### A Vision of Multivariable Calculus

Abstract: This talk will address certain challenges in teaching multivariable calculus. Classical texts emphasize calculus in dimensions two or three, based on 19th and 20th century applications to physics. At present, many of our students are more motivated by data and systems in higher dimensions. How can a calculus course best adapt to these needs, without overwhelming students (or professors)? This talk will outline a plan for increasing both the dimension and sophistication of multivariable calculus instruction with the use of video. Topics covered will include the use of visualization, matrix algebra, and differential forms.