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)