Differences between revisions 113 and 115 (spanning 2 versions)
 ⇤ ← Revision 113 as of 2020-06-02 14:49:18 → Size: 62984 Editor: kcrisman Comment: ← Revision 115 as of 2020-06-02 15:03:42 → ⇥ Size: 63115 Editor: kcrisman Comment: Deletions are marked like this. Additions are marked like this. Line 1044: Line 1044: Line 1070: Line 1069: pretty_print(html('Enter $(x_0 ,y_0 )$ above and see what happens as the number of contour levels $\\rightarrow \infty$.')) pretty_print(html(r'Enter $(x_0 ,y_0 )$ above and see what happens as the number of contour levels $\rightarrow \infty$.')) Line 1083: Line 1082: pretty_print(table([[surface],['hi']])) show(surface) Line 1384: Line 1383: == Lateral Surface Area (FIXME in Jupyter) == == Lateral Surface Area == Line 1389: Line 1388: Note that this works in Sage cell, but causes a zip file error in Jupyter Line 1456: Line 1457: == Parametric surface example (FIXME in Jupyter) == == Parametric surface example == Line 1458: Line 1459: Note that this works in Sage cell, but causes a zip file error in Jupyter. Line 1506: Line 1509: u(t) = u    v(t) = v    w(t) = w

# 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

## Lateral Surface Area

by John Travis

Note that this works in Sage cell, but causes a zip file error in Jupyter

## Parametric surface example

by Marshall Hampton

Note that this works in Sage cell, but causes a zip file error in Jupyter.

## Line Integrals in 3D Vector Field

by John Travis

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