Numerical Analysis

Course number: MATH-UA 252.001
Semester: Spring 2018
Time & Location: Tues & Thurs, 12:30pm - 1:45pm in CIWW 101
Instructor: Mike O'Neil (oneil@cims.nyu.edu)
Office hours: Tues, 2:30pm - 4:30pm in CIWW 1119
 
Recitation: Fri, 12:30pm - 1:45pm in CIWW 101
Recitation Instructor: Mu-Hua Chien (mhc431@nyu.edu)
Office hours: Wed, 9:50am - 10:50am in CIWW 505
Course description

We will use Piazza for communication and organization. If you are registered for this class you will receive an invitation to join the course on Piazza at the beginning of the semester. Otherwise please email me and I will add you.

Various other documents and course schedule will be posted to this website.

Materials

The textbook for the course is An Introduction to Numerical Analysis, Suli and Mayers, Cambridge University Press, 2003. PDF available via NYU. Supplemental texts and references will be suggested along the way.

Relevant code examples will be posted on gitlab.com/oneilm/na18.

Announcements

Important information for the course will appear on the Piazza page.

Homework
  • Assignment 1: [ .pdf, .tex ], due Feb 8.
  • Assignment 2: [ .pdf, .tex ], due Feb 22.
  • Assignment 3: [ .pdf, .tex ], due Mar 8.
  • Assignment 4: [ .pdf, .tex ], due April 5.
  • Assignment 5: [ .pdf, .tex ], due April 19.
  • Assignment 6: [ .pdf, .tex ], due May 3.
Schedule

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

Date Topics Materials
January 23 Overview, bisection and secant methods Trefethen, 1992
Suli & Mayers, Sec 1.1, 1.5-1.6
Lecture notes
January 25 Newton's method Suli & Mayers, Sec 1.4
Lecture notes
January 30 Fixed points, contractions Suli & Mayers, Sec 1.2
Lecture notes
February 1 Stability and convergence of fixed points Suli & Mayers, Sec 1.2
Lecture notes
February 6 Fixed points, floating point arithmetic Lecture notes
February 8 Gaussian elimination, computational cost Suli & Mayers, Sec 2.1-2.2
Lecture notes
February 13 LU factorization, pivoting Suli & Mayers, Sec 2.3-2.6
Lecture notes
February 15 Vector and matrix norms Suli & Mayers, Sec 2.7
Lecture notes
February 20 Condition numbers Suli & Mayers, Sec 2.7
Lecture notes
February 22 Condition number of a matrix Suli & Mayers, Sec 2.7
Lecture notes
February 27 The SVD Suli & Mayers, Sec 2.7, 2.10
Lecture notes
March 1 Least squares Suli & Mayers, Sec 2.9
Lecture notes
March 6 Review for midterm Review topics
March 8 Midterm
March 13 Spring Break
March 15 Spring Break
March 20 Eigenvalues: Motivation Lecture notes
March 22 Eigenvalues: Power method Suli & Mayers, Sec 5.4
Lecture notes
March 27 Eigenvalues: Inverse power method Suli & Mayers, Sec 5.8
Lecture notes
March 29 Eigenvalues: Jacobi's Method Suli & Mayers, Sec 5.3
Lecture notes
April 3 Polynomial interpolation: Lagrange form Suli & Mayers, Sec 6.1-6.3
Lecture notes
April 5 Polynomial interpolation: Barycentric forms, Runge effect Lecture notes
Berrut and Trefethen, 2004
April 10 Function approximation: Infinity-norm Suli & Mayers, Chap 8
Lecture notes
April 12 Function approximation: 2-norm, orthogonal polynomials Suli & Mayers, Chap 9
Lecture notes
April 17 Numerical Integration: Newton-Cotes Suli & Mayers, Sec 7.1-7.4
Lecture notes
April 19 Numerical Integration: Euler-Maclaurin, Gaussian Quadrature Suli & Mayers, Sec 7.5-7.6, 10.1-10.4
Lecture notes
April 24 ODEs: Initial value problems, finite differences Suli & Mayers, Sec 12.1-12.2
Lecture notes
April 26 ODEs: Richardson extrapolation, Local & global error Suli & Mayers, Sec 7.7, 12.2-12.3
Lecture notes
May 1 ODEs: Implicit schemes, stiff equations Suli & Mayers, Sec 12.3-12.4, 12.8, 12.11
Lecture notes
May 3 ODEs: Stiff equations, stability Suli & Mayers, Sec 12.11
Lecture notes
May 10 Final Exam: 12:00pm-1:50pm, CIWW 101 Review topics