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
[Intro survey] [tex] (due 9/11)
2. (9/10)
Linear algebra review, SVD
N3,N4
[hw1] [tex] (due 9/15)
3. (9/17)
SVD, Norms, Factored systems
N4,N5,N9
quiz 1 (9/21)
4. (9/24)
Floating point numbers, Stability
N6,N7
quiz 1 (bonus) (due 9/26); [hw2] [tex] (due 9/29)
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)
8. (10/22)
QR
N11
hw4
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)