# Author Archives: Paul

## Sage: Eigenstuff

This help sheet is very useful! Suppose we want to find the eigenvalues and eigenvectors of the matrix We can find the eigenvalues using A list of eigenvalues, with corresponding eigenvectors and multiplicities, is obtained from The code produces two … Continue reading

## Sage: Numerically solving differential equations

Euler’s method by hand We can easily make Sage do the computations in Euler’s method. Here I explain how to build code to analyze the initial value problem First we define variable and also the function that determines the right … Continue reading

## Sage: Parametric curves and vector fields

This is one in a series of posts containing short snippets of Sage code for my students to use: see my page on Sage. Vector fields can be plotted using the vector_field command: Sometimes it is convenient to plot the … Continue reading

## Sage: plotting functions

This is one in a series of posts containing short snippets of Sage code for my students to use: see my page on Sage. Plotting a single function Simple plotting of functions can be done with the plot command: A … Continue reading

## Sage: Basics – computation, functions, calculus 1

This is one in a series of posts containing short snippets of Sage code for my students to use: see my page on Sage. Basic computations can be done by simply entering in the expression you want to evaluate. For … Continue reading

## First steps with Sagemath

I am spending some time this summer playing around with Sagemath. The hope is that I can learn it well enough to use it in my differential equations course in the near future. In this post I list some resources … Continue reading

## New Paper: Boundary Value Problems and Finite Differences

My article Boundary Value Problems and Finite Differences has just been appeared in the January 2016 issue of the College Mathematics Journal. Here is the abstract: The solvability of boundary value problems differs greatly from that of initial value problems … Continue reading

## Using Overleaf for student papers

In my introductory differential equations course, I assign students to write several papers. I require the students to typeset their papers with LaTeX, and to use graphics imported from Mathematica. This semester, the paper assignments are: Equilibrium solutions for the … Continue reading

## Mathematica — Euler’s method for systems, revisited

An earlier post discusses Mathematica code for Euler’s method. Here is some updated code. A couple preliminary notes: I like to clear all variables at the beginning. For systems it is fun to superimpose the plot on top of the … Continue reading

## Mathematica for linear algebra

Here is some mathematica code to be used by my linear algebra students. The post will be periodically updated as the course progresses. Entering matrices Mathematica views matrices as lists of columns. Thus to enter the matrix we type in … Continue reading