Differences between revisions 59 and 61 (spanning 2 versions)
 ⇤ ← Revision 59 as of 2013-04-24 18:48:29 → Size: 61041 Editor: travis Comment: ← Revision 61 as of 2015-05-24 22:00:09 → ⇥ Size: 62130 Editor: rrubalcaba Comment: find_maximum_on_interval and find_minimum_on_interval are deprecated http://trac.sagemath.org/2607 for details Deletions are marked like this. Additions are marked like this. Line 137: Line 137: #find_maximum_on_interval and find_minimum_on_interval are deprecated     #use find_local_maximum find_local_minimum instead    #see http://trac.sagemath.org/2607 for details -RRubalcaba Line 152: Line 156: min_y = find_minimum_on_interval(func,a,b)[0]    max_y = find_maximum_on_interval(func,a,b)[0] min_y = find_local_minimum(func,a,b)[0]    max_y = find_local_maximum(func,a,b)[0] Line 167: Line 171: #find_maximum_on_interval and find_minimum_on_interval are deprecated     #use find_local_maximum find_local_minimum instead    #see http://trac.sagemath.org/2607 for details -RRubalcaba Line 190: Line 197: x = find_maximum_on_interval(func, q*dx + a, q*dx + dx + a)[1] x = find_local_maximum(func, q*dx + a, q*dx + dx + a)[1] Line 193: Line 200: x = find_minimum_on_interval(func, q*dx + a, q*dx + dx + a)[1] x = find_local_minimum(func, q*dx + a, q*dx + dx + a)[1] Line 204: Line 211: min_y = min(0, find_minimum_on_interval(func,a,b)[0])    max_y = max(0, find_maximum_on_interval(func,a,b)[0]) min_y = min(0, find_local_minimum(func,a,b)[0])    max_y = max(0, find_local_maximum(func,a,b)[0]) Line 1047: Line 1054: Line 1063: Line 1071: Rmax=2@interactdef _(f=input_box(default=(x^3-y^3)/(x^2+y^2)),      N=slider(5,100,1,10,label='Number of Contours'),      x0=(0),y0=(0)):    print html('Enter $(x_0 ,y_0 )$ above and see what happens as the number of contour levels increases.')    print html('A surface will have a limit in the center of this graph provided there is not a sudden change in color there.') var('x,y,z,u')@interact(layout=dict(top=[['f'],['x0'],['y0']], bottom=[['N'],['R']]))def _(f=input_box(default=(x*y^2)/(x^2+y^4),width=30,label='$f(x)$'),        N=slider(5,100,1,10,label='Number of Contours'),        R=slider(0.1,1,0.01,1,label='Radius of circular neighborhood'),        x0=input_box(0,width=10,label='$x_0$'),        y0=input_box(0,width=10,label='$y_0$')):    html('Enter $(x_0 ,y_0 )$ above and see what happens as the number of contour levels $\\rightarrow \infty$.')    html('A surface will have a limit in the center of this graph provided there is not a sudden change in color there.') # Need to make certain the min and max contour lines are not huge due to asymptotes. If so, clip and start contours at some reasonable# values so that there are a nice collection of contours to show around the desired point. Line 1073: Line 1087: surface += parametric_plot([R*cos(u),R*sin(u)],[0,2*pi],color='black')# Nice to use if f=x*y^2/(x^2 + y^4) # var('u')# surface += parametric_plot([u^2,u],[u,-1,1],color='black') Line 1074: Line 1092: show(limit_point+surface)}}} # show(limit_point+surface)    html.table([[surface],['hi']])}}}

# 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

• #find_maximum_on_interval and find_minimum_on_interval are deprecated #use find_local_maximum find_local_minimum instead

#see http://trac.sagemath.org/2607 for details -RRubalcaba

## 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 FIXME

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

by Marshall Hampton

## Line Integrals in 3D Vector Field

by John Travis

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