Foundations for Advanced Mathematics

Catalog description

This course is an advanced treatment of the foundations of calculus, linear algebra and differential equations. Major focus on the proofs of theorems in the ares of analysis, linear algebra and differential equations. Topics are as follows: • Analysis: properties of the real numbers, sequences and series, limits, convergence, continuity, the derivative, and the Riemann integral. • Linear Algebra: matrix theory, system of equations, vector spaces, eigenvalues and eigenvectors, diagonalization and orthogonalization, change of basis. • Differential Equations: ordinary differential equations, solutions in series, solutions using Laplace transforms, systems of dfferential equations, applications.