Differences between revisions 60 and 63 (spanning 3 versions)
 ⇤ ← Revision 60 as of 2013-04-24 18:55:57 → Size: 61772 Editor: travis Comment: ← Revision 63 as of 2015-05-24 22:02:02 → ⇥ Size: 62107 Editor: rrubalcaba Comment: Deletions are marked like this. Additions are marked like this. Line 136: Line 136: by Marshall Hampton #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 Line 152: Line 156: min_y = find_minimum_on_interval(func,a,b)    max_y = find_maximum_on_interval(func,a,b) min_y = find_local_minimum(func,a,b)    max_y = find_local_maximum(func,a,b) 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) x = find_local_maximum(func, q*dx + a, q*dx + dx + a) Line 193: Line 200: x = find_minimum_on_interval(func, q*dx + a, q*dx + dx + a) x = find_local_minimum(func, q*dx + a, q*dx + dx + a) Line 204: Line 211: min_y = min(0, find_minimum_on_interval(func,a,b))    max_y = max(0, find_maximum_on_interval(func,a,b)) min_y = min(0, find_local_minimum(func,a,b))    max_y = max(0, find_local_maximum(func,a,b))

# 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 #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. ## 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 ## Quadric Surface Plotter

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 ## Gaussian (Legendre) quadrature

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 ## 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)