Math 20, Spring 2019 — Schaeffer**Integral Calculus**

**End of quarter**

- Copy of the final exam and solutions.
- Problems that appeared on exam or practice exams: 1, 2*, 4, 5*, 6, 10ab*, 13*, 15ac*

(* = essentially identical to a problem from a midterm that you took). - Once all grading is complete, I will announce the deadline for looking over all your work and requesting any final regrades on HW6, HW7, and the final exam.

**Getting started!**

- The textbook for this course is Calculus by Hughesâ€“Hallett,
**7th edition**. Please ensure you have the correct edition, as problems do not have the same numbering across different editions. **Familiarize yourself with the course policies.****If you are on a Stanford University Athletics team:**Fill out the athletics survey.**If you have an accommodation from the OAE:**Please inform Dr. Schaeffer of the details by email as soon as possible.**Write down the exam dates:**Midterm 1 is on Wednesday,__April 24th__(in class); Midterm 2 is on Wednesday,__May 15th__(in class); and the Final is (almost certainly, but not yet officially) on Friday,__June 7th__(7–10 PM).*If you have a conflict with any of those dates, email Dr. Schaeffer as soon as possible. Please note that pursuant to Math Department policy, there are no alternate exam dates.*- Here are some helpful general tips for success in undergraduate math courses (h/t Adva Wolf).
**The ACE program**is a parallel 1-unit course that meets weekly (Mondays 7-9 PM in Huang 203) to discuss the content of the course and to collaborate on practice problems.

To apply click here. Applications are due Friday of Week 2 (4/12) even though the application form says otherwise.

**Prerequisites**

- The official prerequisite for this course is Math 19 or any equivalent course that covers limits and derivatives (differential calculus). Familiarity with this material will be assumed and not reviewed in class.
- The Math Department has developed an online precalculus refresher that will give you an opportunity to watch mini-lectures on precalculus topics and do many practice exercises.

We encourage you to spend some time using this resource to brush up on these topics and skills if you have concerns about your preparation. For more information, click here.

**Final Exam**

- The final exam is scheduled for
**7-10 PM on Friday, June 7th, in Herrin T175**. - Seat assignments.
- Final Exam expectations and study guide. This document outlines what I consider to be testable material for the final exam. Note that the final is cumulative and the expectations for Parts 1 and 2 can be found under the Midterm 1 and Midterm 2 headings below.
- Practice finals (note that these midterms are from previous quarters, so some cover material outside the scope of your exam—questions related to material we have not covered completely this quarter are highlighted in red):
- Additional practice problems from the textbook:
- 4.8: 21, 23, 25, 27, 29, 31 (for 0 ≤ t ≤ √π), 33, 43, 45ab, 47, 49
- 8.2: 79, 81

**Piazza and Gradescope**

- Piazza is where to go to ask homework questions and anything else about the course material!
- Homework in this class will be submitted and graded using Gradescope (submission guide), and your exams will be graded there as well.

This is also where your grades are recorded and where you can view your graded work. **Students officially enrolled in the course will be automatically registered with Piazza and Gradescope at the beginning of the quarter.**

**Weekly Schedule**

Regularly scheduled office hours will begin on Wednesday, April 3rd.

Monday | Tuesday | Wednesday | Thursday | Friday | |
---|---|---|---|---|---|

George Schaeffer | Lec. 10:30–11:20 (380-W) Lec. 11:30–12:20 (380-W) O.H. 2:50–4:20 (381-G) |
Lec. 10:30–11:20 (380-W) Lec. 11:30–12:20 (380-W) O.H. 3:50–5:20 (381-G)* |
Lec. 10:30–11:20 (380-W) Lec. 11:30–12:20 (380-W) |
||

Zhengqing Zhou | O.H. 3:40–6:10 (381-N)* | O.H. 6:00–9:00 (381-N)* | |||

Sophie Libkind | O.H. 3:00–7:30 (381-B)* | ||||

Mya Havard† | ACE Disc. 7:00–9:00 (Huang 203)† | ||||

SUMO Peer Tutoring** | Tut. 6:00–10:00 (381-T)* | Tut. 6:00–10:00 (381-T)* |

† Mya's discussion section is reserved for students in the ACE program. You must have been accepted into the ACE program for Math 20 in order to attend, starting Week 3.

* Note that in order to enter the first floor of Building 380 after 4:30 PM you may need to use the

** SUMO (Stanford Undergrad Math Org) provides peer tutoring (and homework help) for Math 19/20/21, starting in Week 2. These sessions are drop-in, just like office hours, though tutors are not official course staff.

If you cannot make any of these times, you should ask your question on the Piazza site! Additionally, VPTL provides free individual and drop-in tutoring for the Math 19/20/21 sequence (drop-in tutoring is available Sunday–Thursday evenings). See

**Homework**

- Homework in Math 20 is submitted online using Gradescope.
- Here's a guide on how to submit assignments.
- You may also view your graded work and all recorded grades on Gradescope. (These will not be recorded on Canvas.)

- Assignments are
__due at 10 AM on Friday__every week except on exam weeks (Weeks 4 and 8) and on the first Friday of the quarter.*Please give yourself enough time to submit, and try to upload your submission at least 30 minutes before the deadline just to be sure.* - Late homework is accepted up to one day after the deadline with penalties at instructor discretion—see the course policies for details. No exceptions are made.
- Your lowest score on HWs 1–7 is dropped.
- Homework assignments:
- Homework 1, due Friday, April 12th, by 10 AM
__on Gradescope__— (Solutions) - Homework 2, due Friday, April 19th, by 10 AM
__on Gradescope__— (Solutions) - Homework 3, due Friday, May 3rd, by 10 AM
__on Gradescope__— (Solutions) - Homework 4, due Friday, May 10th, by 10 AM
__on Gradescope__— (Solutions) - Homework 5, due Saturday, May 18th, by 10 AM
__on Gradescope__— (Solutions) - Homework 6, due Wednesday, June 5th, by 10 AM
__on Gradescope__— (Solutions) - Homework 7, due Wednesday, June 5th, by 10 AM
__on Gradescope__. — (Solutions)

- Homework 1, due Friday, April 12th, by 10 AM

**Integration Table**

**Midterm 1**

- Midterm 1 is scheduled to be in class Wednesday, April 24th, in our usual classroom,
**380-380W**. - The last day to notify Dr. Schaeffer of a class conflict, Stanford athletics-related absence, or accommodation letter was 4/17.
- Midterm 1 expectations. This document outlines what we consider to be testable material for the first midterm.
- Practice midterms (note that these midterms are from previous quarters, so some cover material outside the scope of your exam—questions related to material we have not covered completely this quarter are highlighted in red):
- An optional assignment for reviewing integration methods and the second fundamental theorem of calculus (solutions).
- Additional practice problems from the textbook (the answers to odd problems are in the back of the textbook, without work):
- 5.1: 1, 3, 5, 7, 9, 11, 17, 19, 21, 33, 39
- 5.2: 1, 3, 7, 23, 35, 39, 41, 79-84
- 5.3: 1, 3, 7, 9, 13, 15, 19, 21, 23a, 37, 39
- 5.4: 21, 23, 25, 29, 31, 33, 49, 51, 53, 59, 73-81, 89
- 6.1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 23, 25, 29, 31, 41-42
- 6.2: 1-49, 57*, 59*, 61*, 95, 97, 99 (* skip numerical evaluation)
- 6.4: 5, 7, 9, 11, 13, 15, 25, 27, 29, 49-54
- 7.1: 1-43, 51, 53, 55, 57, 59, 61, 73, 75, 77, 79, 129, 162-164
- 7.1: 81, 87-115, 135, 137, 139, 141
- 7.2: 1-37, 47, 49, 51, 59, 61, 63, 65, 67, 69, 88-90
- 7.3**: 1-49, 53, 55, 57, 59, 65, 67, 69, 83-86 (** these generally require the use of an integration table)

- Copy of the midterm (Form A), and solutions (some multiple choice answers were permuted in Form B and the integrals were different—solutions to integrals from both forms are given).

**Midterm 2**

- Midterm 2 is scheduled to be in class Wednesday, May 22nd, in 380-W.
- Seating in the exam is assigned:
- The last day to notify Dr. Schaeffer of a class conflict, Stanford athletics-related absence, or accommodation letter is 5/10.
- Midterm 2 expectations and study guide. This document outlines what I consider to be testable material for the second midterm.
- Practice midterms (note that these midterms are from previous quarters, so some cover material outside the scope of your exam—questions related to material we have not covered completely this quarter are highlighted in red):
- An optional assignment for reviewing separable differential equations, phase diagrams, and equilibria (solutions).
- Additional practice problems from the textbook:
- 8.2: 5, 7, 9, 11, 13, 29, 47, 49, 53
- 6.3: 13, 15, 19, 21, 33
- 11.1: 1, 3, 5, 7, 9, 11, 13, 15, 21, 23, 29, 35, 37, 48-57
- 11.4: 1-31, 33, 37, 39, 41, 43, 45, 47, 49, 51, 64-69
- 11.5: 1, 7, 9, 11, 13, 15, 25, 27, 29, 31
- 11.6: 1, 3, 5, 7, 9, 13, 19, 21, 23, 33
- 11.7: 1, 3

- Copy of the midterm, and solutions.

**Final Exam**

**Lecture Notes**

I will

However, they should help you if you have an extended absence, fall behind, or think you missed something!

Topic(s) | Book | Lecture notes | Handouts | |
---|---|---|---|---|

Lecture 1 (4/01) | What is Math 20 about? | 5.1 | Notes | — |

Lecture 2 (4/03) | The definite integral | 5.2 | Notes | — |

Lecture 3 (4/05) | Definite integral rules, Riemann sums | 5.2 | Notes | — |

Lecture 4 (4/08) | Fundamental Theorem of Calculus, basic antiderivatives | 5.3, 6.1, 6.2 | Notes | — |

Lecture 5 (4/10) | Integration of f(Ax+B)—"baby" substitution |
6.1, 6.2, 7.1 | Notes | — |

Lecture 6 (4/12) | Integration by substitution | 7.1 | Notes | Tips for substitution success! |

Lecture 7 (4/15) | Integration by substitution | 7.1 | Worksheet Solutions |
— |

Lecture 8 (4/17) | Integration by parts | 7.2 | Notes | — |

Lecture 9 (4/19) | Integration using a table, 2nd FTC | 7.3, 6.4 | Notes | — |

Lecture 10 (4/22) | Review for Midterm 1 | 5.1–7.3, minus 6.3 | — | — |

Lecture 11 (4/26) | Integrals for area | 8.1 | Notes | — |

Lecture 12 (4/29) | Integrals for volume | 8.1, 8.2 | Notes | — |

Lecture 13 (5/01) | Area and volume practice, solids of revolution | 8.1, 8.2 | Worksheet Solutions |
— |

Lecture 14 (5/03) | Differential equations and 1-dimensional motion | 6.3 | No notes, read Section 6.3 |
— |

Lecture 15 (5/06) | Separable differential equations | 11.4 | Notes | — |

Lecture 16 (5/08) | Autonomous differential equations, phase diagrams, equilibria | 11.5, 11.7 | Notes | Derivation of the solution to the logistic diffeq |

Lecture 17 (5/10) | Differential equations practice | — | — | Worksheet (Problems 1-4 on HW5) |

Lecture 18 (5/13) | Review week! | — | — | Worksheet (Problems 5-7 on HW5) |

Lecture 19 (5/15) | Review week! | — | — | Worksheet (Problems 8-10 on HW5) |

Lecture 20 (5/17) | Review week! | — | — | Worksheet (Problems 11-12 on HW5) |

Lecture 21 (5/20) | Review for Midterm 2 | — | — | — |

Lecture 22 (5/24) | Parametric equations; 2-dimensional motion | 4.8 | Notes | — |

Lecture 23 (5/29) | Parametric equations; 2-dimensional motion | 4.8 | Notes | — |

Lecture 24 (5/31) | Length of curves | 8.2 (Arclength subsection) | Notes | — |

Lecture 25 (6/03) | Review for final | — | — | — |

Lecture 26 (6/03) | Review for final | — | — | — |

**Extra Help**

- The official Math 20 Piazza page
- Tutoring: VPTL individual appointments (free), VPTL drop-in tutoring (free)

**Important Dates**

- (4/01) First day!
- (4/12) Homework 1 due (10 AM on Gradescope).
- (4/19) Homework 2 due (10 AM on Gradescope).
- (4/19) Add/drop deadline (5 PM).
- (4/24) Midterm 1 (7:00–8:30 PM, location TBA).
- (5/03) Homework 3 due (10 AM on Gradescope).
- (5/10) Homework 4 due (10 AM on Gradescope).
- (5/18) Homework 5 due (10 AM on Gradescope).
- (5/22) Midterm 2 (7:00–8:30 PM, location TBA).
- (5/24) Course withdrawal and change of grading basis deadline (5 PM).
- (5/27)
*Memorial Day*(no class or office hours). - (6/05) Homeworks 6 and 7 due (10 AM on Gradescope).
- (6/07) Final Exam (7:00–10:00 PM, location TBA).