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Grades

Grade sheet

Project options

#1 Spacecraft atmospheric re-entry trajectory by multiple shooting

#2 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!

#3 Time-dependent schroedinger 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!

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

Homework assignments

Homework #1 due 11:59pm, Friday, Feb 12 Solutions
Homework #2 due 11:59pm, Sunday, Feb 21 Solutions
Homework #3 due 11:59pm, Friday, Feb 26 Hints, Solutions
Homework #4 due 11:59pm, Friday, Mar 12 Solutions
Homework #5 due 11:59pm, Friday, Mar 19 Solutions
Homework #6 due 11:59pm, Friday, Mar 26 Solutions
Homework #7 due 11:59pm, Sunday, April 4 Solutions
Homework #8 due 11:59pm, Sunday, April 18 Solutions, animation
Homework #9 (report progress) due 11:59pm, Sunday, April 30  
Homework #10 due 11:59pm, Friday, May 7 Solutions

Exams

Exam #1, March 4 Solutions
Exam #2, April 8 Solutions

Class notes and videos

NEW: Thumbnail galleries of all videos

day date section topics pages video notebook
Day 1 Feb 2 7.1 ODE IVP, E/U pages video  
Day 2 Feb 4 7.1   pages video  
Day 3 Feb 9 7.2 Convergence of Euler's method. Single-step methods. pages video ipynb
Day 4 Feb 11 7.3 Order of accuracy of single-step methods. pre, post   html, ipynb
Day 5 Feb 16 7.3.4.1 Taylor series method. Introduction to sympy. pages video html, ipynb
Day 6 Feb 18 7.3.4.2-3, 7.4 Runge-Kutta methods. Absolute stability. Adaptive error control. pages video html, ipynb
Day 7 Feb 23 7.5-6 Linear multistep formulas. pages video html, ipynb
Day 8 Feb 25 7.5-6 Absolute stability regions. pages videos: redone html, ipynb
Day 9 Mar 2 7.5-7.7 stability,consistency,convergence,implicit,stiffness pre, post video html, ipynb
Day 10 Mar 4 Exam 1 (all of the above)      
Day 11 Mar 9 10.1 BVP for ODE, shooting pages video html, ipynb
Day 12 Mar 11 10.1 Variational equations, finite differences pages video  
Day 13 Mar 16 10.1 SVD, error in finite differences, numpy subtleties,code for FD pages video html1, ipynb1, html2, ipynb2
Day 14 Mar 18 10.1 Neumann BCs. Collocation pages video html, ipynb
Day 15 Mar 23 10.1.3 Galerkin method pages video (lo-fi mic) html, ipynb
Day 16 Mar 25 10.1.3 Galerkin method pages video 1: html, ipynb, 2: html, ipynb
Day 17 Mar 30 Ames PDE, classification of quasilinear PDE pages video  
Day 18 Apr 1   Parabolic (heat) eqn by finite differences pages video ipynb, html
Day 19 Apr 6   BE, CN methods and eigenvalues pages video, errata BE & CN: ipynb, html; eigenvalues: ipynb, html
Day 20 April 8 Exam 2 BVP      
Day -8 April 13   Wave equation, FD stability pages video Eigenvalues: ipynb, html; implementation: plain text
Day -7 April 15   Wave equation, instability, dispersion, elliptic PDE pages class, waves on water heat eqn: wave_instability_demo.py, how dispersion manifests
Day -6 April 20   Direct and iterative solution of Laplace pages class poisson direct small grid: html, ipynb, poisson direct large grid: html, ipynb, poisson iterative: html, ipynb, poisson_jacobi.py, poisson_sor.py
Day -5 April 22   SOR analysis, FD for nonlinear PDE pages class SOR spectrum pics, c_func.c, test_c_func.py
Day -4 April 27   DFT pages class html, ipynb
Day -3 April 29   Spectral differentiation pages class (recording started late) html, ipynb
Day -2 May 4   Nyquist, spectral diff vs. FD, advection equation pages class, hand calc like HW9 1 html, 1 ipynb, advect html, advect ipynb
Day -1 May 6   Exam details, project sharing pages class (no coding)

Class policies and logistics

Class policies and logistics