# Math 128A

## Numerical analysis

Lectures TuTh 14:10-15:30, 100 Lewis Hall

Office Hours Tu 17:10-19:00, SLC, and by appt.

Math 128A on Piazza

#### Topics covered (to be adjusted if necessary)

08/25/16: Logistics of the course. Vector norms.
08/30/16: Matrix norms.
09/01/16: The spectral radius. Convergence of matrix series.
09/06/16: Floating point and rounding errors.
09/08/16: Well-posed problems and computations.
09/13/16: Gaussian elimination.
09/15/16: Arithmetic complexity of Gaussian elimination.
09/20/16: Condition number. A priori error estimates.
09/22/16: A posteriori error estimates.
09/27/16: Contractive mappings.
09/29/16: Functional iteration for a single equation.
10/04/16: Error propagation.
10/06/16: 2nd and higher order iteration methods.
10/11/16: Chord method. Newton's method.
10/13/16: Midterm (in class).
10/18/16: Weierstrass' approximation theorem.
10/20/16: Lagrange interpolation. Pointwise error.
10/25/16: Hermite interpolation.
10/27/16: Newton's interpolation and divided differences.
11/01/16: Equally spaces interpolation points.
11/03/16: Numerical differentiation.
11/08/16: Differentiation using equidistant points.
11/10/16: Numerical integration. Newton-Cotes rules.
11/15/16: Gaussian quadrature.
11/17/16: Initial value problems for ODEs: Euler's method.
11/22/16: Error analysis of Euler's method.
11/29/16: Higher-order Taylor methods.
12/01/16: Runge-Kutta's methods.

#### Books:

- Analysis of numerical methods, by Eugene Isaacson and Herbert Bishop Keller.
- Numerical methods using MATLAB, by John H. Mathews and Kurtis D. Fink,
4th edition.
- Numerical analysis, by Richard L. Burden and J. Douglas Faires, 7th
edition.
- Numerical analysis in modern scientific computing, by Peter Deuflhard
and Andreas Hohmann, 2nd edition.
- Accuracy and stability of numerical algorithms, by Nicholas J. Higham.
2nd edition.

Lectures will be based primarily on the first book.

#### Online notes:

#### MATLAB resources:

Instructions for setting up a UC Berkeley Library Proxy Server for off-campus access to online books and journals.

The course Math 98: Introduction to MATLAB programming is taught by Christopher Policastro.

The instructor welcomes cooperation among students and the use of books.
However, handing in homework that makes use of other people's work (be it from a fellow
student, a book or paper, or whatever) **without** explicit
acknowledgement is considered academic misconduct.

Last modified: Sep 29, 2016