Brief Lecture Notes on Vector Analysis
These are brief lecture notes on Vector Analysis developed when Gautam Iyer was teaching Vector Analysis at Carnegie Mellon University. These notes only list statements of results covered in lectures, and sometimes brief sketches of proofs. Motivation, intuition, and complete proofs will be done in class, and will not be on these notes.
Note – the topics aren’t in the most logical order, and metric spaces are done before real numbers. This is because I initially assumed students who took this class were already familiar with one variable calculus. When I realized this wasn’t the case, I backtracked and covered the basics “very quickly” before returning to analysis in higher dimensions, which is the main focus of this course.
In future iterations of this course, I will likely start with an introduction to one variable calculus and put the material in the correct logical order.
Contents
- Metric Spaces
- Limits and continuity
- The real numbers
- Sequences and series
- Compactness
- Derivatives in one dimension
- Derivatives in higher dimensions
- Higher order derivatives
Source Code
The source code is available on Codeberg.
The notes are written in Markdown, and converted to HTML5 using the Python script md-to-html.
It should be viewable on most modern browsers, but I have only ever tested it on Firefox.
Licence
Brief Lecture Notes on Vector Analysis © 2026 by Gautam Iyer is licensed under Creative Commons Attribution-NonCommercial 4.0 International
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You may adapt and share this work for non-commercial purposes, provided you cite it appropriately. The full terms are in the licence deed.