Differences between revisions 107 and 110 (spanning 3 versions)
 ⇤ ← Revision 107 as of 2020-06-02 13:56:50 → Size: 62958 Editor: kcrisman Comment: ← Revision 110 as of 2020-06-02 14:07:39 → ⇥ Size: 62947 Editor: kcrisman Comment: Deletions are marked like this. Additions are marked like this. Line 446: Line 446: == Coordinate Transformations (FIXME in Jupyter) == == Coordinate Transformations == 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))) Line 571: Line 571: pretty_print(html('

A graphical illustration of $\lim_{x -> 0} \sin(x)/x =1$

'))    pretty_print(html('Below is the unit circle, so the length of the red line is |sin(x)|'))    pretty_print(html('and the length of the blue line is |tan(x)| where x is the length of the arc.'))    pretty_print(html('From the picture, we see that |sin(x)| $\le$ |x| $\le$ |tan(x)|.'))    pretty_print(html('It follows easily from this that cos(x) $\le$ sin(x)/x $\le$ 1 when x is near 0.'))    pretty_print(html('As $\lim_{x ->0} \cos(x) =1$, we conclude that $\lim_{x -> 0} \sin(x)/x =1$.')) pretty_print(html(r'

A graphical illustration of $\lim_{x -> 0} \sin(x)/x =1$

'))    pretty_print(html(r'Below is the unit circle, so the length of the red line is |sin(x)|'))    pretty_print(html(r'and the length of the blue line is |tan(x)| where x is the length of the arc.'))    pretty_print(html(r'From the picture, we see that |sin(x)| $\le$ |x| $\le$ |tan(x)|.'))    pretty_print(html(r'It follows easily from this that cos(x) $\le$ sin(x)/x $\le$ 1 when x is near 0.'))    pretty_print(html(r'As $\lim_{x ->0} \cos(x) =1$, we conclude that $\lim_{x -> 0} \sin(x)/x =1$.'))

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)