MATH 19520 (Mathematics for Social Sciences) is a multivariable calculus course targeted at social sciences majors at the University of Chicago. I taught the course twice, once in Spring 2010-11 and once in Winter 2012-13.

Alternative learning recommendations

If you’re interested in recommendations for learning multivariable calculus, see Cognito Mentoring’s multivariable calculus learning recommendations page, to which I was a primary contributor.

Textbook

The textbook for the course was Multivariable Calculus (7th Edition) by James Stewart. This book is a subset of Stewart’s calculus text. I’ll refer to it as “the textbook” or “the book” or “Stewart” below and in the lecture notes and quizzes. However, the notes are largely independent of the textbook, and do not require you to buy or own the textbook. Having the 6th Edition will also suffice.

My personal teaching experience

I wrote a detailed description of my subjective experience of teaching the course here.

Full downloads

Later in this page, links to each of the lecture notes, quizzes, and review sheets are available. If, however, you want to download all the lecture notes or all the quizzes, saving each link can be a pain. The links below can be useful if you want to download in bulk. Note that page numbers as shown on the pages are for individual files, not for the combined file.

• Single PDF with all lecture notes.
• Single PDF with all quizzes.
• Single PDF with all quiz solutions.
• Single PDF with all review sheets.

Lecture notes plus quizzes

To determine the chronological order of quizzes, please use the dates in the quiz titles. Quizzes related to a given topic may not all have been administered at the time the topic was taught. Some quizzes were deliberately delayed in order to facilitate spaced repetition.

For solutions to any quiz, add -solns to the part of the URL just before the .pdf at the end of the URL. For instance, the solutions file for the quiz with URL http://files.vipulnaik.com/math-195/01-09-parametric.pdf has URL http://files.vipulnaik.com/math-195/01-09-parametric-solns.pdf

Notes	Sections in textbook (Stewart)	Related quiz(zes)	Videos
Parametric stuff	10.1, 10.2	Parametric stuff, Combined	—
Polar coordinates	10.3	Polar coordinates	—
Three-dimensional geometry	12.1	Three dimensions, Combined	—
Vector stuff (introduction)	12.2, 12.3, 12.4	Vectors, Combined	—
Vector-valued functions	13.1, 13.2	—	—
Equations of lines and planes	12.5	—	—
Functions of several variables	14.1	Multivariable function basics: first, continued	playlist (first three videos for beginners)
Limits in multivariable calculus	14.2	Multivariable limit computations	essential playlist, additional playlist
Partial derivatives	14.3	Partial derivatives	Playlists: 1, 2, 3, 4, 5
Tangent planes and linear approximations	14.5	—	—
Chain rule (generic) (see also the additional note on chain rule and second derivatives)	14.5	—	playlist
Double and iterated integrals	15.2, 15.3	Multivariable integration	—
Directional derivatives	14.6	—	playlist
Max-min values	14.7	— (but see the quiz for examples)	playlist
Lagrange multipliers	14.8	—	—
Max-min values: examples	—	Max/min values, two variables	(see playlist for max-min values above)

Relevant material from single-variable calculus

Topic	Quiz(zes)	Videos
Limits, continuity and differentiation	Limits, continuity, and differentiation review	Playlists: 1, 2
Integration	Integration	—
Maxima and minima for functions of one variable	Max/min values (one variable recall)	Playlists: 1, 2, 3

Review sheets

Basic review sheets are unions of executive summaries of the corresponding lecture notes. Advanced review sheets include error-spotting exercises and other practice material.

Review sheet for …	Sections of book covered
midterm 1 (basic)	10.1-10.3, 12.1-12.4, 13.1-13.2
midterm 1 (advanced)	10.1-10.3, 12.1-12.4, 13.1-13.2
midterm 2 (basic)	12.5, 14.1-14.5, 15.2-15.3
midterm 2 (advanced)	12.5, 14.1-14.5, 15.2-15.3
final (basic)	14.6-14.8
final (advanced)	14.6-14.8