Pinned Repositories
a8-building-applications
annotation-tools
Tools for type annotations in Java
azure-cosmosdb-js-server
The JavaScript SDK for server-side programming in Azure Cosmos DB
checker-framework
Pluggable type-checking for Java
Crimes-in-the-City-of-Boston
github-practice
A repo for practicing the basics of using git and GitHub
intellij-community
IntelliJ IDEA Community Edition
intro_to_r
Guest lecture for Mike Freeman's Intro to R class at the University of Washington Information School, March 4th 2016
L2_R_Skills
Stability-Spectrum-for-PDES
An important property for solutions of differential equations is stability. Stability is important in physical applications because it determines whether or not a solution may be seen in the real world. If a solution is unstable, small perturbations of the system will fore the system away from the solution. If a solution is stable, the system will return to that solution after small perturbations. To determine whether or not a solution is stable, one linearizes the differential equation and examines the spectrum of the resulting linear operator. The geometry of the spectrum reveals stability properties, but is typically very difficult to find analytically. The spectral problem may be truncated to a matrix eigenvalue problem. Once the matrix is formed, we use computers to find the eigenvalues and plot them to understand the geometry of the spectrum. In this project, students will be given a partial differential equation (PDE) and class of traveling wave solution to that equation. This class of solutions typically has various parameters that may take a continuum of values in some fixed region of space. From a given solution, students will use the above described method to compute the spectrum using a computer. If there is time, the solution parameter space can be examined to determine regions where the spectrum has qualitatively different shapes. If there is still time, students may look at transition regions by altering their program to allow for dynamic solution parameter changes. In doing this, interesting movies and an applet can be created.
kushg1's Repositories
kushg1/Stability-Spectrum-for-PDES
An important property for solutions of differential equations is stability. Stability is important in physical applications because it determines whether or not a solution may be seen in the real world. If a solution is unstable, small perturbations of the system will fore the system away from the solution. If a solution is stable, the system will return to that solution after small perturbations. To determine whether or not a solution is stable, one linearizes the differential equation and examines the spectrum of the resulting linear operator. The geometry of the spectrum reveals stability properties, but is typically very difficult to find analytically. The spectral problem may be truncated to a matrix eigenvalue problem. Once the matrix is formed, we use computers to find the eigenvalues and plot them to understand the geometry of the spectrum. In this project, students will be given a partial differential equation (PDE) and class of traveling wave solution to that equation. This class of solutions typically has various parameters that may take a continuum of values in some fixed region of space. From a given solution, students will use the above described method to compute the spectrum using a computer. If there is time, the solution parameter space can be examined to determine regions where the spectrum has qualitatively different shapes. If there is still time, students may look at transition regions by altering their program to allow for dynamic solution parameter changes. In doing this, interesting movies and an applet can be created.
kushg1/a8-building-applications
kushg1/annotation-tools
Tools for type annotations in Java
kushg1/azure-cosmosdb-js-server
The JavaScript SDK for server-side programming in Azure Cosmos DB
kushg1/checker-framework
Pluggable type-checking for Java
kushg1/Crimes-in-the-City-of-Boston
kushg1/github-practice
A repo for practicing the basics of using git and GitHub
kushg1/intellij-community
IntelliJ IDEA Community Edition
kushg1/intro_to_r
Guest lecture for Mike Freeman's Intro to R class at the University of Washington Information School, March 4th 2016
kushg1/L2_R_Skills
kushg1/lecture-10-exercises
Exercises for lecture 10: RMarkdown
kushg1/lecture-11-exercises
Exercises for lecture 11: making maps with Plotly
kushg1/lecture-12-exercises
Lecture 12 exercises: Plotly practice
kushg1/lecture-14-exercises
Exercises for lecture 14: Introduction to shiny
kushg1/lecture-15-exercises
Interactive Shiny Applications
kushg1/lecture-16-exercises
Simulations in R
kushg1/lecture-6-exercises
Exercises for lecture 6: lists and dataframes
kushg1/lecture-8-exercises
Exercises for lecture 8: grouped operations and joins with dplyr
kushg1/lecture-9-exercises
Exercises for lecture 9: APIs
kushg1/math126
Math 126 course materials
kushg1/SomeCoolTeamName