# Author Archives: Paul

## Visualizing coordinate transformations

Here is some sage code to help you visualize coordinate transformations. I give three examples: Polar coordinates: Hyperbolic coordinates: One more fun example:

## Sage code for trigonometric forcing

## The teachable student

A recent picture ofÂ Yeovil manager Darren Way shows him with a poster listing the characteristics of “The Coachable Player.” The Coachable Player Humble Respectful Loves the game Stays in control Takes responsibility Thinks long term Keen to learn Excited by … Continue reading

## 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