MATHEMATIC CALCULUS 51, Exercises of Mathematics

Linear Algebra and Multivariable Calculus are two of the most widely used mathematical tools in quantitative work across all fields of study. This course develops conceptual understanding and problem-solving skills in both, highlighting how multivariable calculus is most naturally understood in terms of linear algebra, and the course text addresses a variety of real-world applications. Our focus is on teaching you skills that underlie a wide array of applications and relate the algebra of systems of linear equations to the geometry of vectors, acquiring the ability to "see" in dimensions far beyond 3 (thinking is seeing!); analyze the behavior of multivariable functions via partial derivatives, and combine that information with tools of linear algebra (such as matrices and eigenvalues) to solve optimization problems; apply your newly acquired visual skills in high dimensions to gain insight into a variety of real-world applications across data science, natural sciences, and economics.