Math 405/607E 2016 W1: Numerical Methods for Differential Equations

Instructor: Colin Macdonald
Email:: cbm[at]math[dot]ubc[dot]ca
Office: LSK 303c
Lectures:: Tu/Th 14:00–15:20 at MAT104
Office Hours: M 1pm–2pm, W 12:15pm–1:15pm, Th 11am–noon (subject to change, also by appointment)
Midterm:: Thurs 20th October, in class

Week 1

Motivation why we want numerical methods for differential equations: Grady Wright's mantle convection video

Week 2

Motivation why we should care about differential equations: Fluids are amazing, and fluids are modelled with differential equations.

Demo codes: demo_02_bisection.m, demo_02_newton.m.

HW1 (revised!), HW1 Solutions.

Week 3

Lecture notes: 03_interp.pdf, 04_quadrature.pdf.

Week 4

Lecture notes: 04b_composite_quad.pdf, 05_finite_diff.pdf.

Demo codes from class: I have been posting these on gitlab.math.ubc.ca.

HW2, HW2 Solutions, hw2_bary.m.

Week 5

Lecture notes: 06a_intro_ivp.pdf.

Week 6

Lecture notes: 06b_ivp.pdf.

HW3 Draft (in hope it might be helpful before the midterm).

Week 7

The midterm will cover everything up to (but not including) stiffness.

A previous midterm with solutions.

~~hw3.pdf~~, Revised: hw3-rev1.pdf, HW3 Solutions.

Week 8

Midterm solutions.

Notes: 07a_pdes_mol.pdf, 07b_pdes_adv_2d.pdf.

Week 9

Notes: 08_floating_point.pdf, 09a_linalg_GE.pdf, 09b_LUdecomp.pdf.

~~hw4.pdf~~, Revised: hw4-rev1.pdf, hw4_unsharp.zip, hw4_perona_malik.zip.

HW4 Solutions.

Week 10

Homework 4 updated, see above!

Notes: 09c_hh_givens_qrfac.pdf.

Week 11

hw5.pdf (includes minor updates).

Notes: 10_eigenvalues.pdf. 10b_svd.pdf.

Week 12

Also discussed Topic 11, iterative methods for numerical linear algebra (no notes available).

Notes: 12_spectral.pdf.

Week 13

Notes: 13_fem.pdf.

Also briefly discussed Discontinuous Galerkin, Finite Volume and RBF methods.

Exam: exam_review.txt, 2015 exam (Soln).

HW5 Solutions.

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