Numerical Analysis (Fall 2024)

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: M, W 3:30-4:45pm (19 West 4th 102)
Office Hours: M 1:00-2:00pm, Tu 12:30-1:30pm, F 9:15-10:00am (WWH 905)

Teaching Assistant: Xuanxi Zhang
Recitation: F 8:00-9:15am (WWH 102)
Office Hours: W 9:00-11:00am (WWH 803)

Syllabus
Edstem discussion
Gradescope

Course notes

Approximate Schedule

 
Week
Topic
Homework/Quiz
1. (9/1)
No class Monday, Intro to numerical anlaysis
2. (9/8)
Linear algebra review, SVD
quiz 1 (9/11)
3. (9/15)
SVD, Norms, Factored systems
[hw2] (due 9/24) [ws2]
4. (9/22)
Floating point numbers, Conditioning
quiz 2 (9/25) [ws3]
5. (9/29)
Stability, runtime
[hw3] (due 10/7)
6. (10/6)
Gaussian elimination (LU)
quiz 3 (10/9)
7. (10/13)
Monday class on Tueday, Pivoting, QR
 
8. (10/20)
QR
quiz 4 (10/23)
9. (10/27)
QR, least squares
 
10. (11/3)
Power Method
quiz 5 (11/5)
11. (11/10)
NLA Review
 
12. (11/17)
Inverse Power Method
midterm (11/20)
13. (11/24)
Iterative Methods
 
14. (12/1)
Polynomial interpolation, Chebyshev polynomials
quiz 6 (12/3)
15. (12/8)
Numerical Integration
 
16. (12/15)
Finals week
Final Presentation (TBD)