Linear Algebra and Real Analysis I

This is the first half of an integrated treatment of linear algebra, real analysis, and multivariable calculus. By combining these disciplines into one course, we show important relations between each, which allows us to use results from one topic to gain deeper understanding of other topics. We cover matrices, eigenvectors, dot and cross products, limits, continuity, and differentiability, all in multiple dimensions, with an introduction to manifolds. This course covers both mathematical proofs as well as applications. Students learn to write more than twenty important proofs and see how proof-based mathematics prepares them for applications in engineering, economics, data science, and artificial intelligence.