Tom Denton

We believe the entire book can be taught in twenty-five 50-minute lectures to a sophomore audience that has been exposed to a one-year calculus course. Vector calculus is a useful but unnecessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times throughout the book, often first in a more intuitive setting and then again in a definition, theorem, and proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book.