The approach to vector calculus used in the Study Guide is an essential part of the Vector Calculus Bridge Project.

This approach emphasizes geometric visualization rather than (just) algebraic manipulation. Since most calculus textbooks emphasize the latter, you may occasionally feel that the Study Guide is speaking a different language than the textbook. To some extent, this is correct, and reflects cultural differences between different fields of science. Students in some disciplines, such as physics or electrical engineering, may find the approach used here especially familiar. But being comfortable with both algebraic and geometric representations is an important skill for everybody; it never hurts to be bilingual.

The only way to master the material in this course is to solve problems. Your instructor will most likely assign a few problems each week. Do not expect to succeed in this course if you only attempt the assigned problems. It is your responsibility to attempt as many problems as necessary on your own, both routine problems and more challenging problems, and to seek help as needed.

Familiarity with the following topics will be assumed in this course: basic properties of vectors, the dot and cross products, partial differentiation, multivariable differentials and chain rule, and multiple integration (including polar coordinates). This course will provide you with an opportunity to consolidate your understanding of these topics; a brief review of some of this material appears in the first few lessons.

In addition to your instructor and TA, help is available in the Mathematics Learning Center (MLC) on the ground floor of Kidder Hall. OSU also has an (old) online vector calculus study guide 1) which can be found here.

For those using other texts, a geometric approach to vector calculus can be found in

• William McCallum, Deborah Hughes-Hallett, Andrew Gleason, et al., Multivariable Calculus, 4th edition Wiley, 2005.

which is also available combined with single variable material as

• Deborah Hughes-Hallett, William McCallum, Andrew Gleason, et al., Calculus, 4th edition Wiley, 2005.

A copy of (an earlier edition of) the latter version should be available in the library. Finally, there is an excellent informal book on vector calculus from the point of view of a scientist or engineer, entitled

• Div, Grad, Curl, and All That; an informal text on vector calculus, by H. M. Schey, 4th edition, Norton \& Co., 2005.

It is a pleasure to thank Corinne Manogue, Hal Parks, Roy Rathja, Phil Siemens, and Andreas Weisshaar for discussions leading to the original version of this study guide, which was partially supported by an L L Stewart Faculty Development Award from Oregon State University.

Further discussions with Johnner Barrett, Stuart Boersma, Bill Bogley, Corina Constantinescu, Sam Cook, Tom Dick, Barbara Edwards, David Griffiths, Dianne Hart, Martin Jackson, Corinne Manogue, John Lee, Hal Parks, Harriet Pollatsek, and Nicole Webb have influenced subsequent revisions.

The Vector Calculus Bridge Project has been partially supported by NSF Grants DUE–0088901 and DUE–0231032 and by the Oregon Collaborative for Excellence in the Preparation of Teachers (OCEPT).