CS 314: Numerical Methods

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.

Last Updated: Jun 20, 2025 11:36 AM