# Category Archives: Uncategorized

## Sage code for trigonometric forcing

## 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

## 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

## Quick tips for using Manipulate in Mathematica

We’ve been using the Manipulate function in class a lot. Here are a couple of quick tips and examples. The basic idea is to take something you Mathematica to do and add a parameter. For example, suppose you want to … Continue reading

## Math 235, Spring 2015: Comments on Exam 1, Problem 1

In this problem, students were first asked to verify that was a solution to the differential equation and to plot that function. Remember when verifying that a function is a solution to a differential equation that one cannot assume that … Continue reading

## Statistics and series

Here is a nice application of series which appeared in my Calculus II course. In class we defined a probability density function (pdf) to be a function such that for all , and . We then discussed how to describe … Continue reading