**Instructor**: Tim Chumley

**Office**: Clapp 423

**Phone**: 413-538-2525

**e-mail**: tchumley

**Office Hours**: Mondays & Wednesdays 3:15-4:15; Tuesdays & Thursdays 4:15-5:15; by appointment

**Textbook**: *Calculus: Single Variable, 7th Edition* by Deborah Hughes-Hallett et al, ISBN: 9781119139317;

on library reserve under QA303.2.H845 2017 and as an e-text;

a free pdf of the 6th edition is available (any edition is fine)

Announcements will be posted on the Course Announcements Moodle forum throughout the semester, but essentially all other materials will be posted on this page.

Check the syllabus for all the important class policies (grades, attendance, etc.).

There will be weekly homework assignments throughout the semester to be turned in. Please read these guidelines for writing in our class.

**Webwork**. Some of your homework will be done in an online system called Webwork.- These problems will be due on
**Wednesdays**. - You’ll have unlimited attempts at each problem.

- These problems will be due on
**Written work**. A selection of problems will be assigned to be written up individually and turned in each week.- These problems will also be due
**Wednesdays**. - You may work with others but the writing should be done on your own.

- These problems will also be due
**Gradescope**. Homework will be turned in through Gradescope.- Please add yourself to the Gradescope course using Entry Code
**KYX8XR**. - Gradescope has made a short tutorial on submitting homework.

- Please add yourself to the Gradescope course using Entry Code
**Collaboration**. I want you to work together on the homework! The process of explaining your ideas to one another really helps in learning math. However, you must write up the assignments on your own and avoid copying others’ work directly. Also, please only write what you understand so that I know where to help, and please avoid using online forums like Math StackExchange, solutions manuals, or similar resources. A huge part of learning in this class comes from figuring out how to get unstuck by spending time thinking on your own or talking to me and classmates; these other resources can end up being counter-productive in the long term.**Rewrites**. Homework is for practice, and you are not expected to write perfect answers from the start!- Your revisions will be due on
**Fridays**. - Please resubmit (only the problems you’re revising) on Gradescope.

- Your revisions will be due on

Assignment | Due |
---|---|

Homework 0 | Sep 3 |

Homework 1 | Sep 10 |

Homework 2 | Sep 15 |

Homework 3 | Sep 22 |

Homework 4 | Sep 29 |

Homework 5 | Oct 6 |

Homework 6 | Oct 20 |

Homework 7 | Oct 27 |

Homework 8 | Nov 3 |

Homework 9 | Nov 10 |

Homework 10 | Nov 17 |

Homework 11 | Dec 1 |

There will be (mostly) weekly quizzes that will be given on **Mondays**. The purpose of these is to check in to see that you’re comfortable with fundamental material and homework problems. Problems will always be related to the previous homework and class topics.

Quiz | Date | Material |
---|---|---|

Quiz 1 | Sep 13 | Limits |

Quiz 2 | Sep 20 | Geometric series |

Quiz 3 | Sep 27 | p-series, nth term test, comparison test |

Quiz 4 | Oct 4 | Limit comparison test, ratio test, alternating series test |

Quiz 5 | Oct 18 | Power series |

Quiz 6 | Oct 25 | Basic integration, areas |

Quiz 7 | Nov 3 | Substitution, integration by parts |

Quiz 8 | Nov 10 | Partial fractions |

Quiz 9 | Dec 1 | Volumes |

There will be two midterms and a final. The dates for the mid-terms are subject to change slightly.

Exam | Date | Format | Material |
---|---|---|---|

Exam 1 | Oct 8 | in-class | Sections 9.1 to 9.4 |

Exam 2 | Nov 19 | in-class | Sections 9.5, basics of integration, 7.1, 7.2, 7.4, 7.6 |

Exam 3 | Dec 9 - 13 | self-scheduled | cumulative with a focus on 8.1, 8.2, 10.1, 10.3 |

Our plan is to cover most of chapters 7, 8, 9, and 10 in the textbook, and maybe parts of chapter 11 if we have time. Below is a rough outline of what is to be covered week by week through the semester. Please check back regularly for precise details on what is covered, as well as postings of class materials like lecture notes.

**Topic**: Introduction. We discuss an overview of the class, preview series, and review basics of limits.**Class materials**: Lecture notes**After class**: Read Example 2, Example 5, and Theorem 9.1 in Section 9.1.

**Topic**: Section 9.1: Sequences. We discuss convergence and divergence of sequences.**Class materials**: Lecture notes, Sequences, (worksheet solutions)**After class**: Read the introductory example on Repeated Drug Dosage in Section 9.2.

**Topic**: Section 9.2: Geometric series. We introduce our first example of an infinite series.**Class materials**: Lecture notes**After class**: Read the beginning of Section 9.3 up through Example 1.

**Topic**: Labor Day, no class.

**Topic**: Section 9.2: Geometric series. We continue our discussion on geometric series.**Class materials**: Lecture notes, Geometric series, (worksheet solutions)**After class**: Work on Homework 1. Read Section 9.3 up to Example 2.

**Topic**: Section 9.3: Convergence of series. We begin talking about convergence of series beyond just geometric series.**Class materials**: Lecture notes**After class**: Begin working on Homework 2.

**Topic**: Section 9.3: Convergence of series. We continue talking about examples involving the integral test and the nth term test.**Class materials**: Lecture notes, Convergence of series, (worksheet solutions)**After class**: Work on Homework 2.

**Topic**: Section 9.4: Tests for convergence. We discuss the comparison test, a method for explaining why some series converge or diverge.**Class materials**: Lecture notes, Comparison test, (worksheet solutions)**After class**: Work on redos for Homework 1. Read Examples 3 and 4 of Section 9.4.

**Topic**: Section 9.4: Tests for convergence. We discuss the limit comparison test, a method that helps avoid tricky inequalities.**Class materials**: Lecture notes, Limit comparison test, (worksheet solutions)**After class**: Read Examples 5, 6, and 7 in Section 9.4.

**Topic**: Section 9.4: Tests for convergence. We discuss the absolute convergence and ratio tests.**Class materials**: Lecture notes**After class**: Work on Homework 3.

**Topic**: Section 9.4: Tests for convergence. We continue our discussion of ratio test with more examples.**Class materials**: Lecture notes, Ratio test, (worksheet solutions)**After class**: Work on Homework 2 redos.

**Topic**: Section 9.4: Tests for convergence. We discuss the alternating series test.**Class materials**: Lecture notes, Alternating series test, (worksheet solutions)**After class**: Work on Homework 4.

**Topic**: Series practice. We get more practice with absolute and conditional convergence.**Class materials**: Absolute and conditional convergence, (worksheet solutions)**After class**: Work on Homework 4.

**Topic**: Series practice. We continue our overview of absolute and conditional convergence.**Class materials**: Lecture notes, Series review**After class**: Work on filling out the Series review packet. It will form part of your next homework.

**Topic**: Section 9.5: Power series. We discuss infinite series involving a variable.**Class materials**: Lecture notes, Power series**After class**: Work on Homework 5.

**Topic**: Section 9.5: Power series. We continue practicing with power series.**Class materials**: Power series, (worksheet solutions)**After class**: Work on Homework 5.

**Topic**: Exam review.**Class materials**: Review worksheet, (worksheet solutions)**After class**: Study for exam.

**Topic**: Exam 1. We’ll spend the whole class period on the first exam.**After class**: Enjoy fall break!

**Topic**: Fall break, no class.

**Topic**: Integral basics. We discuss definite integrals and the fundamental theorem of calculus.**Class materials**: Lecture notes, Integral basics, (worksheet solutions)**After class**: Work on Homework 6.

**Topic**: More integral review. We discuss how to use integrals to compute areas of various regions bounded by curves.**Class materials**: Lecture notes, Finding areas, (worksheet solutions)**After class**: Read Examples 1, 3, and 4 in Section 7.1.

**Topic**: Section 7.1: Substitution. We discuss a new method for computing integrals and antiderivatives.**Class materials**: Lecture notes, Substitution, (worksheet solutions)**After class**: Read Examples 9, 10, 11, 12, 13 in Section 7.1.

**Topic**: Section 7.1: Substitution. We continue our practice of substitution.**Class materials**: Lecture notes, More substitution, (worksheet solutions)**After class**: Read the first two pages of Section 7.2.

**Topic**: Section 7.2: Integration by parts. We discuss a deeply important new technique for integration.**Class materials**: Lecture notes, Integration by parts, (worksheet solutions)**After class**: Read Examples 5, 6, and 7 in Section 7.2

**Topic**: Section 7.2: Integration by parts. We talk about new examples using integration by parts.**Class materials**: Lecture notes, More integration by parts, (worksheet solutions)**After class**: Read up through Example 2 in Section 7.4.

**Topic**: Section 7.4: Partial fractions. We talk about a method for integrating rational functions.**Class materials**: Lecture notes, Method of partial fractions, (worksheet solutions)**After class**: Read up through Examples 4 and 5 in Section 7.4.

**Topic**: Section 7.4: Partial fractions. We continue our discussion of partial fractions.**Class materials**: Lecture notes, More partial fractions, (worksheet solutions)**After class**: Read Examples 1, 2, 3, and 5 in Section 7.6.

**Topic**: Section 7.6: Improper integrals. We discuss integrals where a limit of integration is infinite or a singular point of the integrand.**Class materials**: Lecture notes**After class**: Read Examples 6, 7, and 8 in Section 7.6.

**Topic**: Section 7.6: Improper integrals. We discuss some further examples of improper integrals.**Class materials**: Lecture notes, Improper integrals, (worksheet solutions)**After class**: Read Examples 1 and 3 in Section 8.1.

**Topic**: Section 7.6: Improper integrals. We work on examples and homework related to improper integrals.**Class materials**: Improper integrals, (worksheet solutions)**After class**: Read Examples 1 and 3 in Section 8.1.

**Topic**: Section 8.1: Volumes by slicing. We discuss finding volumes of solids by slicing and integration.**Class materials**: Lecture notes**After class**: Read Examples 1 and 2 in Section 8.2.

**Topic**: Section 8.2: Volumes of revolution. We discuss the disc and washer method for finding volumes of revolution.**Class materials**: Lecture notes, Volumes of revolution, (worksheet solutions)**After class**: Read Example 3 in Section 8.2.

**Topic**: Section 8.2: Volumes of revolution. We discuss the shell method for finding volumes of revolution.**Class materials**: Lecture notes, Shell method, (worksheet solutions)**After class**: Begin studying for the next exam.

**Topic**: Section 8.2: Arc length. We discuss finding the length of a curve given by the graph of a function.**Class materials**: Lecture notes**After class**: Continue studying for Friday’s exam.

**Topic**: Exam review. We will spend the day working on a review worksheet and answering questions on exam material.**Class materials**: Review worksheet, (worksheet solutions)**After class**: Study for exam.

**Topic**: Exam 2. We’ll spend the whole class period on the second exam.**After class**: Read up through Example 2 in Section 10.1.

**Topic**: Section 10.1: Taylor polynomials. We discuss approximating functions with polynomials.**Class materials**: Lecture notes**After class**: Enjoy the break!

**Topic**: November break, no class.

**Topic**: November break, no class.

**Topic**: Section 10.1: Taylor polynomials. We discuss more examples of Taylor polynomials and learn about the technique of substitution.**Class materials**: Lecture notes, Taylor polynomials, worksheet solutions**After class**: Read Examples 1, 2, and 3 in Section 10.3.

**Topic**: Section 10.3: Finding and Using Taylor Series. We introduce the notion of a Taylor series, which are power series that we can think of as Taylor polynomials with infinitely many terms.**Class materials**: Lecture notes**After class**: Read Examples 2, 6, and 7 in Section 10.3.

**Topic**: Section 10.3: Finding and Using Taylor Series. We discuss more on finding new Taylor series using known ones.**Class materials**: Lecture notes, More on Taylor series, worksheet solutions**After class**: Begin reviewing for the final exam.

**Topic**: Wrap up. We will spend the day working on a review worksheet and answering questions on exam material.**Class materials**: Review worksheet, worksheet solutions**After class**: Study! Enjoy your break! Keep in touch!

Here are a few ways to get help:

**Office Hours**: Mondays & Wednesdays 3:15-4:15; Tuesdays & Thursdays 4:15-5:15; by appointment

**TA help**. Our class will have some teaching assistants (TAs) who are upper level students that are excited to help. The details of their availability will be posted here as soon as possible.- Hannah M. will hold evening help
**Mondays**, 7 to 9 pm, in Clapp 402. - Hannah O. will hold evening help
**Tuesdays**, 7 to 9 pm, in Clapp 407.

- Hannah M. will hold evening help
**Individual tutoring**: There will be opportunities to meet individually with our TAs too. They are available by appointment, which can be set up by email. Please feel free to send them a message (middl22h and ograd22h) and let them know your availability.**Study groups**: Other students in the class are a wonderful resource. I want our class to feel like a community of people working together. Please get in touch if you’d like me to help you find study partners, and please reach out if you’d like others to join your group. You may work together on homework, explain and check answers, but make sure you write what*you*know on homework in order to get good feedback.

- Wolfram Alpha: a useful way to check your answers on computations. It can do algebra and calculus, among other things, and it understands a mix of English and symbols.
- Desmos: a nice website for graphing functions.