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Summer 2018

Archived:

## Hilbert Spaces for Scientists and Engineers

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.

The three course series MATH 6579, 6580, and 6221 is designed to provide a high level mathematical background for engineers and scientists.

This course is equivalent to MATH 6338. Students should not be able to obtain credit for both MATH 6580 and MATH 6338.

## 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.