Georgia Institute of Technology College of Sciences

Review of linear algebra and ordinary differential equations, brief introduction to functions of a complex variable.

Geometry, convergence, and structure of linear operators in infinite dimensional spaces. Applications to science and engineering, including integral equations and ordinary and partial differential equations.

Functions, the derivative, applications of the derivative, techniques of differentiation, integration, applications of integration to probability and statistics, multidimensional calculus.

Linear equations, matrices, linear programming, sets and counting, probability and statistics.

Methods for obtaining numerical and analytic solutions of elementary differential equations. Applications are also discussed with an emphasis on modeling.

Linear approximation and Taylor’s theorems, Lagrange multiples and constrained optimization, multiple integration and vector analysis including the theorems of Green, Gauss, and Stokes.

An introduction to multivariable calculus through vectors in 3D, curves, functions of several variables, partial derivatives, min/max problems, multiple integration. Vector Calculus not covered.

This is an intensive course on linear algebra, taught at a sophisticated and abstract level.

Linear algebra through eigenvalues, eigenvectors, applications to linear systems, least squares, diagonalization, quadratic forms.

An introduction to linear algebra through eigenvalues and eigenvectors, applications to linear systems, least squares.