Fall 2019: MATH 252-001 Numerical Analysis
Instructor: Charles Puelz
Location and Time: Tues and Thurs, 11-1215pm, CIWW 321
Office hours: Tues and Wed, 5-6pm, CIWW 905
TA: Tristan Goodwill. Session is held Fri, 11-1215pm, CIWW 201
Graders: Runxi Bai and Shuang Guan
We will be working mainly from the book An Introduction to Numerical Analysis by Suli and Mayers. Also, have a look at Trefethen and Bau’s book: Numerical Linear Algebra.
I’ll post pdfs of my notes, along with some sample Matlab codes. Some of the codes are from Georg Stadler… thanks!
- 9/3: sections 1.1, 1.2. nonlinear equations, fixed point iteration. NA_F19_lecture1.pdf
- 9/5: sections 1.1, 1.2. fixed point iteration and convergence. NA_F19_lecture2.pdf, simple_iteration.m,
- 9/10: section 1.2. local contraction mapping. NA_F19_lecture3.pdf
- 9/12: sections 1.2, 1.3, 1.4. stability and Newton’s method. NA_F19_lecture4.pdf
- 9/17: sections 1.4. Newton’s method, order of convergence. NA_F19_lecture5.pdf, parabola_fixed_point.m
- 9/19: section 1.5. convergence of Newton’s method, secant method. NA_F19_lecture6.pdf, Newton_example.m
- 9/24: section 2.1. Gaussian elimination. NA_F19_lecture7.pdf
- 9/26: section 2.2, 2.3. LU factorization. NA_F19_lecture8.pdf
- 10/1: sections 2.5, 2.6, 2.7. Computational work and norms. NA_F19_lecture9.pdf
- 10/3: section 2.7. norms. NA_F19_lecture10.pdf
- 10/8: section 2.7. matrix norms. NA_F19_lecture11.pdf
- 10/10: sections 2.7 and 2.9. condition numbers and least squares. NA_F19_lecture12.pdf
- 10/17: section 2.9. least squares. NA_F19_lecture13.pdf
- 10/22: section 2.9. least squares and QR factorization. NA_F19_lecture14.pdf
- 10/24: section 5.5. building QR with Householder reflectors. NA_F19_lecture15.pdf
- 10/29: section 5.5. building QR with Householder reflectors. NA_F19_lecture16.pdf
- 10/31: section 5.5. building QR with Householder reflectors. NA_F19_lecture17.pdf
- 11/5: section 5.4 and lecture 27 in Trefethen and Bau. Gerschgorin Theorems and the Power method. NA_F19_lecture18.pdf
- 11/7: section 5.4 and lecture 27 in Trefethen and Bau. Gerschgorin Theorems and the Power method. NA_F19_lecture19.pdf, gerschgorin.m
- 11/12: sections 6.1 and 6.2. Lagrange interpolation. NA_F19_lecture20.pdf
Assignment 1, due Sept. 26, assignment1.pdf, solutions_hw1.pdf.
Assignment 2, due Oct. 15 (please turn in to my mailbox), assignment2.pdf, solutions_hw2.pdf.
Assignment 3, due Oct. 24, assignment3.pdf, solutions_hw3.pdf.
Assignment 4, due Nov. 14, assignment4.pdf.
Spring 2019 midterm, midterm_spring2019.pdf.
The figure on the left is from this Wikipedia page for a Newton fractal. It is a fractal created by applying Newton’s method to a complex valued function.
Here is a link to NYU’s accessibility page: Accessibility.