Section 201 meets MWF at 8am on Zoom (see bCourses for link and password).
Section 203 meets MWF at 9am on Zoom (see bCourses for link and password).
Office hours: Thursday 11:30am-12:30pm, Friday 10am-11am via Zoom.
HW will be collected via Gradescope by section time on Mondays.
Quizzes will happen in section on some Mondays. The primary purpose of the quizzes is to make sure you are staying on top of the material.
Midterm 1 was Thursday, September 24 during lecture.
Midterm 2 was Tuesday, November 10 during lecture.
The final exam will be Wednesday, December 16 from 3-6pm.
A (possibly slightly hard) practice final written by me, along with solutions.
A few practice final exams written by your peers (shared with permission):
Practice final 2 and solutions
There were a lot of good practice problems submitted.
Various past Math 53 exams.
Even more past Math 53 exams and solutions.
Student learning center offers drop-in tutoring and study groups; full Fall 2020 schedule for Math 53 support has not yet been released
Some useful trigonometric identities.
Desmos, a nice online 3D graphing tool.
My webpage from Fall 2018 in Math 53 (note that it was with a different professor).
My webpage from Spring 2018 in Math 53 (note that it was with a different professor).
My webpage from Summer 2018 in Math 53 (note that as a summer class, I was in charge of the entire course and not just leading discussion sections).
Some optional challenge problems about calculus with functions of a complex variable (like you see in Math 185) and some more about a more general/abstract framework for vector calculus, the language of differential forms.
These are not totally rigorous/complete, but should give a taste of some of the ways the ideas of chapter 16 are similar to/lead to further topics in math.
Some study strategies I like using (your mileage may vary):
Friday, August 28 -- Parametric curves; slopes of tangents to them | Problems | Selected solutions | Screen captures |
Monday, August 31 -- Calculus with parametric curves | Problems | Selected solutions | Screen captures |
Wednesday, September 2 -- Polar coordinates and calculus with polar curves | Problems | Selected solutions | Screen captures |
Friday, September 4 -- Vectors, dot and cross products, lines, and planes | Problems | Selected solutions | Screen captures |
Wednesday, September 9 -- Vector-valued functions; 3D graphing and level curves | Problems | Selected solutions | Screen captures |
Friday, September 11 -- Limits and continuity in multiple variables; partial derivatives | Problems | Selected solutions | Screen captures |
Monday, September 14 -- Partial derivatives and limits | (No problems) | We discussed HW3 | Screen captures |
Wednesday, September 16 -- Tangent planes; the chain rule | Problems | Selected solutions | Screen captures |
Friday, September 18 -- Directional derivatives and the gradient | Problems | Selected solutions | Screen captures |
Monday, September 21 -- HW4 review/discussion | (No problems) | We discussed HW3 | Screen captures |
Wednesday, September 23 -- Local maxima, local minima, and saddle points | Problems | Selected solutions | Screen captures |
Friday, September 25 -- M1 review | Screen captures | ||
Monday, September 28 -- M1 review | Screen captures | ||
Wednesday, September 30 -- M1 review | Screen captures | ||
Friday, October 2 -- Lagrange multipliers | Problems | Selected solutions | Screen captures |
Monday, October 5 -- HW6 discussion | Screen captures | ||
Wednesday, October 7 -- More Lagrange multipliers practice | Screen captures | ||
Friday, October 9 -- Geometric ideas (open, closed, connected, simply-connected) | Screen captures | ||
Monday, October 12 -- Preparation for multiple integrals | Problems | Selected solutions | Screen captures |
Wednesday, October 14 -- Double integrals | Problems | Selected solutions | Screen captures |
Friday, October 16 -- Double integrals in polar coordinates and for surface area | Problems | Selected solutions | Screen captures |
Monday, October 19 -- HW7/HW8 review/discussion | Screen captures | ||
Wednesday, October 21 -- Triple integrals | Problems | Selected solutions | Screen captures |
Friday, October 23 -- Triple integrals in cylindrical and spherical coordinates | Problems | Selected solutions | Screen captures |
Monday, October 26 -- HW9 review/discussion | Screen captures | ||
Wednesday, October 28 -- Vector fields and line integrals | Problems | Selected solutions | Screen captures |
Friday, October 30 -- Conservative vector fields, the fundamental theorem for line integrals | Problems | Selected solutions | Screen captures |
Monday, November 2 -- HW10 review/discussion | Screen captures | ||
Wednesday, November 4 -- Green's theorem | Problems | Selected solutions | Screen captures |
Friday, November 6 -- Midterm review | A review handout | Solutions | Screen captures |
Monday, November 9 -- Midterm review | Screen captures | ||
Friday, November 13 -- More curl and divergence; parametric surfaces | Problems | Selected solutions | Screen captures |
Monday, November 16 -- HW12 review/discussion | Screen captures | ||
Wednesday, November 18 -- Surface integrals; intro to Stokes' theorem | Problems | Selected solutions | Screen captures |
Friday, November 20 -- Stokes' theorem and the divergence theorem | Problems | Selected solutions | Screen captures |
Monday, November 23 -- HW13 discussion | Screen captures | ||
Monday, November 30 -- HW13 discussion | Screen captures | ||
Wednesday, December 2 -- More on Stokes' theorem and the divergence theorem | Problems | Selected solutions | Screen captures |
Friday, December 4 -- Setting up multiple integrals | Problems | Selected solutions | Screen captures |
Monday, December 7 -- Review: MT1 material | Screen captures | ||
Wednesday, December 9 -- Review: MT2 material | Screen captures | ||
Friday, December 11 -- Review: time for questions | Screen captures |
Quizzes happen 8:50-9:00 and 9:50-10:00 (with an extra 5 minutes for Gradescope submissions) approximately every two weeks in section.
Problems will be visible on Gradescope and at the links below at the start of the quiz.
I will drop the lowest quiz grade and do some renormalization if my two sections have very different quiz averages over the course of the semester.
I recommend trying the other section's quiz for practice.
Quiz 1 - Wednesday, September 9 | 201 Problems | 201 Solutions | 203 Problems | 203 Solutions |
Quiz 2 - Monday, September 21 -- covers Chapter 13 and sections 14.1-14.6 | 201 Problems | 201 Solutions | 203 Problems | 203 Solutions |
Quiz 3 - Monday, October 5 -- covers sections 14.7 and 14.8 | 201 Problems | 201 Solutions | 203 Problems | 203 Solutions |
Quiz 4 - Monday, October 19 -- covers sections 15.1 through 15.5 | 201 Problems | 201 Solutions | 203 Problems | 203 Solutions |
Quiz 5 - Monday, November 2 -- covers sections 15.6 through 16.3 | 201 Problems | 201 Solutions | 203 Problems | 203 Solutions |
Quiz 5 Makeup - Wednesday, November 4 -- covers sections 15.6 through 16.3 | 201 Problems | 201 Solutions | 203 Problems | 203 Solutions |
Quiz 6 - Monday, November 16 -- covers sections 15.4 through 16.6 | 201 Problems | 201 Solutions | 203 Problems | 203 Solutions |
Quiz 7 - Monday, November 30 -- covers sections 16.7 through 16.9 | 201 Problems | 201 Solutions | 203 Problems | 203 Solutions |