## Math 20C (Winter 2020)

### Summary

Math 20C is the third quarter in the calculus series for mathematics, engineering and science majors. It broadly covers vector geometry, differentiation and integration in two- and three-dimensional space.

The course textbook is *Vector Calculus* (sixth edition) by Marsden and Tromba.

In this course, there is an emphasis on understanding these things conceptually, not just being able to perform calculations routinely. In any calculation, you should be able to interpret what is being computed and why the computation works, as well as finding the correct result.

### Contacts

The instructor is Freddie Manners (email `fmanners`; office AP&M 7343). The TA's are Xin Tong (`xit040`) and Gary Peng (`g1peng`). [All emails are at `ucsd.edu`, but gotta fool those scraper bots.]

### Class and office hours

Lectures are held on Mondays, Wednesdays and Fridays, 1200—1250, in WLH–2005.
Note there is *no* lecture on Monday January 20 (MLK Day) or Monday February 17 (Presidents' Day).

See Blink or the calendar below for section times, and see the calendar below for office hours.

Attendance at lectures and sections is mandatory but not enforced.

### Exams

There are **in-class midterms** on Monday January 27 and Monday February 24.
The **final exam** is on Wednesday March 18, 1130—1429.

There will *not* be alternative times or make-up exams. You should ensure that you are available at all those times. (Authorized accommodations, with an AFA letter received sufficiently far in advance, will be scheduled separately.) Absences for off-site university sporting activities will be dealt with by the usual mechanism.

Please raise any concerns as soon as possible. Also note the grading policy below.

### Homework

Homework will be set every week, **due by 2359 each Sunday night**. The first homework deadline is on Sunday January 12; the last on Sunday March 8. There will be some optional homework in week 10 as exam practice.

There are two parts to the homework. One first is a worksheet requiring full written answers to be handed in for grading, via **Gradescope**, by the deadline. Note full written solutions, not just answers, are required.

The second part consists of reading the given sections of the textbook and solving a given set of the exercises. This part is **mandatory but not graded**. Exam questions are likely to be inspired by these questions.

When you submit the written assignment, one "dummy" question will be to state which of the textbook exercises you did. This is for my information, *not for credit*, so please answer honestly.

Midterm weeks will have reduced homework loads, but still some homework.

Please note: while discussing homework problems in groups is permitted (and encouraged), your final written-up solutions **must be written by you, by yourself, in your own words**. If your homework appears to have been copied directly from another student (or another source) that may constitute an academic integrity issue.

### Grading

Your **combined grade** for the course is calculated as follows.

In other words, your worse midterm score may be replaced by your final score if this improves your grade.

The letter grade cut-offs will be at least as generous as the following table (but may be more generous).

A+ | A | A- | B+ | B | B- | C+ | C | C- | F |
---|---|---|---|---|---|---|---|---|---|

97 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 | < 70 |

### Resources

In addition to this website, the course has a Canvas page, a Gradescope page and a Piazza site. The sign-up codes for Gradescope and Piazza are listed on the Canvas home page.

Note that tutoring and peer supplemental instruction are also available. (The second in particular is highly recommended.)

### Provisional schedule

The rough, provisional, subject-to-change course schedule is given below. Note Week 1 starts on Monday January 6, etc..

Week | Lecture | Section | Topic |
---|---|---|---|

1 | 1 | 1.1 | Vectors in two- and three-dimensional space |

2 | 1.2 | The inner product, length and distance | |

3 | 1.2 | — | |

2 | 4 | 1.3 | Matrices, determinants and the cross product |

5 | 1.3 | — | |

6 | 2.1 | The geometry of real-valued functions | |

3 | MLK Day |
||

7 | 2.2 | Limits and continuity | |

8 | Catch-up and review |
||

4 | Midterm 1 |
||

9 | 2.3 | Differentiation | |

10 | 2.3 | — | |

5 | 11 | 2.4 | Introduction to paths and curves |

12 | 2.5 | Properties of the derivative | |

13 | 2.6 | Gradients and directional derivatives | |

6 | 14 | 2.6; 3.1 | —; iterated partial derivatives |

15 | 3.3 | Extrema of real-valued functions | |

16 | 3.3; 3.4 | — ; constrained optimization and Lagrange multipliers | |

7 | Presidents' Day |
||

17 | 3.4 | — | |

18 | Catch-up and review |
||

8 | Midterm 2 |
||

19 | 4.1 | Acceleration and Newton's Second Law | |

20 | 4.2 | Arc length | |

9 | 21 | 5.1 | Introduction to double and triple integrals |

22 | 5.2 | The double integral over a rectangle | |

23 | 5.3 | The double integral over more general regions | |

10 | 24 | 5.4 | Changing the order of integration |

25 | 5.5 | The triple integral | |

26 | 1.2 | Catch-up and review |

### Homework assignments

Those assignments that have not been created yet link to a placeholder.

Week | Deadline | |
---|---|---|

1 | Sunday January 12, 2359 | p1.pdf |

2 | Sunday January 19, 2359 | p2.pdf |

3 | Sunday January 26, 2359 | p3.pdf |

4 | Sunday February 2, 2359 | p4.pdf |

5 | Sunday February 9, 2359 | p5.pdf |

6 | Sunday February 16, 2359 | p6.pdf |

7 | Sunday February 23, 2359 | p7.pdf |

8 | Sunday March 1, 2359 | p8.pdf |

9 | Sunday March 8, 2359 | p9.pdf |

10 | Never (optional pset) | p10.pdf |

### Office hours

Regular office hours and locations are listed in the table below. However, please **check the calendar below** for any one-off changes or cancellations.

Instructor / TA | Location | Regular hours |
---|---|---|

Freddie Manners | AP&M 7343 | Mondays 3:30pm – 5:00pm, Wednesdays 9:30am – 11:00am |

Gary Peng | AP&M 5218 | Tuesdays 6:00pm – 7:00pm, Fridays 6:00am – 7:00pm |

Xin Tong | AP&M 5829 | Fridays, 11:00am – 11:59am and 1:00pm – 4:00pm |