Summer 2019

## Real Analysis II

Topics include L^p, Banach and Hilbert spaces, basic functional analysis.

## Survey of Calculus

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

## Finite Mathematics

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

## Differential Equations

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

## Multivariable Calculus

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

## Introduction to Multivariable Calculus

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.

## Linear Algebra with Abstract Vector Spaces

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

## Linear Algebra

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

## Introduction to Linear Algebra

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

## Integral Calculus

Definite and indefinite integrals, techniques of integration, improper integrals, infinite series, applications.