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.