https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=12966 We propose a novel and innovative combination of methods and materials for the teaching of vector calculus in the undergraduate curriculum. Having taught vector calculus at various levels in our own careers, we feel that in the era of interdisciplinary science and technology it is important that the examples and applications of vector calculus mirror the students? experience and expectations. We focus on the fields of Machine Vision, Robotics, and Oceanography, as three contemporary areas that together cover the gamut of mathematical complexity in vector calculus. Thus, machine vision is a perfect metaphor for functions of two-variables (still camera images); functions of three variables (video images), and functions into 2 or 3 variables (color images); robotics presents a highly contemporary domain for the examples and applications of functions of n variables for large n (robotics manipulators), and finally oceanography reframes some of the applications of vector calculus in fluid dynamics in a much larger domain (that is easier for students to identify with) and provides a connection to atmospheric and environmental science. Our approach to the teaching is tripartite: we introduce new concepts through a series of motivating examples in these interdisciplinary fields, we then present shortened but accurate explanations of the new concepts (which we prefer to detailed proofs), finally we come back to the examples and examine them in greater detail and complexity (conducive to the level of preparation of the class). Our method will be flexible and modular allowing instructors to pick and choose the materials to suit the level of complexity of their particular course. In addition, we will develop software which will be freely available at a web site we will maintain. https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=12966 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=12967 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=12967 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=14606 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=14606 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=13348 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=13348 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=14607 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=14607 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=43946 https://www.whoi.edu/sbl/liteSite.do?litesiteid=8652&articleId=43946