This book grew out of class notes for several different courses at Oregon State University (OSU) in both mathematics and physics. In mathematics, these courses included the two second-year calculus courses, covering Multivariable Calculus and Vector Calculus, respectively, which form part of the Bridging the Vector Calculus Gap project at OSU, begun in 2000 with funding from the National Science Foundation (NSF). In physics, these courses included the two third-year “paradigms” courses entitled Symmetries and Idealization, and Vector Fields, which together provide an introduction to electromagnetism for physics majors. These courses make up just one part of a major upper-division curriculum reform effort at OSU, entitled Paradigms in Physics, which was begin in 1997, again with funding from the NSF.

We are grateful to all of the faculty and postdoctoral fellows involved in these two projects, and especially to Liz Gire, Mary Bridget Kustusch, David Roundy, and Emily van Zee, as well as to our many TAs, including Johnner Barrett, Stuart Boersma, Kerry Browne, Sam Cook, Emily Townsend, and Aaron Wangberg, several of whom won departmental and/or university teaching awards for their efforts on behalf of these projects. Last but not least, we thank the many students who attempted to master this material in courses taught by one of us, and in some cases both.

This work has been supported in part by NSF grants DUE–965320, 0088901, 0231032, 0231194, 0618877, 1023120, and 1323800.