Multivariable Calculus

This course is an introduction to multivariable calculus. We will cover the following topics:

  1. Vectors and matrices: We will learn about vector algebra, dot products, matrix operations, and determinants.
  2. Calculus of functions of several variables: We will study limits, continuity, derivatives, and applications of all these concepts.
  3. Multiple integrals: We will explore double and triple integrals, as well as applications such as volume and surface area.
  4. Vector calculus: We will cover vector fields, line integrals, surface integrals, Green’s theorem, Stokes’ theorem, and the divergence theorem.

Course information

Instructor: John Myers
Office: Marano 175
Office hours: 12-12:30 MWF, and by appointment
Syllabus: link

Schedule, slides, exercises, and info

week date topics slides exercises info
Finals week 05.15 fri Section 800 Final exam
Marano 225, 10:30-12:30pm
05.14 thu
05.13 wed
05.11 mon Section 810 Final exam
Shineman 132, 2-4pm
Week 15 05.08 fri
05.07 thu
05.06 wed
05.04 mon Sec 30: Gradient fields, part 1 Sec 30 Slides Sec 30 Exercises
Week 14 05.01 fri Sec 29: Line integrals Sec 29 Slides Sec 29 Exercises
04.30 thu Sec 28: Vector fields Sec 28 Slides Sec 28 Exercises Quiz on Secs 25 and 26
04.29 wed Sec 27: Motion, velocity, and acceleration Sec 27 Slides Sec 27 Exercise
04.27 mon Sec 26: Parametrized curves Sec 26 Slides Sec 26 Exercises
Week 13 04.24 fri Continue Sec 25 Same as below ↓ Same as below ↓
04.23 thu Exam 2
04.22 wed No class — Quest
04.20 mon Sec 25: Integrals in cylindrical and spherical coordinates, part 2 Sec 25 Slides Same as below ↓
Week 12 04.17 fri Sec 24: Integrals in cylindrical and spherical coordinates, part 1 Sec 24 Slides Sec 24 Exercises
04.16 thu Sec 23: Double integrals in polar coordinates Sec 23 Slides Sec 23 Exercises Quiz on Secs 20 and 21
04.15 wed Sec 22: Polar coordinates Sec 22 Slides Sec 22 Exercises
04.13 mon Sec 21: Triple integrals, part 2 Sec 21 Slides Same as below ↓
Week 11 04.10 fri Same as below ↓ Same as below ↓ Same as below ↓
04.09 thu Sec 20: Triple integrals, part 1 Sec 20 Slides Sec 20 Exercises Quiz on Secs 18 and 19
04.08 wed Same as below ↓ Same as below ↓ Same as below ↓
Week 10 04.03 fri Sec 19: Iterated integrals Sec 19 Slides Sec 19 Exercises
04.02 thu Sec 18: The definite integral of a function of two variables Sec 18 Slides Sec 18 Exercises Quiz on Sec 16
04.01 wed Same as below ↓ Same as below ↓ Same as below ↓
03.30 mon Sec 17: Lagrange multipliers Sec 17 Slides Sec 17 Exercises
Week 9 03.27 fri Same as below ↓ Same as below ↓ Same as below ↓
03.26 thu Sec 16: Optimization Sec 16 Slides Sec 16 Exercises Quiz on Sec 15
03.25 wed Same as below ↓ Same as below ↓ Same as below ↓
03.23 mon Sec 15: Gradients Sec 15 Slides Sec 15 Exercises
Week 8 Spring break
Week 7 03.13 fri Sec 14: Second derivatives, part 2 Same as below ↓ Same as below ↓
03.12 thu Exam 1
03.11 wed Review for Exam 1
03.09 mon Sec 14: Second derivatives, part 2 Sec 14 Slides Same as below ↓
Week 6 03.06 fri Same as below ↓ Same as below ↓ Same as below ↓
03.05 thu Sec 13: Second derivatives, part 1 Sec 13 Slides Sec 13 Exercises Quiz on Secs 9-12
03.04 wed Same as below ↓ Same as below ↓ Same as below ↓
03.02 mon Sec 12: Chain rule Sec 12 Slides Sec 12 Exercises
Week 5 02.27 fri Sec 11: Partial derivatives, part 3 Sec 11 Slides Sec 11 Exercises
02.26 thu Sec 10: Partial derivatives, part 2 Sec 10 Slides Sec 10 Exercises Quiz on Sec 8
02.25 wed Sec 9: Partial derivatives, part 1 Sec 9 Slides Sec 9 Exercises
02.23 mon Same as below ↓ Same as below ↓ Same as below ↓
Week 4 02.20 fri Same as below ↓ Same as below ↓ Same as below ↓
02.19 thu Sec 8: The definition of the derivative Sec 8 Slides Sec 8 Exercises Quiz on Sec 5, 6, and 7
02.18 wed Same as below ↓ Same as below ↓ Same as below ↓
02.16 mon Sec 7: Functions of multiple variables, part 3 Sec 7 Slides Sec 7 Exercises
Week 3 02.13 fri Sec 6: Functions of multiple variables, part 2 Sec 6 Slides Sec 6 Exercises
02.12 thu Sec 5: Functions of multiple variables, part 1 Sec 5 Slides Sec 5 Exercises Quiz on Sec 2 and 3
02.11 wed Sec 4: Planes and linear spaces, part 2 Sec 4 Slides Sec 4 Exercises
02.09 mon Same as below ↓ Same as below ↓ Same as below ↓
Week 2 02.06 fri Sec 3: Planes and linear spaces, part 1 Sec 3 Slides Sec 3 Exercises
02.05 thu Same as below ↓ Same as below ↓ Same as below ↓ Quiz on Sec 1
Just vectors in \(\mathbb{R}^2\) and \(\mathbb{R}^3\), no matrices
02.04 wed Sec 2: Vectors and matrices, part 2 Sec 2 Slides Sec 2 Exercises
02.02 mon Same as below ↓ Same as below ↓ Same as below ↓
Week 1 01.30 fri Sec 1: Vectors and matrices, part 1 Sec 1 Slides Same as below ↓
01.29 thu Another “remote day”: Watch the videos below if you haven’t already, continue working on exercises. Same as below ↓
01.28 wed Another “remote day”: Watch the videos below if you haven’t already, continue working on exercises. Same as below ↓
01.26 mon “Remote day”: Watch the videos here, here, here, here, and here. Complete the exercises (see the link to the right). Sec 1 Exercises