Differences between revisions 108 and 109
 ⇤ ← Revision 108 as of 2020-06-02 14:03:09 → Size: 62939 Editor: kcrisman Comment: ← Revision 109 as of 2020-06-02 14:04:33 → ⇥ Size: 62941 Editor: kcrisman Comment: Deletions are marked like this. Additions are marked like this. Line 527: Line 527: pretty_print(html('$f(x)\;=\;%s$'%latex(f)))    pretty_print(html('$\hat{f}(x;%s)\;=\;%s+\mathcal{O}(x^{%s})$'%(x0,latex(ft),order+1))) pretty_print(html(r'$f(x)\;=\;%s$'%latex(f)))    pretty_print(html(r'$\hat{f}(x;%s)\;=\;%s+\mathcal{O}(x^{%s})$'%(x0,latex(ft),order+1)))

# Sage Interactions - Calculus

by William Stein

## Newton's Method

Note that there is a more complicated Newton's method below.

by William Stein

by William Stein

## A simple tangent line grapher

by Marshall Hampton

## Numerical integrals with the midpoint rule

by Marshall Hampton

## Numerical integrals with various rules

by Nick Alexander (based on the work of Marshall Hampton)

## Some polar parametric curves

by Marshall Hampton. This is not very general, but could be modified to show other families of polar curves.

## Function tool

Enter symbolic functions f, g, and a, a range, then click the appropriate button to compute and plot some combination of f, g, and a along with f and g. This is inspired by the Matlab funtool GUI.

## Newton-Raphson Root Finding

by Neal Holtz

This allows user to display the Newton-Raphson procedure one step at a time. It uses the heuristic that, if any of the values of the controls change, then the procedure should be re-started, else it should be continued.

by Jason Grout

## Taylor Series

by Harald Schilly

## Illustration of the precise definition of a limit

by John Perry

I'll break tradition and put the image first. Apologies if this is Not A Good Thing.

## A graphical illustration of sin(x)/x -> 1 as x-> 0

by Wai Yan Pong

by Marshall Hampton. This is pretty simple, so I encourage people to spruce it up. In particular, it isn't set up to show all possible types of quadrics.

## The midpoint rule for numerically integrating a function of two variables

by Marshall Hampton

by Jason Grout

The output shows the points evaluated using Gaussian quadrature (using a weight of 1, so using Legendre polynomials). The vertical bars are shaded to represent the relative weights of the points (darker = more weight). The error in the trapezoid, Simpson, and quadrature methods is both printed out and compared through a bar graph. The "Real" error is the error returned from scipy on the definite integral.

## Vector Calculus, 2-D Motion

By Rob Beezer

A fast_float() version is available in a worksheet

## Vector Calculus, 3-D Motion

by Rob Beezer

Available as a worksheet

by John Travis

## Directional Derivatives

This interact displays graphically a tangent line to a function, illustrating a directional derivative (the slope of the tangent line).

## 3D graph with points and curves

By Robert Marik

This sagelet is handy when showing local, constrained and absolute maxima and minima in two variables. Available as a worksheet

by Robert Marik

## Taylor approximations in two variables

by John Palmieri

This displays the nth order Taylor approximation, for n from 1 to 10, of the function sin(x2 + y2) cos(y) exp(-(x2+y2)/2).

by John Travis

by John Travis

## Parametric surface example (FIXME in Jupyter)

by Marshall Hampton

## Line Integrals in 3D Vector Field

by John Travis

interact/calculus (last edited 2020-08-11 14:10:09 by kcrisman)