$\newcommand{\eps}{\varepsilon} \newcommand{\kron}{\otimes} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\trace}{trace} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator*{\minimize}{minimize} \DeclareMathOperator*{\maximize}{maximize} \DeclareMathOperator{\subjectto}{subject to} \newcommand{\mat}{\boldsymbol{#1}} \renewcommand{\vec}{\boldsymbol{\mathrm{#1}}} \newcommand{\vecalt}{\boldsymbol{#1}} \newcommand{\conj}{\overline{#1}} \newcommand{\normof}{\|#1\|} \newcommand{\onormof}{\|#1\|_{#2}} \newcommand{\MIN}{\begin{array}{ll} \minimize_{#1} & {#2} \end{array}} \newcommand{\MINone}{\begin{array}{ll} \minimize_{#1} & {#2} \\ \subjectto & {#3} \end{array}} \newcommand{\MINthree}{\begin{array}{ll} \minimize_{#1} & {#2} \\ \subjectto & {#3} \\ & {#4} \\ & {#5} \end{array}} \newcommand{\MAX}{\begin{array}{ll} \maximize_{#1} & {#2} \end{array}} \newcommand{\MAXone}{\begin{array}{ll} \maximize_{#1} & {#2} \\ \subjectto & {#3} \end{array}} \newcommand{\itr}{#1^{(#2)}} \newcommand{\itn}{^{(#1)}} \newcommand{\prob}{\mathbb{P}} \newcommand{\probof}{\prob\left\{ #1 \right\}} \newcommand{\pmat}{\begin{pmatrix} #1 \end{pmatrix}} \newcommand{\bmat}{\begin{bmatrix} #1 \end{bmatrix}} \newcommand{\spmat}{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)} \newcommand{\sbmat}{\left[\begin{smallmatrix} #1 \end{smallmatrix}\right]} \newcommand{\RR}{\mathbb{R}} \newcommand{\CC}{\mathbb{C}} \newcommand{\eye}{\mat{I}} \newcommand{\mA}{\mat{A}} \newcommand{\mB}{\mat{B}} \newcommand{\mC}{\mat{C}} \newcommand{\mD}{\mat{D}} \newcommand{\mE}{\mat{E}} \newcommand{\mF}{\mat{F}} \newcommand{\mG}{\mat{G}} \newcommand{\mH}{\mat{H}} \newcommand{\mI}{\mat{I}} \newcommand{\mJ}{\mat{J}} \newcommand{\mK}{\mat{K}} \newcommand{\mL}{\mat{L}} \newcommand{\mM}{\mat{M}} \newcommand{\mN}{\mat{N}} \newcommand{\mO}{\mat{O}} \newcommand{\mP}{\mat{P}} \newcommand{\mQ}{\mat{Q}} \newcommand{\mR}{\mat{R}} \newcommand{\mS}{\mat{S}} \newcommand{\mT}{\mat{T}} \newcommand{\mU}{\mat{U}} \newcommand{\mV}{\mat{V}} \newcommand{\mW}{\mat{W}} \newcommand{\mX}{\mat{X}} \newcommand{\mY}{\mat{Y}} \newcommand{\mZ}{\mat{Z}} \newcommand{\mLambda}{\mat{\Lambda}} \newcommand{\mPbar}{\bar{\mP}} \newcommand{\ones}{\vec{e}} \newcommand{\va}{\vec{a}} \newcommand{\vb}{\vec{b}} \newcommand{\vc}{\vec{c}} \newcommand{\vd}{\vec{d}} \newcommand{\ve}{\vec{e}} \newcommand{\vf}{\vec{f}} \newcommand{\vg}{\vec{g}} \newcommand{\vh}{\vec{h}} \newcommand{\vi}{\vec{i}} \newcommand{\vj}{\vec{j}} \newcommand{\vk}{\vec{k}} \newcommand{\vl}{\vec{l}} \newcommand{\vm}{\vec{l}} \newcommand{\vn}{\vec{n}} \newcommand{\vo}{\vec{o}} \newcommand{\vp}{\vec{p}} \newcommand{\vq}{\vec{q}} \newcommand{\vr}{\vec{r}} \newcommand{\vs}{\vec{s}} \newcommand{\vt}{\vec{t}} \newcommand{\vu}{\vec{u}} \newcommand{\vv}{\vec{v}} \newcommand{\vw}{\vec{w}} \newcommand{\vx}{\vec{x}} \newcommand{\vy}{\vec{y}} \newcommand{\vz}{\vec{z}} \newcommand{\vpi}{\vecalt{\pi}} \newcommand{\vlambda}{\vecalt{\lambda}}$ # 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.