Differences between revisions 53 and 54
 ⇤ ← Revision 53 as of 2012-04-23 00:28:01 → Size: 57675 Editor: rbeezer Comment: Five derivatives now explicity with respect to t ← Revision 54 as of 2012-04-26 15:50:40 → ⇥ Size: 57403 Editor: jason Comment: Deletions are marked like this. Additions are marked like this. Line 460: Line 460: def trans(x=input_box(u^2-v^2, label="x=",type=SR), \         y=input_box(u*v+cos(u*v), label="y=",type=SR), \         t_val=slider(0,10,0.2,6, label="Length of curves"), \ def trans(x=input_box(u^2-v^2, label="x",type=SR),         y=input_box(u*v+cos(u*v), label="y",type=SR), Line 465: Line 464: u_range=input_box(range(-5,5,1), label="u lines"),         v_range=input_box(range(-5,5,1), label="v lines")): t_val=slider(0,10,0.2,6, label="Length"), u_range=input_box('[-5..5]', label="u lines"),         v_range=input_box('[-5..5]', label="v lines")): Line 468: Line 468: Line 472: Line 473: g1=sum([parametric_plot((i,v), (v,t_min,t_max), rgbcolor=(1,0,0)) for i in u_range])     g2=sum([parametric_plot((u,i), (u,t_min,t_max), rgbcolor=(0,0,1)) for i in v_range])     vline_straight=parametric_plot((u,v_val), (u,t_min,t_max), rgbcolor=(0,0,1), linestyle='-',thickness=thickness)     uline_straight=parametric_plot((u_val, v), (v,t_min,t_max),rgbcolor=(1,0,0), linestyle='-',thickness=thickness) uvplot=sum([parametric_plot((i,v), (v,t_min,t_max), color='red',axes_labels=['u','v'],figsize=[5,5]) for i in u_range])     uvplot+=sum([parametric_plot((u,i), (u,t_min,t_max), color='blue',axes_labels=['u','v']) for i in v_range])     uvplot+=parametric_plot((u,v_val), (u,t_min,t_max), rgbcolor=(0,0,1), linestyle='-',thickness=thickness)     uvplot+=parametric_plot((u_val, v), (v,t_min,t_max),rgbcolor=(1,0,0), linestyle='-',thickness=thickness) Line 477: Line 478: (g1+g2+vline_straight+uline_straight).save("uv_coord.png",aspect_ratio=1, figsize=[5,5], axes_labels=['$u$','$v$']) Line 482: Line 482: g3=sum([parametric_plot((partial(xuv,i),partial(yuv,i)), (v,t_min,t_max), rgbcolor=(1,0,0)) for i in u_range])     g4=sum([parametric_plot((partial(xvu,i),partial(yvu,i)), (u,t_min,t_max), rgbcolor=(0,0,1)) for i in v_range])     uline=parametric_plot((partial(xuv,u_val),partial(yuv,u_val)),(v,t_min,t_max),rgbcolor=(1,0,0), linestyle='-',thickness=thickness)     vline=parametric_plot((partial(xvu,v_val),partial(yvu,v_val)), (u,t_min,t_max), rgbcolor=(0,0,1), linestyle='-',thickness=thickness)     (g3+g4+vline+uline).save("xy_coord.png", aspect_ratio=1, figsize=[5,5], axes_labels=['$x$','$y$'])     print jsmath("x=%s, \: y=%s"%(latex(x), latex(y)))     print "
" xyplot=sum([parametric_plot((partial(xuv,i),partial(yuv,i)), (v,t_min,t_max), color='red', axes_labels=['x','y'],figsize=[5,5]) for i in u_range])     xyplot+=sum([parametric_plot((partial(xvu,i),partial(yvu,i)), (u,t_min,t_max), color='blue') for i in v_range])     xyplot+=parametric_plot((partial(xuv,u_val),partial(yuv,u_val)),(v,t_min,t_max),color='red', linestyle='-',thickness=thickness)     xyplot+=parametric_plot((partial(xvu,v_val),partial(yvu,v_val)), (u,t_min,t_max), color='blue', linestyle='-',thickness=thickness)     html("$$x=%s, \: y=%s$$"%(latex(x), latex(y)))     html.table([[uvplot,xyplot]])

# Sage Interactions - Calculus

## Root Finding Using Bisection

by William Stein ## Newton's Method

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

by William Stein ## A contour map and 3d plot of two inverse distance functions

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. ## Coordinate Transformations

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 ## Multivariate Limits by Definition

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 ## Approximating function in two variables by differential

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). ## Volumes over non-rectangular domains

by John Travis ## Lateral Surface Area

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)