Course Discussion

We will use Zulip Chat for the class discussion, you can access it through the invitation linkLinks to an external site. (recommend using Github to signup, you will need to get a GitHub accountLinks to an external site., we will use that quite often in this class).

You do not have to use a desktop app, any web browser should be able to work. There are similar apps like Slack and Discord, but they do not quite support math symbols.

Course Information

Syllabus

The course introduces numerical analysis and computing for undergraduate/graduate students in mathematics, science, and engineering. The course covers the following topics:

Floating point arithmetic
Root finding
Interpolation
Numerical integration
Numerical differentiation
Ordinary differential equations

The course requires programming experience, MATLAB and Python are preferred, other programming languages can be used but would have limited feedback and support.

Solid knowledge and understanding of Calculus, Linear Algebra and ODE are more or less necessary. Reviewing your calculus, linear algebra and ODE textbooks and notes might be a good start.

If you do not have any experience in programming, you need first to learn how to write codes before taking this course.

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Textbook

The textbook is

A First Course in Numerical Methods by U. M. Ascher and C. Greif, 2011

We will cover the related chapters, but we will not completely follow the textbook, the assignments may not come from the book. A supplemental note by myself can be found here: Introduction to Numerical Analysis I (math-5630-6630.readthedocs.io). Note, my note may not be the same as the textbook in notation, definition, etc.

For those students who are taking 6630 or are interested in more details, you are encouraged to read all the following books (see Files for more details).

Numerical Mathematics by A. Quarteroni, R. Sacco, F. Saleri, 2007
Approximation Theory and Approximation Practice by Lloyd N. Trefethen, 2019
Numerical Methods for Ordinary Differential Equations: Initial Value Problems by D Griffith, D. Higham, 2010
Concise Numerical Mathematics by R. Plato, 2003
Numerical computing with IEEE floating point arithmetic by M. Overturn, 2001

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Assignments

The weekly assignments will be submitted to Canvas. There will be two kinds of assignments.

Regular homework: You will either write down or type out your solution. Scan or convert into a single PDF file.
Programming assignments: You will be given a GitHub repository hosting the assignments. Download or fork the repository and finish the work according to the README. You will submit your complete work either by a shared link to your public repository or a zipped file to Canvas.

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Exams

There are two in-class midterm exams on 09/26, and 10/31 and one final exam on 12/10. Programming is not included in any of the exams, but you might be asked to describe/explain some algorithms instead.

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