MAT307 Multivariable Calculus with Linear Algebra

Introduction to linear algebra: vectors, matrices, systems of linear equations, bases and dimension, dot product, determinants. Multivariate differential and integral calculus, divergence and curl, line and surface integrals, theorems of Green, Gauss, and Stokes.

Lectures: Mondays and Wednesdays 4:00 -- 5:20pm in Physics P113

Recitation sections: R01 Mondays 5:30 -- 6:35pm in Physics P117
R02 Thursdays 5:30 -- 6:35pm in Physics P125

Office hours: Additional office hours: Monday (Dec 11) 12:30 -- 2:30pm, and Tuesday (Dec 12) 11:00 onwards, except 2 -- 3pm when I am in MLC.
Mondays 12:30 -- 1:30pm, Wednesdays 1 -- 2pm, or by appointment in my office (Math 3-114)
MLC: Tuesdays 2 -- 3pm in Math Tower S-235.

Office: Math Tower 3-114

Textbooks: R. E. Williamson and H. F. Trotter, Multivariable Mathematics, 4th edition
OpenStax Calculus Vol. 3
D. Margalit and J. Rabinoff, Interactive Linear Algebra
Comments on textbooks: Multivariable Mathematics integrates multivariable calculus and linear algebra, and we aim to cover topics from the first half of the book (the second half makes up the content of MAT 308). Calculus Vol. 3 and Interactive Linear Algebra are open source, and include all (and perhaps more) topics we want to cover, but as separate texts, they are less integrated. For assigned reading, either Multivariable Mathematics alone, or the combination of Calculus Vol. 3 and Interactive Linear Algebra should be sufficient.

Syllabus: pdf (preliminary, subject to change!)

Grades: 20% homework + 80% midterms (2) and final, check the syllabus for details.

We will use Brightspace and Gradescope (entry code: 8EGE66)

Midterm 1, scheduled in class on Oct 4.
Practice Midterm 1 and solutions.
Midterm 2, scheduled in class on Nov 15.
Practice Midterm 2 and solutions.
Midterm 2 reattempts, due Nov 29 on Gradescope.
Final Exam, scheduled on Dec 12, 8:30--11:00pm
Practice Final Exam and solutions.
The homepage for 2021 iteration of the course contains links to Final Exams that cover similar topics; these can be used as extra practice.

Here are some additional notes on select topics:

Analytic geometry of parametric curves, Mathematica workbook showing the intersection of two surfaces

Week 1 (Thursday Aug 31): Problems, Solutions
Week 2 (Thursday Sept 7 & Monday Sept 11): Problems, Solutions
Week 3 (Thursday Sept 14 & Monday Sept 18): Problems, Solutions
Week 4 (Thursday Sept 21 & Monday Sept 25): Problems, Solutions, Mathematica notebook
Week 5 (Thursday Sept 28 & Monday Oct 2): Problems, Solutions
Week 6 & 7 (Thursday Oct 12 & Monday Oct 16): Problems, Solutions
Week 8 (Thursday Oct 19 & Monday Oct 23): Problems, Solutions
Week 9 (Thursday Oct 26 & Monday Oct 30): Problems, Solutions
Week 10 (Thursday Nov 2 & Monday Nov 6): Problems, Solutions
Week 11 (Thursday Nov 9 & Monday Nov 13): Problems, Solutions
Week 12 & 13: Midterm 2 Problems 1-3. Thanksgiving break.
Week 14 (Thursday Nov 30 & Monday Dec 4): Problems, Solutions