Math/CSE 451, Spring 2002: NUMERICAL COMPUTATIONS

Instructor: Constantin Bacuta

Contents:

1.2

Taylor series.

2.1

Representation of numbers in different bases.

2.2

Floating Point Representation.

2.3

Loss of Significance.

3.1

Bisection method.

3.2

Newton's method.

3.3

Secant method.

4.1

Polynomial Interpolation.

4.3

Estimating derivatives and Richardson Extrapolation.

Midterm

5.1

Definite Integral.

5.2

Trapezoid rule.

5.3

Romberg Algorithm.

5.5

Gaussian quadrature formulas.

6.1

Naive Gaussian elimination.

6.2

Gaussian Elimination with scaled partial pivoting.

Midterm

6.3

Tri-diagonal and banded systems.

6.4

LU-Factorization.

7.1

First degree and second degree splines.

7.2

Natural cubic splines.

8.1

Taylor series methods for ODEs.

8.2

Runge Kutta methods.

(If time permits)

9.1

Methods for first order systems of ODE.

9.2

Higher order systems and equations.

Final examination

Total: 24 subsections

This schedule is to be viewed as an approximation to the real one. Midterms and the final might be scheduled differently

The numbering corresponds to the section numbering in the book by Kincaid and Cheney, ``Numerical Mathematics and Computing'', 4th edition