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

Resources (books, notes, more)
Academic honesty
Assignments
Solutions
Misc handouts
Demos, mfiles, etc

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.

Resources

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:

Wikipedia article "Floating Point".
D. Goldberg "What Every Computer Scientist Should Know About Floating-Point Arithmetic".
W. Kahan's webpage with many useful articles on various floating point issues.

MATLAB resources:

Introduction to MATLAB Programming by J. Dorfman, available at Krishna Copy Center on University Avenue. Please email them your order at orders@krishnacopy.com, with name and phone number, for a later pickup.
Scientific Computing wih MATLAB and Octave by Quarteroni and Saleri.
Learning programming using MATLAB by K. Sayood.

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.