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Project options

To access papers behind a paywall, go to library.buffalo.edu and search there. You will be prompted to sign in, and then you'll have access to all the journals to which UB subscribes.

#1

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The discovery of solitons: reproduce the results of this classic paper by Zabusky and Kruskal. Make the best pictures you can - you have much better technology than they had!

#2

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Time-dependent Schrodinger equation: reproduce these quantum-mechanical scattering experiments of a particle hitting a barrier. Make the best pictures you can - you have much better technology than they had!

#3

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Spontaneous spatio-temporal patterns in a chemical reaction: generate an interesting movie of a solution of this reaction-diffusion equation.

#4

Something else of particular interest to you - discuss with me ASAP.

Gradesheet

Gradesheet

Exams

Exam #1 Solutions
Exam #2 Solutions
Comprehensive Final Exam: Questions, Tuesday, May 17, 11:45am-2:45pm. Solutions

Homework

Please write your name on the first page of what you submit to Gradescope. Thanks.

Homework #1 due 11:59pm, Sunday, Feb 13 Solutions
Homework #2 (revised) due 11:59pm, Sunday, Feb 20 Solutions
Homework #3 due 11:59pm, Sunday, Feb 27 Solutions
Homework #4 due 11:59pm, Sunday, March 6 Solutions
Homework #5 due 11:59pm, Thursday, March 31 Solutions
Homework #6 due 11:59pm, Sunday, April 10 Solutions
Homework #7 due 11:59pm, Sunday, April 17 Solutions
Homework #8 due 11:59pm, Sunday, May 1 Solutions
Homework #9 due 11:59pm, Sunday May 15 Solutions.

Lecture notes and illustrations

Day 1, Feb 01  
Day 2, Feb 03  
Day 3, Feb 08  
Day 4, Feb 10  
Day 5, Feb 15  
Day 6, Feb 17  
Day 7, Feb 22  
Day 8, Feb 24  
Day 9, Mar 01  
Day 10, Mar 03 Diagonalization, BVPs by shooting, Newton implementation
Day 11, Mar 08 Variational equations, existence theorem, multiple shooting, finite difference method
Day 12, Mar 10 Exam 1
Day 13, Mar 15 Implementation of finite difference method for ODE BVP, error bound
Day 14, Mar 17 HW5, SVD, collocation
Day 15, Mar 29 Galerkin
Day 16, Mar 31 more Galerkin
Day 17, Apr 05 PDEs, classification of quasilinear
Day 18, Apr 07 Heat eqn by finite differences
Day 19, Apr 12 Heat eqn, Crank-Nicolson, wave eqn
Day 20, Apr 14 Wave eqn, FD implementation, instability, spurious dispersion
Day 21, Apr 19 Exam 2
Day -7, Apr 21 Lax, convergence, Poisson/Laplace
Day -6, Apr 26 Solving Poisson: direct full, direct banded, iterative (Jacobi, GS, SOR)
Day -5, Apr 28 discrete Fourier transform
Day -4, May 03 trigonometric interpolation
Day -3, May 05 spectral derivative, application to advection equation
Day -2, May 10 Final exam review
Day -1, May 12 Project presentations

Class policies and logistics

Class policies and logistics