Multivariable Calculus will begin by exploring vector geometry and functions in more than one variable. Then, after expanding the concepts of limits and continuity to include multivariate functions, students will develop a rich understanding of concepts and methods relating to the main topics of Partial Differentiation and Multiple Integration. After generalizing a number of tools from single-variable to multivariate calculus, we will explore topics of optimization and geometric applications in areas including physics, economics, probability, and technology. We will expand our fluency with topics to address vector fields and parametric functions, and we will understand applications of Green’s and Stokes’ Theorems. We will employ multidimensional graphing programs to aid in developing a more thorough understanding of the myriad ways for describing and analyzing properties of multivariate functions. At the conclusion of the course, students will have the opportunity to further explore applications of and/or concepts relating to topics covered by the course.
Emphasis will be placed on students expressing fluency with numerical, algebraic, visual, and verbal interpretations of concepts. Students can expect to collaborate weekly on homework, problem-sets, and projects in small groups and in tutorial with their instructor online; face-to-face sessions may include visits with experts analyzing functions in multiple variables as well as group problem-solving activities and assessments.
Prerequisites: Completion of one full year of Single Variable Calculus AB or BC
Riley Maddox – The Urban School
Riley has been teaching Math at The Urban School of San Francisco since 2010, working as an advisor and running the after-school strength and conditioning program. Before that, Riley taught math and coached varsity rowing at Tabor Academy. Having graduated with a BA in Economics and History from Williams College, Riley is compelled in his work by the beauty of mathematics and its countless applications for understanding the world we live in.