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642:574 NUMERICAL ANALYSIS SPRING 2010

**INSTRUCTOR:**

Richard S. Falk

Hill 722 (848-445-6916)

email: falk@math.rutgers.edu

Course Web Page

**TIME:** TTH6 - 5:00-6:20

**PLACE:** Hill SEC 217

This is the second part, independent of the first, of a general survey of the
basic topics in numerical analysis -- the study and analysis of numerical
algorithms for approximating the solution of a variety of generic problems
which occur in applications.

This semester (642:574), we will study the numerical solution of
linear systems of equations, the approximation of matrix eigenvalues and
eigenvectors, the numerical solution of nonlinear systems of equations,
numerical techniques for unconstrained function minimization, finite
difference and finite element methods for two-point boundary value problems,
and finite difference methods for some model problems in partial differential
equations.

In the fall semester, we considered the approximation of functions by
polynomials and piecewise polynomials, numerical integration, and the
numerical solution of initial value problems for ordinary differential
equations, and showed how all these problems are related.

Despite the many solution techniques presented in elementary calculus and
differential equations courses, mathematical models used in applications often
do not have the simple forms required for using these methods. Hence, a
quantitative understanding of the models requires the use of numerical
approximation schemes. This course provides the mathematical background for
understanding how such schemes are derived and when they are likely to work.

To illustrate the theory, in addition to the usual pencil and paper problems,
some short computer programs will be assigned. To minimize the effort
involved, however, the use of *Matlab* will be encouraged. This program
has many built in features which make programming easy, even for those with
very little prior programming experience.

**PREREQUISITES:** Advanced calculus, linear algebra,
and familiarity with differential equations.

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Maintained by
falk@math.rutgers.edu
and last modified 1/05/2016.
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