List of Topics (By Week): 1. Numerical Algorithms and mathematical software. Sources and propagation of errors. Condition of problems and stability of algorithms. Introduction to MATLAB. 2. Floating-point computation. 3. Linear systems: Gaussian elimination and triangular factorization. 4. Residuals and error estimates in solving linear systems. First Hour-Examination. 5. Least squares approximation: orthogonal factorization. 6. Interpolation: existence, uniqueness, and the Vandermonde form of the interpolating polynomial. 7. Lagrange and Newton forms of the interpolating polynomial, errors in polynomial interpolation, and 8. Natural spline interpolation. 9. Numerical integration: Approximation based on the interpolating polynomial. 10. Second Hour-Examination composite rules, Richardson extrapolation. 11. Spline and adaptive quadrature. 12. The single nonlinear equation: bisection, Newton method and its variants, including the secant method. 13. Functional iteration, convergence, and higher order methods. 14. Initial-value problem for ordinary equations: differential equations, Euler's method. 15. Taylor and Runge-Kutta methods. Suggested Textbooks: 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.