# 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

**Syllabus**

**Edstem discussion**

**Gradescope**

**Course notes**

**Final project details**

## Schedule

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

**Week**

**Topic**

**Reading**

**Homework/Quiz**

**1.** (1/22)

Intro to numerical analysis

syllabus, GC1, GC2, N1-N4,

[ws1]
**2.** (1/29)

Floating point arithmetic, stability/conditioning

GC5, GC6, N4, N5, N6,

[ws2]
**3.** (2/05)

Rounding error analysis, Solving structured linear systems

quiz 1 (2/06)

**4.** (2/12)

LU / PLU / Gaussian elimination

**5.** (2/19)

LU cont. (no class 2/20)

quiz 2 (2/22)

**8.** (3/19)

Norms, conditioning of linear systems, least squares

**9.** (3/26)

Eigenvalue/vector

quiz 4 (03/27), project proposal (due 3/30)

**10.** (4/02)

Power method

GC7.6, GC7.4, N13

**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)