Numerical Analysis

This course is a one semester course meant to introduce graduate students from science and engineering disciplines to the fundamentals of numerical mathematics. (But any graduate student seriously interested in applied mathematics should take it.) It will be an introductory course covering a broad range of topics such as: interpolation, numerical differentiation, numerical quadrature, linear systems, and least squares problems. Advanced topics such as approximation theory, fast algorithms, and eigenvalue problems will also be covered either in the form of extended readings or invited talks.

Office hour

Thur (2:30-4:30pm), Jin Chun Yuan West Building, Room 136, or by appointment.

Announcements, etc.

Announcements, notes, and assignments etc. will be posted both on this website and on the Tsinghua University Web Learning site. This course is taught online and offline simultaneously. Online students please head to the Web Learning site to get the meeting ID.

Prerequisites

• Required
  • Calculus
  • Linear algebra
  • Some experience in programming
• Highly recommended
  • Mathematical analysis
  • Complex Variables
• Recommeded
  • Ordinary Differential Equations
  • Partial Differential Equations

Textbook

The course textbook is Scientific Computing - An Introduction Using Maple and MATLAB by W. Gander, M.J. Gander, and F. Kwok. It is available for download in PDF format.

Recommended Texts

• Numerical Mathematics (2nd ed.) by A. Quarteroni, R. Sacco and F. Saleri
• Approximation Theory and Approximation Practice by L. N. Trefethen
• Numerical Linear Algebra by L.N. Trefethen and D. Bau III

Assignments and grading

There will be weekly homework assignments involving a mix of theory and (small-scale) computational experiments and a (closed-book) final exam.

Since the emphasis is on developing the ability of problem solving and effective communication between disciplines, none of the above is meant to be heavily mathematical. However scientific rigor to some extent is to be expected (as it should be).

Weekly Schedule (tentative)

… to be continued …