# Numerical Analysis (Fall 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.

**Instructor**: Tyler Chen

**Email**: tyler.chen@nyu.edu

**Class**: T, Th 12:30-1:45pm (WWH 201)

**Office Hours**: T 1:45-2:45 (WWH201), T 4:30-5:30pm (WWH905), Th 4:00-5:00pm (WWH905)

**Teaching Assistant**: Marguerite Brown

**Recitation**: F 9:30-10:45am (WWH 201)

**Office Hours**: W 11:00-12:00pm (WWH905)

**hw7 and quiz 7 are optional, see the annoucement on Edstem for details**

**Syllabus**

**Edstem discussion**

**Gradescope**

**Course notes**

**Final Project**

**Review Sheet**

## Approximate Schedule

Numbers are chapter #s.

**Week**

**Topic**

**Reading**

**Homework/Quiz**

**1.** (9/3)

Intro to numerical anlaysis

N1,N2

**2.** (9/10)

Linear algebra review, SVD

N3,N4

**3.** (9/17)

SVD, Norms, Factored systems

N4,N5,N9

**4.** (9/24)

Floating point numbers, Stability

N6,N7

**5.** (10/1)

Conditioning,runtime

N7,N8

**6.** (10/8)

No class Tuesday, Gaussian elimination (LU)

N10

**7.** (10/15)

Pivoting, QR

N10,N11

**9.** (10/29)

QR, least squares

N12

**10.** (11/5)

Power Method

N13

**12.** (11/19)

Inverse Power Method, No Class Thursday

N14

project proposal (11/21),

quiz 5 (11/24, online)

**13.** (11/26)

Iterative Methods

**18.** (12/3)

Polynomial interpolation, Chebyshev polynomials

N15,N16,N17

quiz 6 (12/7)

**14.** (12/10)

Numerical Integration

N19

**15.** (12/17)

Finals week

Final Presentation (12/18, 2-3:50pm), quiz 7 (12/19)