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gibson:teaching:fall-2016:math753

# MATH 753/853 Numerical Methods

Lecture: MWF 12:40-2:00pm Kingsbury N129
Instructor: John Gibson. Office hours t.b.d.
Prerequisite: Math 426; Math 445 or CS 410 or IAM 550.

## Notices

• 09/15/2016: HW1 due date has been revised to Friday 9/16 at midnight. I have also added some clarifications and fixes to HW1.
• 08/30/2016: Please bring your laptop to class on Wednesday 8/30 if you have one. Otherwise please bring a USB drive.

## Julia resources

Numerics for this course will be done in the Julia programming language. Here are links to a few key resources.

## Course outline and schedule

Introduction, Julia
date topic exercises/homework
M 08/29 Why numerics? Why Julia?
W 08/31 Installing Julia, Starting a Julia notebook ex1
F 09/02 Working with Julia notebooks ex2
Floating-point numbers & arithmetic
date topic exercises/homework
M 09/05 (Labor Day, no class)
W 09/07 Floating point numbers ex3
F 09/09 Floating point arithmetic hw1 due Fri 9/16 Solutions
Nonlinear equations, 1d
date topic exercises/homework
M 09/12 Bisection hw2 due Sun 9/25. Hints, solutions
W 09/14 Newton's method
F 09/16
M 09/19 convergence of Newton and bisection
Numerical linear algebra
date topic homework
W 09/21 Gaussian elimination
F 09/23 LU decomp, without pivoting
M 09/26
W 09/28 Solving Ax=b with LU, forward/backward substitution HW3 due Sun 10/9. Solutions.
F 09/30 LU with pivoting
M 10/03
W 10/05 Norms and orthogonality
F 10/07 QR decomposition, Gram-Schmidt algorithm
M 10/10 QR and the least-squares problem
W 10/12
F 10/14 exam 1 Topics
Interpolation and modeling
date topic homework
M 10/17 Horner's method
W 10/19 Lagrange interpolating polynomial
F 10/21 Newton's divided differences HW4 due Sun 10/30 solutions
M 10/24 Chebyshev interpolating polynomial
W 10/26 Least-squares polynomial models
F 10/28
M 10/31 Least-squares nonlinear models HW5 due Sun 11/13 solutions
Numerical differentiation and integration
date topic homework
W 11/02 Finite differencing
F 11/04
M 11/07 Finite differences application: the heat equation
W 11/09
F 11/11 (Veteran's Day, UNH closed)
M 11/14 Quadrature HW6 quadrature, ungraded
W 11/16
F 11/18 exam 2
Ordinary differential equations
date topic homework
M 11/21
T 11/22
W 11/23 (Thanksgiving, UNH closed)
F 11/25 (Thanksgiving, UNH closed)
M 11/28
W 11/30
F 12/02 Forward Euler, Midpoint methods HW7 due Sun 12/11 midnight
M 12/05
W 12/07
F 12/09
W 12/14 Final exam, 10:30am-12:30pm Kingsbury N343 topics
gibson/teaching/fall-2016/math753.txt · Last modified: 2016/12/12 18:12 by gibson