This course covers fundamental mathematical tools useful in all areas of applied mathematics, including statistics, data science, and differential equations. The course covers basic principles in linear algebra, multivariate calculus, and complex analysis. Within linear algebra, topics include matrices, systems of linear equations, determinants, matrix inverse, and eigenvalues/eigenvectors. Relative to multivariate calculus, the topics include vector differential calculus (gradient, divergence, curl) and vector integral calculus (line and double integrals, surface integrals, Green’s theorem, triple integrals, divergence theorem and Stokes’ theorem). For complex analysis, the course covers complex numbers and functions, conformal maps, complex integration, power series and Laurent series, and, time permitting, the residue integration method.

Course prerequisites: 

Differential and integral calculus.

Course notes: 

Not for graduate credit.

Course instructor: 
Faculty

View Course Homepage(s) for this course.