Mathematical Tools for Physics

Index 476

reality, 296, 315
reciprocal basis, 373 , 377, 381, 383, 393
reciprocal vector, 387
rectifier, 138
regular point, 91
regular singular point, 91
relation, 355
relativity, 57, 388
residue, 427 , 461
residue theorem, 427
resistor, 241, 245
resonance, 129
Reynolds’ transport theorem, 411, 415
Riemann Integral, 12, 421
Riemann Surface, 435, 436 , 437, 438, 447
Riemann-Stieljes integral, 15, 204
rigid body, 169, 176, 189, 354
roots of unity, 72
rotation, 168, 172, 175, 184, 254, 261, 367
components 176
composition 183
roundoff error, 335, 349
Runge-Kutta, 329, 352
Runge-Kutta-Fehlberg, 331
.
saddle point, 227, 228, 244
scalar product, 121, 130, 152 –158, 161, 162,
292, 302, 356, 372, 384
scattering, 234–239
Schwarzenegger, 218
secant method, 320
semiperimeter, 26
separated solution, 292
separation of variables, 98 , 285 –307

series, 30–46

series of series, 37

series:

absolute convergence, 37

common 31

comparison test 34, 36

convergence 34, 56

differential equation 91, 115

double 306, 330

examples 30

exponential 204

faster convergence 59

Frobenius 92 –95, 422

geometric 204

hyperbolic sine 293

integral test 35

Laurent 422

power 32, 257, 315

ratio test 34

rearrange 37

secant 38, 56

telescoping 59, 138

two variables 38, 58

sheet, 436, 439

dσ/dΩ, 235–239, 246

similarity transformation, 193

simple closed curve, 427

simply-connected, 407, 408

Simpson’s rule, 325

simultaneous equations, 100, 104

sine integral, 135, 140

sine transform, 462

singular point, 91

singularity, 423, 427, 441

sketching, 21