Student’s Guide to Basic Multivariable Calculus

This study guide is intended to aid your understanding of multivariable calculus. We have organized it into chapters and sections corresponding to Basic Multivariable Calculus by Jerrold E. Marsden, Anthony ]. Tromba, and Alan Weinstein (Springer-Verlag/W.H. Freeman, 1993). Each section contains Goals, Study Hints, and (most important) Solutions to Every Other Odd Exercise. In addition, we have written chapter tests at the end of each review section.
The Goals are a short summary of what you ought to learn in the section and what you should understand before going on to the next one. The Goals should also help you review for examinations.
The Study Hints are definitions and facts that you should keep in mind when you do your homework. Here, too, we warn you about mistakes that are commonly made.
We have written solutions to every other odd exercise, i.e., numbers 1, 5, 9, 13 …. Sometimes we ask you to verify something or to fill in a detail, but most of our solutions are as complete as possible. However, we did not work the problems out so that you can copy them and hand them in as your own work. That's called cheating. We (as well as your instructors) believe that mathematics is not a spectator sport. To understand what's going on, you must do exercises. If you are lost, working through our detailed solutions can help you to find your way back. If you feel insecure before exams or quizzes, doing extra exercise problems and comparing your answers with ours is the best way to study. If you are simply studious and want to do extra exercise problems, you will not have to do them blindly because we have provided many solutions.
The chapter tests contains some questions that may be more challenging than some of the exercises. They are intended to stimulate your thinking and to prepare you for your exams.
Even if you do no more than just flip through the pages of our little book ten minutes before the exam, you should feel better about multivariable calculus! We wish you great success!