|
Size: 62925
Comment: add assumption to fix TypeError and remove FIXME flag in Vector Calculus, 3-D Motion
|
Size: 63005
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 27: | Line 27: |
| raise ValueError, "f must have a sign change in the interval (%s,%s)"%(a,b) | raise ValueError("f must have a sign change in the interval (%s,%s)"%(a,b)) |
| Line 33: | Line 33: |
| print "eps = %s"%float(eps) | print("eps = %s" % float(eps)) |
| Line 37: | Line 37: |
| print "f must have opposite sign at the endpoints of the interval" | print("f must have opposite sign at the endpoints of the interval") |
| Line 40: | Line 40: |
| print "root =", c print "f(c) = %r"%f(x=c) print "iterations =", len(intervals) |
print("root =", c) print("f(c) = %r" % f(x=c)) print("iterations =", len(intervals)) |
| Line 69: | Line 69: |
| for i in xrange(maxiter): | for i in range(maxiter): |
| Line 81: | Line 81: |
| print "eps = %s"%float(eps) | print("eps = %s"%float(eps)) |
| Line 83: | Line 83: |
| print "root =", z print "f(c) = %r"%f(x=z) |
print("root = {}".format(z)) print("f(c) = %r" % f(x=z)) |
| Line 86: | Line 86: |
| print "iterations =", n | print("iterations = {}".format(n)) |
| Line 127: | Line 127: |
| print 'Tangent line is y = ' + tanf._repr_() | print('Tangent line is y = ' + tanf._repr_()) |
| Line 156: | Line 156: |
| print "\n\nSage numerical answer: " + str(integral_numerical(func,a,b,max_points = 200)[0]) print "Midpoint estimated answer: " + str(RDF(dx*sum([midys[q] for q in range(n)]))) |
print("\n\nSage numerical answer: " + str(integral_numerical(func,a,b,max_points = 200)[0])) print("Midpoint estimated answer: " + str(RDF(dx*sum([midys[q] for q in range(n)])))) |
| Line 257: | Line 257: |
| except TypeError, msg: print msg[-200:] print "Unable to make sense of f,g, or a as symbolic expressions." |
except TypeError as msg: print(msg[-200:]) print("Unable to make sense of f,g, or a as symbolic expressions.") |
| Line 597: | Line 597: |
| def quads(q = selector(quadrics.keys()), a = slider(0,5,1/2,default = 1)): | def quads(q = selector(list(quadrics)), a = slider(0,5,1/2,default = 1)): |
| Line 718: | Line 718: |
| print "Trapezoid: %s, Simpson: %s, \nMethod: %s, Real: %s"%tuple(error_data) | print("Trapezoid: %s, Simpson: %s, \nMethod: %s, Real: %s" % tuple(error_data)) |
| Line 825: | Line 825: |
| print "Position vector defined as r(t)=", position print "Speed is ", N(speed(t=t0)) print "Curvature is ", N(curvature) |
print("Position vector defined as r(t)={}".format(position)) print("Speed is {}".format(N(speed(t=t0)))) print("Curvature is {}".format(N(curvature))) |
| Line 908: | Line 908: |
| pos_tzero = position(t0) | pos_tzero = position(t=t0) |
| Line 951: | Line 951: |
| print "Position vector: r(t)=", position(t) print "Speed is ", N(speed(t=t0)) print "Curvature is ", N(curvature) ## print "Torsion is ", N(torsion) print "Right-click on graphic to zoom to 400%" print "Drag graphic to rotate" |
print("Position vector: r(t)=", position) print("Speed is ", N(speed(t=t0))) print("Curvature is ", N(curvature)) ## print("Torsion is ", N(torsion)) print() print("Right-click on graphic to zoom to 400%") print("Drag graphic to rotate") |
| Line 1252: | Line 1252: |
| order=(1..10)): | order=[1..10]): |
Sage Interactions - Calculus
goto interact main page
Contents
-
Sage Interactions - Calculus
- Root Finding Using Bisection
- Newton's Method
- A contour map and 3d plot of two inverse distance functions
- A simple tangent line grapher
- Numerical integrals with the midpoint rule
- Numerical integrals with various rules
- Some polar parametric curves
- Function tool
- Newton-Raphson Root Finding
- Coordinate Transformations (FIXME in Jupyter)
- Taylor Series
- Illustration of the precise definition of a limit
- A graphical illustration of sin(x)/x -> 1 as x-> 0
- Quadric Surface Plotter
- The midpoint rule for numerically integrating a function of two variables
- Gaussian (Legendre) quadrature
- Vector Calculus, 2-D Motion
- Vector Calculus, 3-D Motion
- Multivariate Limits by Definition
- Directional Derivatives
- 3D graph with points and curves
- Approximating function in two variables by differential
- Taylor approximations in two variables
- Volumes over non-rectangular domains
- Lateral Surface Area (FIXME in Jupyter)
- Parametric surface example (FIXME in Jupyter)
- Line Integrals in 3D Vector Field
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 (FIXME in Jupyter)
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
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
http://sagenb.mc.edu/home/pub/97/
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 (FIXME in Jupyter)
by John Travis
http://sagenb.mc.edu/home/pub/89/
Parametric surface example (FIXME in Jupyter)
by Marshall Hampton
Line Integrals in 3D Vector Field
by John Travis
