Welcome to the multivariable calculus readings
This web site contains readings designed to introduce some topics in multivariable calculus and vector analysis. Many readings were designed to be read before students attended lecture, so they are intended to be somewhat readable introductions to the basic ideas. The readings err on the side of qualitative description rather than getting all technical details precise.
You can access the readings organized by topics or organized by lecture (as we present them in Math 2374). A complete list of readings is also available.
New: You are viewing the beta MathML version of this site. You can also view the original non-MathML version or read more about the MathML version.
Overview
The readings on this web site were designed as part of the IT Multivariable Calculus and Vector Analysis course at the University of Minnesota. Students in this course are expected to read some of these documents (those marked with an asterisk * in the lecture list) before attending the lecture on the topic. The intent was to allow lecturers in the course spend more lecture time helping students understand and apply the material and less time on simply presenting the theory.
The remaining pages are a loosely organized collection of lecture notes, example problems, and other resources for students in the course. As no effort has been made to turn this into a comprehensive source of information on multivariable calculus and vector analysis, the coverage of different topics is uneven, with some important topics (such as Lagrange multipliers) missing altogether. Moreover, some of the readings not marked by asterisks assume content that is presented in lecture and not in the online readings. Nonetheless, I hope that what is available will be helpful for those trying to learn multivariable calculus and vector analysis.
One can view these readings more like a lecture than a textbook. They are not a replacement of a mathematics textbook because they don't cover all the theoretical details behind the main ideas. For the same reason, they should be easier to understand than a textbook. Many of the readings contain interactive graphics that I term concept visualization tools (or CVTs). I hope you can read them and make sense out of them. If you encounter explanations that are confusing, please let me know.