Math 195

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.


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.

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 has URL

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

Basic information