Study Guide with Solutions for Vector Calculus

This book is intended to help you, the student, navigate the 6th edition of Vector Calculus by Jerrold E. Marsden and Anthony Tromba. The chapters and sections of this study guide correspond exactly to those of the textbook, and every exercise solved here appears in blue type there.
For each section, we have provided a short list of Goals to help you prioritize the material and remain mindful of the bigger picture. Each section also includes a list of Study Hints where we give commentary on the ideas contained in the corresponding section of the textbook. The subject of vector calculus is vast and these hints attempt to distill the most important material from each section into a few concise statements. The remainder of this study guide consists of Solutions to Selected Exercises. The exercises selected include easier problems as well as very challenging ones. You should try to refer to these solutions only when you are stuck, or to check your work. You will not learn the material properly by copying our solutions and turning them in to your professor.
The 6th edition of this study guide has been greatly revised, with entirely new Goals and Study Hints and over 100 new solutions. In addition, many of the old solutions have been rewritten. The companion website to Vector Calculus can be found at whfreeman.com/MarsdenVC6e. The site includes downloadable practice tests for every chapter, sample exams for Chapters 1-4 and Chapters 5-8, and two comprehensive exams for the entire textbook. If you should find any errors in either the textbook, this book, or the website, please let us know by contacting the publisher via the website or by sending an email to tokorcheckcorrections@gmail.com.