In this course, students will learn how the notions of calculus are extended to functions of more than one variable in ways that facilitate both computational and geometric aspects. The course will have a strong geometric emphasis and will furnish the students with expertise in higher dimensional theorems such as Green’s theorem, Stokes’s theorem, and Gauss’s divergence theorem.

Students of this course will learn about ordinary differential equations and partial differential equations which form the central core of many branches of sciences as well as finance and economics. They will learn to apply many powerful analytical tools, such as the series method, Laplace transforms, and Fourier transforms, to solve these equations.

As a result of this course, students in many branches of physical sciences, mathematics, and machine learning, will have the powerful tool of analyzing the geometry of higher dimensional curved spaces and describe the dynamics of systems of interest. The students will learn about the formal aspects of derivatives and integration of functions and their generalizations on such curved spaces of arbitrary dimensions.