http:^^athos.rutgers.edu^dcs_library^510^syllabus.html

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Date: Tue, 14 Jan 1997 20:02:34 GMT
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<html><head><title>Computer Science 510 - Numerical Analysis</title></head><body><h1>Computer Science 510 - Numerical Analysis</h1><b>Instructor:</b><br>Professor Andrew Gelsey, (gelsey@cs.rutgers.edu)<br>402 Hill Center, Busch Campus, 5-4869<br>Office Hours: Wed 11am-noon<br><p><b>TA:</b><br>Daqing Li, (daqing@paul.rutgers.edu)<br>429 Hill Center, Busch Campus, 5-3766 (ext. 40)<br>Office Hours: Fri 2pm-4pm<br><p><b>Course Objective:</b> derivation, analysis, and implementation of algorithms fornumerical problems.<p><b>Optional</b> text books (should be available at Rutgers Bookstore):<br><ul><li>S. D. Conte, Carl de Boor, <i>Elementary Numerical Analysis: anAlgorithmic Approach</i>, 3rd edition.<li>Gene Golub, James M. Ortega, <i>Scientific Computing : anIntroduction with Parallel Computing</i>.</ul>Additional references:<br><ul><li>Kendall E. Atkinson, <i>An Introduction to Numerical Analysis</i>,2nd edition.<li>Germund Dahlquist and Ake Bjorck, <i>Numerical Methods</i>.</ul>(All of these books are <b>on reserve</b> for CS 510 in the Hill CenterMath library.)<p><b>Prerequisites:</b> Calculus, Linear Algebra, ability to program in a highlevel language (preferably Fortran or C)<p><b>Grading:</b><ul><li>written homework(approx 10) + computer programs(approx 4) -- approx 25%<li>midterm	approx 30%<li>final	approx 45%</ul><p><b>Course Outline:</b><br><ul><li><b>Floating point numbers and roundoff error</b>: (brief treatment)<p><li><b>Solution of nonlinear algebraic equations</b>:<br>	 bisection method, regula falsi (binary and interpolation	 search), fixed point iteration, Newton's method,	 convergence rates (linear, quadratic), secant method,	 systems of nonlinear equations --- Newton's method.<p><li><b>Solution of linear algebraic systems</b>:<br>	  Gaussian elimination/ LU decomposition, pivoting schemes,	  complexity, matrix inversion,	  variants of elimination for symmetric and banded matrices,	  sparse matrices (connections to graph theory),	  norms, condition number,	  error analysis,	  iterative methods (SOR, convergence rates),	  parallel solution of linear systems.<p><li><b>Interpolation, approximation of functions</b>:<br>	  the interpolating polynomial (construction and error term),	  piecewise polynomial interpolation, splines,	  multidimensional interpolation,	  least squares approximation, orthogonal polynomials,	  trigonometric approximation, fast Fourier transform.<p><li><b>Numerical differentiation and integration</b>:<br>	  derivation of polynomial-based quadrature formulas, error terms,	  adaptive quadrature, Romberg integration, Gaussian quadrature,	  numerical differentiation, error terms.<p><li><b>Numerical solution of ordinary differential equations</b>:	  basic methods (e.g., Euler's method, quadrature-based methods),	  truncation error,	  higher order equations, systems.<p></ul></body></html>

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