# 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 4:30-5:30pm, F 8:30-9:25am (WWH905)

**Teaching Assistant**: Marguerite Brown

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

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

**Syllabus**

**Edstem discussion**

**Gradescope**

**Course notes**

## 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

quiz 2 (10/5)

**6.** (10/8)

Gaussian elimination (LU)

N10

hw3

**7.** (10/15)

Pivoting, QR

N10,N11

quiz 3 (10/19)

**9.** (10/29)

QR, least squares

N12

quiz 4 (11/2)

**10.** (11/5)

Power Method

N13

hw5

**11.** (11/12)

NLA Review

Midterm (11/16)

**12.** (11/19)

Root finding, No Class Thursday

N14

quiz 5 (online)

**13.** (11/26)

Polynomial approximation/interpolation

N15,N16

hw6

**18.** (12/3)

Chebyshev polynomials

N17

quiz 6 (12/7)

**14.** (12/10)

Numerical Integration

N19

hw7

**15.** (12/17)

Finals week

Final Presentation, quiz 7 (online)