the hypercircle in mathematical physics

Front Cover
CUP Archive
 

Contents

GEOMETRY OF FUNCTIONSPACE WITHOUT
7
Addition subtraction and multiplication by a scalar p 19 Logic
23
Straight lines p 24 Linear dependence of two Fvectors p 24 Linear
34
Conditions to be satisfied by the scalar product p 37 Examples
43
Length and distance in Fspace p 44 Example p 44 Unit Fvectors
50
Orthonormality and linear independence p 50 Orthogonal transforma
67
Neighbourhoods p 76 No closed boxes in functionspace p 76 nspheres
84
Linear subspaces and orthogonality p 98 The vertices V V of two non
102
section p 224 Approximation to stress and warping p 225 Torsion
233
General plan p 241 Use of approximate solutions for the weights of
269
General plan p 270 Use of approximate solutions for the weights of
280
The approximation n8 p 283 The approximation n 16 p
286
VARIOUS BOUNDARY VALUE PROBLEMS
292
unknown p 292 Splitting the differential equation p 293 The scalar
299
Pyramid Fvectors for threedimensional Pspace p 301 First mixed
311
viscous flow in a channel p 312 Flow problem
332

Summary of formulae for application of the method of the hypercircle
118
Use of nonlinear subspaces p 121 Bounds on S2 obtained with
124
problem p 125 Electrostatics p 128 Current flow in a conductor
131
Case where the boundary value function ƒ is only piecewise continuous
140
The Greens Fvector p 155 Bounds for the solution p 157 Checks
163
Pyramid functions p 168 Pyramid Fvectors of the first class p
170
Pyramid Fvectors of the second class p 171 Triangulation and poly
176
Summary of plan for the use of pyramid Fvectors p 178 The linear
185
Definition and normalization p 188 Scalar products p 190 Determina
199
Definition and normalization p 200 Scalar products p 202 Determina
209
The torsion problem stated p 214 Torsional rigidity p 216 Transforma
219
Equations of equilibrium and compatibility p 336 Splitting the problem
345
The Greens tensor of elasticity p 347 Bounds at a point in elastic
354
Biharmonic functions and their conjugates p 355 The biharmonic
366
Résumé of available facts p 371 Null Fvectors p 372 Null cones p
372
Orthogonality and orthogonal projection p 373 Orthonormalization
380
Hyperplanes p 380 Pseudohyperspheres p 381 Pseudohypercircles
385
The separation of two straight lines p 389 The separation of two linear
392
The scalar wave equation p 394 Splitting the problem p 395 Eigenvalue
402
Stationary principles for elastic vibrations p 405 Maxwells equations
409
Index page
419
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