MA 4424
Spring 2020
Mike O'Neil (
TTh 2pm - 3:15pm JABS 473

Office hours
T 11am - 12pm, Th 12:30pm - 1:30pm
2 MetroTech 854

Gaston Gonzalez (
F 1:30pm - 2:45pm RGHS 503
Office hours
F 12:25pm - 1:25pm
2 MetroTech, 8th floor

The main textbook for the course is Suli and Mayers, An Introduction to Numerical Analysis, 2012. The textbook is available for free (electronically) to NYU students on Cambridge University Press.

Additionally, a one-stop source for floating point arithmetic is Michael Overton, Numerical Computing with IEEE Floating Point Arithmetic, 2001, which is also available for free to NYU affiliates via SIAM.

Overall numerical grades will be computed from homework (10%), two preliminary exams (25% each), and one final exam (40%). The final letter grade will be determined from the overall numerical grade.

UPDATE: Since the course has moved online, the new grade weighting will be: homeworks one through three (10%), one preliminary exam (25%), homeworks four through six (65%).
  • The first class will meet on Jan 28, 2020.
  • Recitations will start on Feb 7, 2020.
  • The course syllabus is available here.
  • As of March 12, the course has moved online. Please attend lectures, office hours, etc. via the Zoom links accessible via NYU Classes.
This course will serve as an introduction to modern numerical analysis and will cover subjects such as the solution of systems of nonlinear equations, numerical linear algebra, numerical differentiation and integration, interpolation, Monte Carlo methods, and numerical methods for ordinary differential equations. The stability and accuracy of all the previous methods will also be analyzed in the context of floating-point arithmetic. The course will have a focus on the analysis of numerical methods, but also require you to use numerical software (Matlab, Python, or Julia).


Homework will be assigned roughly every other week and due by the start of class on the day on which it is due. A PDF of the homework may be sent in lieu of a hard-copy but the instructor must receive it by the start of class. No late homework is accepted without prior approval from the instructor, and in those cases, generally exemptions will only be made for medical reasons with documentation. Students are encouraged to work together on their homework, but each student must write-up and submit the assignments independently.

Item Due date Materials
HW 1 Feb 18 hw01.pdf hw01.tex
HW 2 Mar 3 hw02.pdf hw02.tex
HW 3 Mar 13 hw03.pdf hw03.tex

Below is an updated list of discussion topics along with any documents that were distributed, notes, or relevant code.

Date Topics Materials
Jan 28 Intro to the course
Bisection method
Suli & Mayers: 1.1, 1.6
Lecture notes
Jan 30 Secant and Newton's methods Suli & Mayers: 1.4-1.5
Lecture notes
Feb 4 Convergence of Newton's method Suli & Mayers: 1.4
Lecture notes
Feb 6 Multidimensional Newton's method Lecture notes
Feb 11 Fixed point iterations,
Contraction mapping theorm
Suli & Mayers: 1.2
Lecture notes
Feb 13 Contractions, stability, rates of convergence Suli & Mayers: 1.2-1.3
Lecture notes
Feb 18 Matlab demo
Floating point calculations
Lecture notes
Feb 20 Floating point calculations macheps.m
Lecture notes
Feb 25 Gaussian elimination, LU factorization Suli & Mayers: 2.1-2.3
Lecture notes
Feb 27 Prelim Exam 1
Mar 3 Pivoted LU, norms Suli & Mayers: 2.4-2.7
Lecture notes
Mar 5 Matrix norms, conditioning Suli & Mayers: 2.7
Lecture notes
Mar 10 Condition number of a matrix Suli & Mayers: 2.7
Lecture notes
Mar 12 Least squares Suli & Mayers: 2.9
Lecture notes
Mar 17 No class: Spring break
Mar 19 No class: Spring break
Mar 24 Least squares, QR factorization Suli & Mayers: 2.9
Lecture notes
Mar 26 Gerschgorin's Thm, Power method Suli & Mayers: 5.1-5.2, 5.4
Lecture notes
Mar 31 Inverse power method, Jacobi's method Suli & Mayers: 5.8, 5.3
Lecture notes
Apr 2 Convergence of Jacobi's method Suli & Mayers: 5.3
Lecture notes
Apr 7 Lagrange interpolation Suli & Mayers: 6.1-6.2
Lecture notes
Apr 9 Barycentric interpolation, Runge effect,
minimax approximation
Suli & Mayers: 6.3, 8.1-8.3
Lecture notes
Apr 14 Chebyshev polynomials, 2-norm function approximation Suli & Mayers: 8.4-8.5, 9.1-9.3
Lecture notes
Apr 16 Orthogonal polynomials Suli & Mayers: 9.4
Lecture notes
Apr 21 Trapezoidal rule, Newton-Cotes, Euler-MacLaurin Suli & Mayers: 7.1-7.3, 7.6
Lecture notes
Apr 23 Gaussian quadrature Suli & Mayers: 10.1-10.4
Lecture notes
Apr 28 ODEs: Forward Euler, finite differences, Richardson extrapolation Suli & Mayers: 12.1-12.2
Lecture notes
Apr 30 ODEs: Local vs. global error; Midpoint, trapezoidal methods Suli & Mayers: 12.3-12.4
Lecture notes
May 5 ODEs: Consistency, stability, convergence Suli & Mayers: 12.7-12.11
Lecture notes
May 7 ODEs: A-stability
Fast Fourier transform
Suli & Mayers: 12.7-12.11
Lecture notes