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University of Maryland University College My website contains most of the materials I use for teaching calculus, including video lectures recorded during the 2011 summer semester. I will spend class time mostly on doing projects with students when they have to apply calculus to their favorite topic. This fall semester I will take it even further: all my lectures will be recorded and made available on YouTube. Students read my lecture notes as notebook files and complete an online homework assignment before I talk about the corresponding material in class. I have incorporated a significant conceptual component into tests, making the tests more coherent with my concepts-oriented teaching. I would like to share my experience of using Wolfram|Alpha together with Google Docs for homework assignments and tests. That would illustrate the complexity of mathematical questions that need to be resolved before we teach calculus at a higher conceptual level. In this talk, I will briefly mention a theorem I proved that can be considered as the fundamental theorem of multivariable calculus. Such a fundamental change in the course raises a whole spectrum of questions: from content-specific questions like "What is the fundamental theorem of multivariable calculus?" to technical questions of managing homework assignments completed by students in the Mathematica notebook format. That frees significant time to be spent on a conceptual understanding of calculus. Wolfram|Alpha and Mathematica take care of all computational problems in a multivariable calculus class.

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