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CS 314: Numerical Methods
List of Topics (By Week):
Numerical Algorithms and mathematical software. Sources and propagation of errors. Condition of problems and stability of algorithms. Introduction to MATLAB.
Linear systems: Gaussian elimination and triangular factorization.
Residuals and error estimates in solving linear systems. First Hour-Examination.
Least squares approximation: orthogonal factorization.
Interpolation: existence, uniqueness, and the Vandermonde form of the interpolating polynomial.
Lagrange and Newton forms of the interpolating polynomial, errors in polynomial interpolation, and
Natural spline interpolation.
Numerical integration: Approximation based on the interpolating polynomial.
Second Hour-Examination composite rules, Richardson extrapolation.
Spline and adaptive quadrature.
The single nonlinear equation: bisection, Newton method and its variants, including the secant method.
Functional iteration, convergence, and higher order methods.
Initial-value problem for ordinary equations: differential equations, Euler's method.
Taylor and Runge-Kutta methods.
Introduction to Scientific Computing by Charles Van Loan, Prentice Hall; or Elementary Numerical Computing with Mathematica by Skeel and Keiper, McGraw-Hill; or Lecture Notes by A. Sameh and V. Sarin.