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Math 226 and 227 are multivariable calculus classes recommended for Honours students in Mathematics at the University of British Columbia. They are aimed at students who have a deeper interest in mathematics, with more emphasis on rigorous proofs and mathematical maturity than in our general-purpose multivariable calculus courses. Accordingly, less time is spent on computational techniques (such as evaluating integrals) and applications (physics, engineering).
I taught each course at least 10 times since 2005. These notes started with the handwritten notes I developed during that time and used as class scripts. During the Covid pandemic, I prepared a cleaned-up and improved version (still handwritten) that I made available to my students. The current book version was created over a 3-year period from Fall 2023 to Summer 2026, with the department's support. The notes were first typeset by Caleb Marshall, a doctoral student at UBC at the time, who is acknowledged here as a co-author. Caleb worked on the project with me from September 2023 to August 2025. He has also prepared the professional-quality versions of my hand-drawn pictures. We both edited the files, and I finalized this version during the 2025-26 academic year. Most of the problems and solutions are from my exams and homework assignments. Some routine practice is included because this is always necessary. The homework questions are often more challenging, proof-oriented, and require some creative thinking.
This is an open source project, so that both the PDF files and the source files are available below. Caleb Marshall and I hold the copyright, and we are making this work available under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. You can view a copy of the license here.
For more information about these notes, and about MATH 226 and 227 in general, see the preface to each book.
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