# Numerical analysis

## Announcements

- 2021-03-23
- Please complete Homework 4 and submit
on Gradescope by 2021-04-05 at 5am
- 2021-03-10
- Please complete Homework 3 and submit
on Gradescope by 2021-03-22 at 5am
- 2021-02-11
- Please complete Homework 2 and submit
on Gradescope by 2021-02-22 at 5am.
- 2021-01-26
- Please complete Homework 1 and submit
on Gradescope before around 5am on 2021-02-08
- 2021-01-26
- Please complete the intro video survey and submit
on Brightspace by 2021-01-28 at 5pm.
- 2021-01-15
- Welcome to the class!

## Overview

Numerical analysis is the study of *computer-based numerical methods*
for working with common mathematical and scientific operations. The
emphasis of the course is on numerical algorithms, represented as
computer codes, their mathematical abstractions, represented as
rigorously as possible, and the resulting approximation errors. This
is a graduate class on these methods that would serve a fondation for
students in computer science, mathematics, computational science and engineering, statistics,
engineering, and releated fields that will use numerical algorithms
and approximations in their work.

The topics we'll cover include:

- Computer-friendly representations of numbers including floating-point arithmetic
- Approximations to functions
- Numerical methods to differentiate and integrate functions
- Methods to solve non-linear equations (CS 51500 focuses on linear equations)
- Numerical solutions to ODEs

An undergraduate version of this course is available as CS314,
and for students from disciplines other than CS and Mathematics, this might be more suitable
depending on your previous knowledge of this material.

### Books and reading materials

The following textbook is officially required. But you won't need it for any of
the homework problems.

Walter Gautschi, *Numerical Analysis 2nd Edition*. Birkhauser/Springer, 2012
http://dx.doi.org/10.1007/978-0-8176-8259-0

See the readings page for additional references
as well as a set of recommended readings associated with each lecture.
These will be updated after the lecture and not before. There is
a rough reading guide in the syllabus.

### Coursework

This is a lecture class. You (the student) will be expected to attend
lectures and there will be regular homeworks. These will include
writing computer codes in the Matlab or Julia languages. There will also be a
midterm and a final. More detailed requirements are explained in
the syllabus including the course policies.