# Numerical Analysis (Spring 2023)

Welcome to Numerical Analysis! Numerical analysis studies algorithms and mathematical problems in the presence of (small) errors. In practice, such errors are unavoidable, so it is important to understand their impacts. Numerical analysis is one of the core fields in applied math, and this class will cover a number of key topics in numerical analysis. Linear algebra is a prerequisite, as much of numerical analysis is based on linear algebra. There is no prerequisite for coding.

Instructor: Tyler Chen
Email: tyler.chen@nyu.edu
Class: M,W 3:30-4:50PM; JABS 775B
Office Hours: M,W 5:00-6:00PM; 370 Jay Street Floor 11

Teaching Assistant: Fanghe (Athena) Liu
Recitation: F 2:00-3:20PM; RGSH 325
Office Hours: F 3:40-4:40PM; 2 Metrotech Floor 8

Course notes

Final project details

## Schedule

N=Course notes, GC = Greenbaum & Chartier. Numbers are chapter #s.

Week
Topic
Homework/Quiz
1. (1/22)
Intro to numerical analysis
syllabus, GC1, GC2, N1-N4, [ws1]
Intro Survey [pdf] [tex] (due 1/25)
2. (1/29)
Floating point arithmetic, stability/conditioning
GC5, GC6, N4, N5, N6, [ws2]
HW1 (due 2/02) [pdf] [tex]
3. (2/05)
Rounding error analysis, Solving structured linear systems
GC7.2, [ws3]
quiz 1 (2/06)
4. (2/12)
LU / PLU / Gaussian elimination
GC7.2, N8, [ws4]
HW2 (due 2/16) [pdf] [tex]
5. (2/19)
LU cont. (no class 2/20)
GC7.6.2, N9, [ws5]
quiz 2 (2/22)
6. (2/26)
QR
N10
quiz 2 bonus (due 02/27) [pdf] [tex]; HW3 (due 3/02) [pdf] [tex]
7. (3/5)
SVD
quiz 3 (3/06) [online]
(3/12)
SPRING BREAK

8. (3/19)
Norms, conditioning of linear systems, least squares
N11, N12, [ws7]
HW4 (due 03/23) [pdf] [tex]
9. (3/26)
Eigenvalue/vector
GC7.6, GC7.4, N13, [ws8]
quiz 4 (03/27), project proposal (due 3/30)
10. (4/02)
Power method
GC7.6, GC7.4, N13
HW5 (due 4/06) [pdf] [tex]
11. (4/09)
Root finding, Orthogonal polynomials
GC4
quiz 5 (due 4/10)
12. (4/16)
Polynomial approximation

HW6 (due 4/20)
13. (4/23)
Numerical Integration
GC10
quiz 6 (4/24), Final Report (4/27)
14. (4/30)
Numerical Differentiation
GC9
HW7 (due 5/04)
15. (5/07)
Review

quiz 7 (5/08), Final Presentations (5/15)