Frederick Manners' academic website

Math 20C (Winter 2020)


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.


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, 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.


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 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.


Your combined grade for the course is calculated as follows.

First, your lowest homework score is dropped. Then, take whichever is larger of (20% homework + 20% midterm 1 + 20% midterm 2 + 40% final exam) or (20% homework + 20% best midterm + 60% final exam).

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


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 PDF
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

Course calendar