some of these just generate figures for the book, others are for student use
(or at least bob in class)
last upload: 7-oct-2014
this index file is in progress, many more worksheets are available; Exercise
numbers may be slightly off if I add extra problems.
Chapter 0.
Chapter 1.
- linmapvu.mw diagram of how a linear map
distorts images in the plane, Figure 1.1 [see also chapter 4 grid addition]
- gl2R-traceinnerproduct.mw trace
inner products on 2x2 matrices, Exercise 1.2.1, 1.2.2,1.6.1, 1.6.9
- quadratics.mw up to quadratic functions as a
3-d vector space, Exercise 1.2.3
- asymmatrices-crossprod.mw
relation between antisymmetric matrices and double cross product in 3d,
Exercise 1.2.4, 1.7.6, 4.5.3
rotation-matrices.mw duplicates first
worksheet but adds spin discussion of Exercise 1.7.12
- c2algebra.mw complex numbers as a real vector
space, Exercise 1.2.5, 1.7.13
- tensortransform.mw
changing basis in plane {[2,1], [1,1]}, transforming the components of a second rank tensor,
Exercises 1.3.2. 1.4.4
- matrixexponential2by2.mw,
rotations and boosts in the plane, Exercise 1.4.1
- oneforms.mw visualizing 1-forms, covector
addition, Figures 1.4, 1.5
- lincomforback.mw visualizing a change of
coordinates, basis, basis parallelopiped, Figure 1.9, reciprocal basis,
Appendix
- basischgsr.mw
change of basis in the plane {[2,1], [1,2]}, special relativity boost
- basischgde.mw
change of basis in the plane {[2,1], [1,3]}, Exercise 1.5.2, see also
gridsinplane.mw
- basischgde-hw.mw
changing basis in plane {[1,1], [-2,1]},
Grid figures for Examples 1.3,
1.4 and
Exercises 1.3.2, 1.5.1, 1.5.2, and Figure 3.2.
-
eigenvectors_uppertriangular.mw Example 1.5.5, Exercise 1.5.3
- emfieldmatrix.mw, Maxwell 4x4 matrices
for electromagnetic field, Exercise 1.6.5, 2.3.7
- covectorvector.mw relation of covector
to its corresponding vector, Figure 1.21, Exercise 1.6.6.
-
basischg-gramschmidt.mw
Gram-Schmidt Exercise 1.6.11
see also:
gramschmidt.mw
-
basischg-secondderivative.mw
diagonalize quadratic form Exercise 1.6.12.
- covectorcircleellipse.mw
geometric interpretation of index lowering Figures 1.6.?.
- matrixinnerproducts.mw symmetric/antisymmetric
parts, two natural inner products, example 1.6.?
- matrixexponential2by2.mw
exponentiating symmetric or antisymmetric 2x2 matrices Exercise 1.7.1,
4.5.1, 4.5.9
- GLplusT.mw inhomogeneous linear
transformations of the plane: linear transformations plus translations
Exercise 1.7.3
- rotationgroup-eulerangles.mw
exponentiating a rotation generator, Exercises 1.7.9, 1.7.10, 4.5.7
- rotationmatrixeigenvectors.mw
eigenvector of a rotation to determine the axis of the rotation ??
Chapter 2.
Chapter 3.
Chapter 4.
- basischgde-hwchapter4.mw example
of changing basis and grid,
diagram for chapter 1 distortion of figure in plane with new grid
-
eulerangles.mw parametrizing rotations by 3 angles
- 2vectorsinr3.mw visualizing the
parallelogram of two vectors and their projections onto the coordinate
planes in 3d
- 2vectorsinr4.mw exercise on 2d subspaces
in 4d [move to later chapter?]
-
matrixinnerproducts-nullrotations.mw
SL(2,R), Lorentz group in M^3: null rotations, SO(3,R), SO(4,R), SU(2),
Exercise 4.5.2
-
threesphererotations.mw rotations of
the 3-sphere, Exercise 4.5.6
-
su2matrices.mw Paoli matrix algebra, Exercise
4.5.9, 4.5.11
-
sl2rmatrices.mw sl(2,R) and the Lorentz group,
Exercise 4.5.12
-
Chapter 5.
Chapter 6.
Chapter 7.
- polarlaplacian.mw polar coordinate
Laplacian converted from Cartesian expression using the chain rule
Chapter 8.
- tensortemplate.mw
to use for a new Riemannian metric
- tensortemplatelorentz.mw
to use for a new Lorentz metric
- tensor_package_test.mw
many examples
- blackholetensorcalcs.mw
orthonormal frame calculations using Schwarzschild metric, then specialized
to equatorial plane
- rotationgroup-eulerangles.mw many things besides euler
here, spherical coordinate frame calculations,
parallel transport around parallels as rolling of the intrinsic
osculating circle around the parallel loops
- surfaceofrevolution.mw surfaces of
revolution tutorial
- tangentcone.mw tangent to surfaces of
revolution, black hole embedding surface, sphere
- geoplane.mw straight lines as geodesics in the
plane in polar coordinates
- spheregeointegral.mw
integration step by step change of variable needed!
- sphere-pseudospheres.mw 2-sphere
and Lorentz analogs
- torus-demo.mw template for numerical
investigation of geos, game to find closed geos
- hyperboloidonesheet-demo.mw
version of previous worksheet for hyperboloid of one sheet, boomerang game
- ../../torus/torus_geodesics.mw
really big encyclopedia worksheet on torus geos and Newtonian and GR gravity
orbits [24MB!]
- gyroid.mw, gyroidgeos.mw,
gyroidK.mw
- kleinbagel.mw,
kleinbagelgeos.mw
Chapter 9.
Chapter 10.
- extrinsicsaddle.mw extrinsic curvature
for the parabolic hyperboloid graph, intrinsic curvature
- futurepseudosphere.mw extrinsic
curvature of future pseudosphere in 3-d Minkowski spacetime
- extrinsiccurvaturesphere.mw
[and the monkey surface, and coloring by Gaussian curvature]
- [see also chapter 9 listed files: tensor_package_test.mw, tensortemplate.mw,
tensortemplatelorentz.mw, blackholetensorcalcs.mw]
Chapter 11
- threesphere.mw as an example of Stokes
Theorem (Gauss): integrate a radial 1-form over the sphere, equal to the
integral of its differential, which is 4 times the volume 4-form. see the
induced orientation (opposite sign to 3D intuition).
- chapter11.mw parallelogram, sector, cone
measures
Chapter 12
Appendix A
Appendix ?
- tensor_package_test.mw many
examples using Maple tensor package to calculate connection and curvature
- tensortemplate.mw template to use to
calculate new examples, Riemannian, including 2-surface extrinsic curvature
- tensortemplatelorentz.mw template
to use to calculate new examples, Lorentz, including 2-surface extrinsic
curvature
- cavatappi helical tubelike 2-surfaces, Euclidean and Lorentz examples to
link
9-nov-2014