the hypercircle in mathematical physicsCUP 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 |
419 | |
Common terms and phrases
approximation B₁ B₂ biharmonic equation boundary conditions boundary value problem calculation centre circle conjugate harmonic function Consider constant coordinates cross-section defined Dirichlet problem domain elastic Euclidean 3-space F-point F-space finite formulae function-space geometry given gives gradient harmonic function hence hexagonal pyramid F-vectors hollow square hypercircle method hypercircle of class hyperplane of class hypersphere I₁ inequality inside integral intersection L₁ linear n-space linearly independent lower bound multiply connected n-sphere neighbours Neumann problem normal obtained octant orthogonal linear subspaces orthogonal projection orthonormal P-vector field parameters plane polygon polyhedral position-vector positive-definite positive-definite metric pyramid functions radius reduced weights regular hexagon S₁ satisfy scalar product second class shown in Fig solution square pyramid F-vectors straight line stress strip F-vectors summation symmetry torsion problem torsional rigidity triangle upper bound vanishes vectors lying vertex vertices zero