This course ended May 9, 2017.

Math 131: Calculus II

   Department of Mathematics and Computer Science
   Hobart and William Smith Colleges

   Spring 2017.

   Instructor:  David J. Eck  (


   Monday, Wednesday, Friday, 12:20–1:15 PM
       Room Eaton 111.

   Lab: Tuesday, 1:30–2:55 PM
       Room Gulick 206A.

Direct Link to WebWork site for this course

Lab 1, January 17 Lab 2, January 24 Lab 3, January 31 Lab 4, February 7
Lab 5, February 14 Lab 6, February 21 Lab 7, February 28 Lab 8, March 7
Lab 9, March 21 Lab 10, March 28 Lab 11, April 4 Lab 12, April 11
Lab 13, April 18 Lab 14, April 25 Lab 15, May 2 Lab 15 Answers

Written Homework Assignments
Due Tuesday, January 24 Section 5.1, # 18, 38, 40, 57, 62
(for #57, use only Theorem 5.1)
Due Wednesday, February 1 Section 5.2, # 28, 44, 50
Section 5.3, # 30, 46, 52, 62, 64
Due Wednesday, February 8 Section 5.4, # 26, 34
Section 5.5, # 18, 46, 70, 90, 106
Due Tuesday, February 14 Section 6.1 # 8, 30, 34, 40, 60 Answers
Due Friday, February 24 Section 6.2, # 14, 26, 28
Section 6.3, # 8, 10, 20, 36, 50
Due Friday, March 3 Chapter 6 Review, Page 507:
          # 14, 24, 28, 36
Due Friday, March 10 Section 7.1, # 28, 30, 33
Section 7.2, # 14, 16, 18, 24, 40, 46
Due Monday, April 3 Section 7.8, # 6, 28, 40
Section 7.9, # 18, 32
Due Wednesday, April 12 Section 8.2, # 10, 12, 34, 50
Section 8.3, # 28, 40, 46, 56
Due Monday, April 17 (or Tuesday) Section 8.4, # 20, 26, 34, 36, 48, 52
Due Friday, April 28 Section 8.5, # 10, 16, 28, 38, 46
Section 8.6, # 18, 30, 34, 46, 56

End of Semester: May 1 and 9

Sample answers for the sample problems from the final exam study guide are now available here:

Sample Exam Answers

I have also posted the answers for Lab 15, in case you lost your copy.

The final exam for this course is scheduled for 1:30 PM on Tuesday, May 9, in our usual classroom. A study guide was handed out in class last Friday. See also the study guides for the first test, for the second test, and for the third test.

On Monday, May 1, and during the final lab of the semester on Tuesday, we will be reviewing for the test (except for maybe a bit of new material on Taylor series and Taylor polynomials).

Fourteenth Week: April 24, 26, and 28

In the last full week of the course, we will finish Chapter 8 (on sequences and series) and do as much of Chapter 9 as we have time for. Chapter 9 covers power series, Taylor polynomials, and Taylor series.

Thirteenth Week: April 17, 19, and 21

There is a test on Wednesday. A study guide was handed out in class last Friday.

Aside from the test, we will continue to work on Chapter~8. The reading is Sections 8.5 and 8.6, although that will carry over until next Monday. Section 8.5 covers several new convergence tests: Comparison Test, Ratio Test, Limit Comparison Test, and Root Test. Section 8.6 covers Alternating Series as well as absolute convergence and conditional convergence.

Twelfth Week: April 10, 12, and 14

Note that there is a test coming up next week, on Wednesday, April 19. It will cover Sections 7.8 through 8.4.

We will cover Section 8.4 (the Divergence Test and the Integral Test) on Monday and Wednesday. This will complete the material that will be on the test next week.

After completing Section 8.4, we will be covering some new material that will not be on the test.

Eleventh Week: April 3, 5, and 7

We will work on geometric sequences and series, from Section 8.3, on Monday and in the lab on Tuesday. On Wednesday or Friday at the latest, we should finish up any remaining topics from Sections 8.1, 8.2, and 8.3. By Friday, we should be able to start Section 8.4, covering the Divergence Test and the Integral Test.

You can expect another quiz on Friday.

Tenth Week: March 27, 29, and 31

We will finish Section 7.8 (improper integrals) on Monday and start 7.9 (introduction to differential equations). By Wednesday, we will start Chapter 8, which covers sequences and series. We will spend the rest of the semester talking mostly about infinite series.

The WebWork assignment on Sections 7.5, 7.8, and 7.9 must be completed by midnight on Friday, April 7.

There will be a quiz on Friday.

Ninth Week: March 20, 22, and 24

There is a test on Wednesday, March 22. A study guide is available. This week's lab will be a review for the test.

Aside from the test and review for the test, we will cover Section 7.8 this week. This section is about improper integrals. Several improper integrals, on intervals of the form [a,∞) have already been encountered on labs. If time permits, we will start Section 7.9.

Eighth Week: March 6, 8, and 10

We will continue with Chapter 7. On Monday, we will finish up Section 7.2, Integration By Parts, which we started on Friday. We will look at trig substitution, section 7.4, on Wednesday, but you will not be testes or quizzed on that topic. On Friday, we will do some of the simpler cases of Partial Fractions (Section 7.5). Along the way, we will also be done some integrals of trigonometric functions in a more informal way.

Next week is Spring Break. There is a test coming up on the Wednesday after Spring Break, March 22.

The next topic, coming up after Spring Break, will be Improper Integrals, Section 7.8.

Seventh Week: February 27; March 1 and 3

The reading for the week is Sections 6.8 and 7.1. Section 6.8 is a mathematical interlude in which we investigate how the natural logarithm function, ln(x), can be defined in terms of an integral. We will see that all the usual properties of the logarithm can be proved using just this definition. We will also define the exponential function as the inverse of the logarithm.

Chapter 7 is mostly about techniques of integration. We will cover only a few of them. Since computers can now find any indefinite integral that can be expressed as a normal formula, finding integrals by hand is less important. However, some techniques are important for theoretical and applied work, where they are used more often to transform integrals than to explicitly solve them. We will cover just a few of the important techniques.

There is no quiz this week, but you can expect one on Monday or Wednesday next week.

Sixth Week: February 20, 22, and 24

The reading for the week is Sections 6.4 and 6.5. Section 6.4 covers finding the volume of a solid of rotation using the method of cylindrical shells. Section 6.5 covers finding the length of a curve.

We will not cover Section 6.6 or 6.7. It is possible that we will start Section 6.8 on Friday. Section 6.8 will be the last section that we cover from Chapter 6.

There is no lab due this week, but there is a homework assignment on Sections 6.2 and 6.3 that is due in class on Friday. There is also a new WebWork assignment about volumes. The WebWork assignment closes on Wednesday of next week.

You can expect a quiz in class on Friday.

Fifth Week: February 13, 15, and 17

There is a test on Wednesday, February 15. A study guide is available.

Aside from the test, we will begin looking at using integration to find the volume of a solid. The reading for the week is Section 6.3, on finding volumes by slicing.

Both Lab 4 and Homework 4 are due in class on Tuesday.

Fourth Week: February 6, 8, and 10

We will cover Section 6.1 and 6.2 this week. Chapter 6 is about applications of integration. In 6.1, it is applied to a changing quantity to find the net change over a time interval from t=a to t=b, when the derivative of the quantity on that interval is known. In 6.2, integration is used to find the area between curves. This is a simple extension of the area between a curve and the x-axis, but the main point of the section is really how to set up an integral over a region in the plane.

There is a test on Wednesday of next week. It will cover Sections 5.1 to 5.5 and Section 6.1. (Section 6.2 is not included.)

Third Week: January 30; February 1 and 3

After finishing up the proof of the Fundamental Theorem of Calculus, we will cover Sections 5.5 and 5.4 this week. (We will start 5.5 first because you will need some of it for the lab on Tuesday.) Section 5.5 covers the technique of integration know as "substitution," also called "change of variables." From Section 5.4, we are mostly interested in the average value of a function on an integral and in the mean value theorem for integrals.

Second Week: January 23, 25, and 27

The reading for the week is Sections 5.2 and 5.3. Section 5.2 defines the definite integral in terms of the Riemann sums that were covered in 5.1. Section 5.3 introduces the Fundamental Theorem of Calculus. This theorem is fundamental because it relates the two branches of calculus, the differential calculus and the integral calculus.

The first written homework assignment is due at the beginning of lab on Tuesday. The first WebWork assignment is now available. And you can expect the first quiz on Friday. Both the WebWork assignment and the quiz cover Sections 5.1 and 5.2. It would be a good idea to complete the WebWork assignment before Friday, although it doesn't actually close until February 6.

First Week: January 17 and 19

Welcome to the course!

The reading for the week is Section 5.1, which covers Reimann sums and summation notation. However, I also expect to spend some time in class this week reviewing antiderivatives and the indefinite integral.

The syllabus is also a reading assignment! A copy will be handed out on Tuesday, January 16 at the first lab.

We have our first lab of the semester before the first class, which is a little awkward. It consists of a few problems that I hope that you will find interesting. Your report on the first lab is due in class on Friday of this week, January 19.

There is no WebWork assignment this week. The first WebWork assignment will be available next Monday and will cover Sections 5.1 and 5.2.

The first written homework assignment covers Section 5.1. It is due at the beginning of lab next Tuesday, January 24. The assigned problems are shown in the table at the top of this page. Remember that you can work together on written homework but that you should write up your own solutions in your own words. And remember to always show your work!