Kusse B.R., Westwig E.A. Mathematical Physics: Applied Mathematics for Scientists and Engineers

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676

INDEX

Hemholtz's theorem, 38-40

Hermitian

matrix, 80,435

operator,

436-440

Homogeneous

boundary

conditions,

see

Homogeneous

difbmtd

equation,see

Hyperbolic

coordinates,

Boundary

conditions.

homogeneous

Memntid

equstions,

homogeneous

Impulse,

ideal,

101-102

hdicial

equations,

355

ImKr

product,

see

Dot product

classification

of,

492493

Follrer

transfm

SoIutiOns,

499

Laplace

transform

solutions,

499-500

relation

diffenatipl

Mom.

separable hl

soluriom.

504-506

series

soluti~

501-503

Integral

eq~ations,

491-506

493-498

Integrals

analytic

functions.

144-150

closed, 21,175-189,510-513

line,

7,21,53

multivalued

functions,

10-5 13,534-542

operator

form,

20-21

principal

part,

184-188

volume, 23,54

s&,

22-23,53

Integrating

factor,

345-346

Irreducible

matrix

representation,

see

Representations,

group

Irrotational vector field,

Jordan's

inequality,

285

Kernel, 492

causal,

498

separable,

504-506

translationally

invariant,

498

Kronecker

delta, 8-10,563464,574,581

L'Hopital's rule, 170

Laguerre

polynomials,

488

Laplace

contour,

313,333

Laplace equation, 424475

Cartesian

coordham, 424-433

confonnal

map

solutions, 1921%

cylindrical coordinates. 441,457

spherical coordinates, 458-475

Laplace

transform,

313-335

circuit

analogy,

326-331

a convolution. 320-323

delayed

function, 319

a delta

function,

314-316

de.rivative, 319-320

double-sided, 331-335

growing

sinusoid,

3 17-3 1

integral

equation

solutions, 499-500

inversion

contour,

313,333

orthogonality

condition,

316

product,

323-326

relation

Green"s

function,

377-381

step

function, 316-317

transform

pair,

differentid

equation

SOJU~~O~S,

371-376

Laplacian,

33,34

Laurent

series

complex functions, 159-171

real

functions, 152

Left-hand

rule,

10,88

Left-handed

COordiDBte

system, 10,8692

hge*

polynomials,

464-466

Levi-Civita

symbol,

11-92,639-641

Line distributions,

singular,

119-121

Linearly

dependent

functions, 350,354

Lorentz

transfdon,

582585.592

Low-pass

Mter,

292

Mapping, 138

conformal,

18P-202

Riemann

sheets,

532-534

Schwiuiz-CbristoEel. 1!?6-202

array

notation,

Hemitian, 80,435

multiplication,

3-4

notation,

trace,

16,610

transpose,

unimodular,

633

unitary,

633-634

Matrices,

3-5

Maxwell

equations,

367-368

Metric

tensol;

569470,575,579,581,

Minkowski

space,

591

Mhor

test,

forpseudovectors, 653-654

Moment

inertia

tensor,

Moments

a distribution, 121-125

Monopole, 122-123

Monopole moment, 122

Multiplication tabie,

see

Groups,

multiplication

Multiple expansion, 121-125

Neighborhood, 142

Neumann

boundary

conditions, 429

588-592

table

INDEX

677

Neumann functions

Bessel equation solution,

444-446

spherical, 357

Neumann series, 501-503

Nonhomogeneous boundary conditions,

see

Nonhomogeneous differential equation,

see

Nonisotropic materials, 68

Normal modes

vibration, 624630

Notation, overview,

1-5

Nyquist sampling rate, 294

Boundary conditions, nonhomogeneous

Differential equations, nonhomogeneous

Ohm’s

law, 67-70

Operators

group representations, 606607

Hermitian, 436-440

linear differential, 341

SNrm-Liouvilk, 438439

of a hfferential equation, 341-342

of a group, 598

associated Legendre polynomials, 472

Bessel functions,

448450

exponential Fourier series, 228-229

Fourier series, 221-223

Fourier transform, 253-254

Laplace transform, 3 16

Legendre polynomials, 4655466

Order

Orthogonality relations

Outer product,

see

dyadic product

Parity conservation, 90

Period, 220

Permutation group, 607

Permutations, even and odd,

Phasors, 148

Piecewise smooth function, 232,233

Point mass, 102-103, 114-1 16

Polar vector, 89

Pole, 169

Position vector,

44-45

cylindrical coordinates, 46

spherical coordinates, 49

Positive definite function, 436

Principal part, 184-188

Pseudo-objects, 86-92

pseudoscalar, 90-9

pseudotensor, 91-92

pseudovector, 11,86-90,653-654

Quadrapole, 133

Quadrapole moment, I22

Quadrature, method

of,

358-366

Ratio test,

151

Rearrangement

lemma,

599

Reducible

matrix

representation,

see

Representations, group

Relativity

general, 565-566

special,

564-565.583-592

Removable singularity, 169

Representations, group,

600

completeness, 622-623

decomposition

of,

622

equhlent vs inequivalent, 614

irreducible, 6 13-623

matrix

notation, 6 12-6 14

operator, 606-607

orthogonality,

17-62

reducible, 613-617

Residue

theorem

171-175.510-513

Riemann integration, 125-126,256,327

Riemann

sheets,

513-516.532-534

Right-hand rule, 10,22,87

Right-handed coordinate system, 10,46,48,53,

82,86-92

Rodrigues’s formula

associated Legendre polynomials, 472

Legendre

polynomials,

464

Rotation

matrix,

6, 12-13

Saddle point, 545-547.554555

Samplmg theorem, 290-295

Scalar fields, 18-1 9

Scalar potential,

38.40

Scale factors, 49-5

Schwartz-Christoffel mapping,

see

Mapping,

Separation of variables

Schwartz-Christoffel

first-order differential equations, 342-343

Laplace equation in Cartesian coordinates,

Laplace equation in cylindrical coordinates,

Laplace equation in spherical coordinates,

424-433

441457

458-475

Sequence functions, 104-105,107-108

Sheet distributions, singular, 116-119

Shur’s lemma, 623-630

Sifting

intern,

106,112

Similarity

aansform,

610

Sinc function, 107-108,268

Singularity circle, 156, 163-167

Skewed coordinates, 565-567,585-588

Solenoidal vector field,

Special relativity, 564-565.583-592

Speed

light, invariance,

564,585

678

INDEX

Spherical coordinates, 4849

Spherical harmonics, 474475

Step function,

see

Heaviside

step function

Stirling’s

approximation,

554

Stokes’s

theorem,

37-38

String

problem, 385-391

Stunn-Liouville form, 438-439

Subgroups,

607-608

Subscript notation, 2

Subscriphumation notation, 3,12-15.32-34

Subscript/supedpt

notation, 573-575,581

Summation convention, Einstein,

Superposition principle,

341,

382

Symmetry operations,

599

Taylor series

steepest

descent,

method

of,

542-555

complex functions, 139-140,153-159

real

functions,

152

Tensors, 6746,562-592

contravariant vs. covariant, 579-581

coordinate

transformations,

76-78,84-86,

diagonalization, 78-84

metric,

569-570,575-579,581,58&592

in non-orthogonal coordinates, 562-592

notation, 69-71

rank,

562-564.580

Tokamak, 61

Toroidal

coordinates,

61,62

Tour,

Trace,

see

Matrices, trace

Transfer function, 293

Transformation matrix, 73-75,8546.570-574

Translational

invariance,

378,398,498

Transpose, 5

Unimodular,

633

Unitary

matrix, 633-634

Vector fields,

18-20

Vector potential, 40

Vector/te.nsor notation, 70,7

Vectors

coordinate transfomations, 71-76,90,570-573

identities, 14-15,17

notation,

rotation of, 5-7, 12-13

Vierergruppe,

see

Groups,

Volterra equation

fmt

kind, 492499

second

kind. 492-493

Wave equation, 398-403

Weighting function, 436

Wronskian, 349-354

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