Problem sets will usually be due twice a week, on Mondays and Thursdays. This is the most important part of the course. Solutions should be turned in at the beginning of the class in which it is due. If you think illness or emergency will prevent you from completing a problem set by the due time, you should speak with me, or send me an email, to make suitable arrangements. This must be done before the problem set is due.


There will be three mid-term tests in class. The dates for these are subject to change, but are tentatively:

  • Friday September 30
  • Friday October 28
  • Friday December 2

There will be a 3-hour final exam, at a time to be decided.


Your final grade for the class will be decided by weighting your scores on the problem sets and exams as follows:

  • problem sets: 10%
  • mid-terms: 20% each
  • final exam: 30%

In borderline cases, I may use other factors, such as class attendance, class participation and homework completion rate, to decide on final grades.


There are many sources of help and support if you are having difficulty with the course, material or anything else. You can:

  • ask your fellow students and form study groups (see policies below on collaboration);
  • email me a question;
  • come to my office hours;
  • email or ask me to arrange a time to come and talk outside of office hours;
  • go to the QCenter (202 Merrill Science) for drop-in tutoring;
  • get a peer-tutor: see me or ask at the QCenter.


Calculators will not be permitted in the mid-terms or final exam. It is highly recommended that you do problems sets without using calculators (unless specific instructions are given otherwise).


Attendance in class is mandatory but an occasional absence is not the end of the world. You will of course be responsible for getting notes for any material you miss. There will be no make-up exams for the mid-termes. If you miss an exam without a valid excuse, your grade will be zero.

Special Aid:

Students with disabilities or other special needs who require classroom accommodations or other arrangements should make this known to me as soon as possible at the beginning of the semester.


Collaboration on problem sets is allowed and encouraged. Working with other students is a good way to help learn the material. However, each student must write up her/his solutions to the problems individually and in her/his own words. Copying from another student's paper is prohibited. The problem sets are the essential part of learning the course material. Failing to give them proper attention will significantly harm your performance on the exams and your overall grade for the class.

Academic honesty:

All students are responsible for knowing the College's policy on academic honesty. All academic work submitted in this course must be your own (that is, must reflect your understanding of the problems set) and be written by you in your own words.

Summary of Topics

Submitted by Michael C. Ching on Tuesday, 9/6/2011, at 3:53 PM

The following is a list of the topics we plan to cover in this course. Everything is subject to change depending on how fast things go, but it should give you an idea of what is in store for you. Note that this list is not suitable for studying for exams.

Introduction: what is calculus?


  • Ways to represent a function (1.1)
  • Functions you need to know about (1.2)
  • New functions from old (1.3)


  • The limit of a function (1.5)
  • Limit laws (1.6)
  • The precise definition of a limit (1.7)
  • Continuity (1.8)


  • Rates of change and the derivative (2.1)
  • The derivative as a function (2.2)
  • Formulas for differentiation (2.3)
  • Derivatives of trigonometric functions (2.4)
  • The chain rule (2.5)
  • Implicit differentiation (2.6)
  • Rates of change in science (2.7)
  • Related rates (2.8)
  • Linear approximation (2.9)

Applications of Differentiation:

  • Maximum and minimum values (3.1)
  • The Mean Value Theorem (3.2)
  • The relationship between derivatives and the shapes of graphs (3.3)
  • Horizontal asymptotes (3.4)
  • Curve sketching (3.5)
  • Optimization problems (3.7)
  • Antiderivatives (3.9)


  • Areas and distances (4.1)
  • Definite integrals (4.2)
  • The Fundamental Theorem of Calculus (4.3)
  • Indefinite integrals (4.4)
  • The substitution rule (4.5)

Exponential and Logarithmic Functions:

  • Inverse functions (6.1)
  • Exponential functions and their derivatives (6.2)
  • Logarithmic functions (6.3)
  • Derivatives of logarithmic functions (6.4)

Applications of Integration:

  • Areas between curves (5.1)
  • Volumes of revolution (5.2)