Numerical Methods I

The course covers the standard techniques of numerical computation from a theoretical as well as a practical perspective with a particular emphasis on large-scale high-performance computation, and provides the foundation for more specialized third year courses in computation and modeling.

It is assumed that participants have the mathematical background equivalent to two semesters of Engineering and Science Mathematics - attendance of the first year B track (Multivariable Calculus, ODE; Linear Algebra, Fourier Methods, Probability) is highly recommended but not formally required - or Analysis I/II and Linear Algebra I.

The course is appropriate as a home school elective for students of all majors with a particular interest in computation. It is recommended that students commit to this course for the full year. Students interested in a more compact introduction to methods of numerical computation are advised to take the one-semester Engineering and Science Mathematics 4A (Numerical Methods) instead.

Topics covered throughout the year are: computer arithmetic, condition of algorithms, systems of linear equations including iterative methods, computation of eigenvalues, interpolation and least square methods, numerical quadrature, numerical solution of ordinary differential equations (including stiff equations and boundary value problems); introduction to linear and nonlinear optimization. The last part of this course consists of special topics which may change from year to year.

• Hardcopy printouts of the code.
• A detailed description of the computer experiment including, if applicable, a description of the code, a discussion of the input data, a description of the output, a discussion of possible errors, efficiency, and implementation difficulties, and a verbose answer to the question posed.
• If applicable, hardcopy printouts of the results.
• The code should, moreover, be sent in a single email to to TBA.

Collaborative project work in groups of two or three is permissible provided:

• Each member of the group maintains a runnable version of the code (on their personal laptop or teaching lab account) and is able to demonstrate and explain the code without help from others.
• Each member of the group submits a discussion, clearly distinct from the others', using their own words. The only exception to this rule are source code comments (which are encouraged!) and algorithmically generated output.
• You state who you collaborated with (both in your written exposition and in the source cod)

You may consult books and internet resources provided you always quote the source.