Multivariate Calculus - Bruce E. Shapiro

Preface: A note to the Student
These lecture notes are meant to accompany the textbook, not to replace it.
It has been my experience that students who attempt to use lecture notes (even
mine, which I have to admit, are practically perfect) in lieu of the textbook receive
abysmally poor final term grades. However, properly using the lecture notes can
help you.
Here is how I would suggest you study in this class.
• Read the pertinent sections in the textbook prior to attending the class lecture.
• Come to class.
• Pay attention. Although I use the notes during class, I will not follow the notes
verbatum, and I will most certainly not stand in front of the class and read
the notes out loud to you. I will frequently also include additional material so
you need to keep sharp.
• Take notes in class. Some students find it helpful to have a copy of these
lecture notes in front of them, but others do not. It is a personal style, and
you will have to decide what is right for you.
• Review your notes after class, before you try to do the homework. Compare
your notes with the lecture notes; you can use the lecture notes to check to
see if you copied the formulas correctly, or if you don’t understand something
in your notes.
• Reread or at least skim back over the chapter after reviewing your notes.
• Do the exercises at the end of the chapter. Note that this step comes AFTER
you have read the chapter, not before.
• If you don’t understand something, go back over the chapter, your class notes,
and the lecture notes, in that order. If that doesn’t help, ask me during office
hours, during class, or via email for help.
Sometimes you will run into something in either the notes or the text that just
plain does not make sense. If you can manage it, skip over the problem, or go on
with the next step or sentence in what you are reading. Come back to it later,
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