Mathematical Methods for Physicists: A concise introduction - Site Map

More documents

Recommendations

Info

$The Comprehensive LaTeX Symbol List$

SERIES REPRESENTATIONS OF ANALYTIC FUNCTIONS ">0 there exists an integer N depending in general on " and on the particular value of z under consideration such that and we write jS n …z†S…z† j
FUNCTIONS OF A COMPLEX VARIABLE Ratio test Given the series f 1 …z†‡f 2 …z†‡f 3 …z†‡‡f n …z†‡, the series converges absolutely if f 0 < jr…z† j ˆ lim n‡1 …z† n!1 f n …z† < 1 …6:30† and diverges if jr…z†j > 1. When jr…z†j ˆ 1, the ratio test provides no information about the convergence or divergence of the series. Example 6.19 Consider the complex series X S n ˆ X1 n nˆ0 … 2 n ‡ ie n † ˆ X1 nˆ0 2 n ‡ i X1 nˆ0 e n : The ratio tests on the real and imaginary parts show that both converge: 2 …n‡1† lim n!1 2 n ˆ 1 , which is positive and less than 1; 2 e …n‡1† lim n!1 e n ˆ 1 , which is also positive and less than 1. e One can prove that the full series converges to X 1 nˆ1 S n ˆ 1 1 1=2 ‡ i 1 1 e 1: Uniform convergence and the Weierstrass M-test To establish conditions, under which series can legitimately be integrated or di€erentiated term by term, the concept of uniform convergence is required: A series of functions is said to converge uniformly to the function S(z) in a region R, either open or closed, if corresponding to an arbitrary " N: One of the tests for uniform convergence is the Weierstrass M-test (a sucient test). 268
Page 1 and 2:
Mathematical Methods for Physicists
Page 3 and 4:
PUBLISHED BY CAMBRIDGE UNIVERSITY P
Page 5 and 6:
Contents Preface xv 1 Vector and te
Page 7 and 8:
CONTENTS 3 Matrix algebra 100 De®n
Page 9 and 10:
CONTENTS The adjoint operators 219
Page 11 and 12:
CONTENTS Sturm±Liouville systems 3
Page 13 and 14:
CONTENTS The Runge±Kutta method 47
Page 15 and 16:
Preface This book evolved from a se
Page 17 and 18:
VECTOR AND TENSOR ANALYSIS Figure 1
Page 19 and 20:
VECTOR AND TENSOR ANALYSIS Vector a
Page 21 and 22:
VECTOR AND TENSOR ANALYSIS We can g
Page 23 and 24:
VECTOR AND TENSOR ANALYSIS Using th
Page 25 and 26:
VECTOR AND TENSOR ANALYSIS The trip
Page 27 and 28:
VECTOR AND TENSOR ANALYSIS will be
Page 29 and 30:
VECTOR AND TENSOR ANALYSIS orthonor
Page 31 and 32:
VECTOR AND TENSOR ANALYSIS A(u) is
Page 33 and 34:
Page 35 and 36:
VECTOR AND TENSOR ANALYSIS a circle
Page 37 and 38:
VECTOR AND TENSOR ANALYSIS The vect
Page 39 and 40:
VECTOR AND TENSOR ANALYSIS operate
Page 41 and 42:
VECTOR AND TENSOR ANALYSIS We ®rst
Page 43 and 44:
VECTOR AND TENSOR ANALYSIS system w
Page 45 and 46:
VECTOR AND TENSOR ANALYSIS we have
Page 47 and 48:
VECTOR AND TENSOR ANALYSIS with sim
Page 49 and 50:
VECTOR AND TENSOR ANALYSIS where A
Page 51 and 52:
VECTOR AND TENSOR ANALYSIS Z P2 P 1
Page 53 and 54:
VECTOR AND TENSOR ANALYSIS name is
Page 55 and 56:
VECTOR AND TENSOR ANALYSIS while th
Page 57 and 58:
VECTOR AND TENSOR ANALYSIS Next we
Page 59 and 60:
VECTOR AND TENSOR ANALYSIS This imp
Page 61 and 62:
VECTOR AND TENSOR ANALYSIS Proof:
Page 63 and 64:
VECTOR AND TENSOR ANALYSIS Here we
Page 65 and 66:
VECTOR AND TENSOR ANALYSIS (2) Addi
Page 67 and 68:
VECTOR AND TENSOR ANALYSIS A genera
Page 69 and 70:
VECTOR AND TENSOR ANALYSIS two poin
Page 71 and 72:
VECTOR AND TENSOR ANALYSIS which sh
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
2 Ordinary di€erential equations
Page 79 and 80:
ORDINARY DIFFERENTIAL EQUATIONS The
Page 81 and 82:
ORDINARY DIFFERENTIAL EQUATIONS Sol
Page 83 and 84:
ORDINARY DIFFERENTIAL EQUATIONS It
Page 85 and 86:
Page 87 and 88:
ORDINARY DIFFERENTIAL EQUATIONS whe
Page 89 and 90:
ORDINARY DIFFERENTIAL EQUATIONS Gen
Page 91 and 92:
ORDINARY DIFFERENTIAL EQUATIONS and
Page 93 and 94:
ORDINARY DIFFERENTIAL EQUATIONS (1)
Page 95 and 96:
ORDINARY DIFFERENTIAL EQUATIONS Now
Page 97 and 98:
ORDINARY DIFFERENTIAL EQUATIONS Obv
Page 99 and 100:
ORDINARY DIFFERENTIAL EQUATIONS Sol
Page 101 and 102:
ORDINARY DIFFERENTIAL EQUATIONS Ord
Page 103 and 104:
Page 105 and 106:
ORDINARY DIFFERENTIAL EQUATIONS Cas
Page 107 and 108:
ORDINARY DIFFERENTIAL EQUATIONS Int
Page 109 and 110:
ORDINARY DIFFERENTIAL EQUATIONS of
Page 111 and 112:
ORDINARY DIFFERENTIAL EQUATIONS and
Page 113 and 114:
ORDINARY DIFFERENTIAL EQUATIONS Fig
Page 115 and 116:
3 Matrix algebra As vector methods
Page 117 and 118:
MATRIX ALGEBRA Four basic algebra o
Page 119 and 120:
MATRIX ALGEBRA then ~A ~B ˆ ˆ 2
Page 121 and 122:
MATRIX ALGEBRA Figure 3.1. Coordina
Page 123 and 124:
MATRIX ALGEBRA in®nite sum of matr
Page 125 and 126:
MATRIX ALGEBRA The product of two s
Page 127 and 128:
MATRIX ALGEBRA ~B ~ A ˆ ~I. Multip
Page 129 and 130:
MATRIX ALGEBRA but so that ~A 1 …
Page 131 and 132:
MATRIX ALGEBRA But if ~ A is an in
Page 133 and 134:
MATRIX ALGEBRA Taking the dot produ
Page 135 and 136:
MATRIX ALGEBRA change the handednes
Page 137 and 138:
MATRIX ALGEBRA preserves the norm o
Page 139 and 140:
MATRIX ALGEBRA Then ~A 0 R 0 ˆ…
Page 141 and 142:
MATRIX ALGEBRA Once the eigenvalues
Page 143 and 144:
MATRIX ALGEBRA Example 3.15 Show th
Page 145 and 146:
0 1 x 11 x 1i x 1n x 21 x 2i x
Page 147 and 148:
MATRIX ALGEBRA Since 0 1 1 B @ 1 0
Page 149 and 150:
MATRIX ALGEBRA We now proceed to pr
Page 151 and 152:
MATRIX ALGEBRA distance between any
Page 153 and 154:
MATRIX ALGEBRA This matrix equation
Page 155 and 156:
~A ~B ˆ a11 B ~ ! a 12 ~B ˆ a 21
Page 157 and 158:
MATRIX ALGEBRA 3.18 If A ~ ~B ˆ 0,
Page 159 and 160:
4 Fourier series and integrals Four
Page 161 and 162:
FOURIER SERIES AND INTEGRALS Fourie
Page 163 and 164:
FOURIER SERIES AND INTEGRALS Soluti
Page 165 and 166:
FOURIER SERIES AND INTEGRALS Figure
Page 167 and 168:
FOURIER SERIES AND INTEGRALS but b
Page 169 and 170:
FOURIER SERIES AND INTEGRALS Parsev
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
FOURIER SERIES AND INTEGRALS the A
Page 177 and 178:
FOURIER SERIES AND INTEGRALS Orthog
Page 179 and 180:
FOURIER SERIES AND INTEGRALS Substi
Page 181 and 182:
FOURIER SERIES AND INTEGRALS and th
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
FOURIER SERIES AND INTEGRALS We sho
Page 191 and 192:
FOURIER SERIES AND INTEGRALS and th
Page 193 and 194:
FOURIER SERIES AND INTEGRALS contin
Page 195 and 196:
FOURIER SERIES AND INTEGRALS amount
Page 197 and 198:
FOURIER SERIES AND INTEGRALS Using
Page 199 and 200:
FOURIER SERIES AND INTEGRALS It is
Page 201 and 202:
FOURIER SERIES AND INTEGRALS Parsev
Page 203 and 204:
FOURIER SERIES AND INTEGRALS This i
Page 205 and 206:
FOURIER SERIES AND INTEGRALS Soluti
Page 207 and 208:
FOURIER SERIES AND INTEGRALS The de
Page 209 and 210:
FOURIER SERIES AND INTEGRALS By the
Page 211 and 212:
FOURIER SERIES AND INTEGRALS 4.10 F
Page 213 and 214:
FOURIER SERIES AND INTEGRALS 4.22 V
Page 215 and 216:
LINEAR VECTOR SPACES Figure 5.1. A
Page 217 and 218:
LINEAR VECTOR SPACES We now proceed
Page 219 and 220:
LINEAR VECTOR SPACES Linear combina
Page 221 and 222:
LINEAR VECTOR SPACES is a basis for
Page 223 and 224:
LINEAR VECTOR SPACES then Eq. (5.10
Page 225 and 226:
LINEAR VECTOR SPACES Step 3. Clearl
Page 227 and 228:
LINEAR VECTOR SPACES then hujvi ˆh
Page 229 and 230:
LINEAR VECTOR SPACES Eq. (5.16) det
Page 231 and 232: LINEAR VECTOR SPACES In general A ~
Page 233 and 234: LINEAR VECTOR SPACES The inverse of
Page 235 and 236: LINEAR VECTOR SPACES It is also eas
Page 237 and 238: LINEAR VECTOR SPACES or U ~ ‡ ˆ
Page 239 and 240: LINEAR VECTOR SPACES Change of basi
Page 241 and 242: LINEAR VECTOR SPACES Multiplying Eq
Page 243 and 244: LINEAR VECTOR SPACES For a vibratin
Page 245 and 246: LINEAR VECTOR SPACES the integratio
Page 247 and 248: LINEAR VECTOR SPACES (b) T…a† i
Page 249 and 250: FUNCTIONS OF A COMPLEX VARIABLE and
Page 251 and 252: FUNCTIONS OF A COMPLEX VARIABLE We
Page 253 and 254: FUNCTIONS OF A COMPLEX VARIABLE Fig
Page 255 and 256: FUNCTIONS OF A COMPLEX VARIABLE ver
Page 257 and 258: FUNCTIONS OF A COMPLEX VARIABLE z 0
Page 259 and 260: FUNCTIONS OF A COMPLEX VARIABLE If
Page 261 and 262: FUNCTIONS OF A COMPLEX VARIABLE How
Page 263 and 264: FUNCTIONS OF A COMPLEX VARIABLE Sim
Page 265 and 266: FUNCTIONS OF A COMPLEX VARIABLE Di
Page 267 and 268: FUNCTIONS OF A COMPLEX VARIABLE fun
Page 269 and 270: FUNCTIONS OF A COMPLEX VARIABLE Sin
Page 271 and 272: FUNCTIONS OF A COMPLEX VARIABLE pro
Page 273 and 274: FUNCTIONS OF A COMPLEX VARIABLE Alt
Page 275 and 276: FUNCTIONS OF A COMPLEX VARIABLE Exa
Page 277 and 278: FUNCTIONS OF A COMPLEX VARIABLE Exa
Page 279 and 280: FUNCTIONS OF A COMPLEX VARIABLE For
Page 281: FUNCTIONS OF A COMPLEX VARIABLE Sol
Page 285 and 286: FUNCTIONS OF A COMPLEX VARIABLE Not
Page 287 and 288: FUNCTIONS OF A COMPLEX VARIABLE The
Page 289 and 290: FUNCTIONS OF A COMPLEX VARIABLE (b)
Page 291 and 292: FUNCTIONS OF A COMPLEX VARIABLE to
Page 293 and 294: FUNCTIONS OF A COMPLEX VARIABLE Sol
Page 295 and 296: FUNCTIONS OF A COMPLEX VARIABLE the
Page 297 and 298: FUNCTIONS OF A COMPLEX VARIABLE Thu
Page 299 and 300: FUNCTIONS OF A COMPLEX VARIABLE If
Page 301 and 302: FUNCTIONS OF A COMPLEX VARIABLE the
Page 303 and 304: FUNCTIONS OF A COMPLEX VARIABLE onl
Page 305 and 306: FUNCTIONS OF A COMPLEX VARIABLE To
Page 307 and 308: FUNCTIONS OF A COMPLEX VARIABLE Tak
Page 309 and 310: FUNCTIONS OF A COMPLEX VARIABLE 6.2
Page 311 and 312: 7 Special functions of mathematical
Page 313 and 314: SPECIAL FUNCTIONS OF MATHEMATICAL P
Page 333 and 334:
SPECIAL FUNCTIONS OF MATHEMATICAL P
Page 335 and 336:
Page 337 and 338:
Page 339 and 340:
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
Page 349 and 350:
Page 351 and 352:
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
THE CALCULUS OF VARIATIONS Figure 8
Page 365 and 366:
THE CALCULUS OF VARIATIONS This is
Page 367 and 368:
THE CALCULUS OF VARIATIONS p Lettin
Page 369 and 370:
THE CALCULUS OF VARIATIONS provided
Page 371 and 372:
THE CALCULUS OF VARIATIONS and Eq.
Page 373 and 374:
THE CALCULUS OF VARIATIONS Example
Page 375 and 376:
THE CALCULUS OF VARIATIONS must van
Page 377 and 378:
THE CALCULUS OF VARIATIONS mechanic
Page 379 and 380:
THE CALCULUS OF VARIATIONS Solution
Page 381 and 382:
THE CALCULUS OF VARIATIONS The acti
Page 383 and 384:
THE CALCULUS OF VARIATIONS is to ®
Page 385 and 386:
THE CALCULUS OF VARIATIONS y…"; x
Page 387 and 388:
9 The Laplace transformation The La
Page 389 and 390:
THE LAPLACE TRANSFORMATION This est
Page 391 and 392:
THE LAPLACE TRANSFORMATION or L‰x
Page 393 and 394:
THE LAPLACE TRANSFORMATION Recall L
Page 395 and 396:
THE LAPLACE TRANSFORMATION Let u ˆ
Page 397 and 398:
THE LAPLACE TRANSFORMATION But f
Page 399 and 400:
THE LAPLACE TRANSFORMATION but and
Page 401 and 402:
THE LAPLACE TRANSFORMATION 9.6 Find
Page 403 and 404:
PARTIAL DIFFERENTIAL EQUATIONS prob
Page 405 and 406:
PARTIAL DIFFERENTIAL EQUATIONS If
Page 407 and 408:
PARTIAL DIFFERENTIAL EQUATIONS In t
Page 409 and 410:
PARTIAL DIFFERENTIAL EQUATIONS The
Page 411 and 412:
PARTIAL DIFFERENTIAL EQUATIONS We a
Page 413 and 414:
PARTIAL DIFFERENTIAL EQUATIONS Let
Page 415 and 416:
PARTIAL DIFFERENTIAL EQUATIONS brin
Page 417 and 418:
PARTIAL DIFFERENTIAL EQUATIONS We n
Page 419 and 420:
PARTIAL DIFFERENTIAL EQUATIONS whic
Page 421 and 422:
PARTIAL DIFFERENTIAL EQUATIONS to t
Page 423 and 424:
PARTIAL DIFFERENTIAL EQUATIONS Subs
Page 425 and 426:
PARTIAL DIFFERENTIAL EQUATIONS Now
Page 427 and 428:
PARTIAL DIFFERENTIAL EQUATIONS Figu
Page 429 and 430:
SIMPLE LINEAR INTEGRAL EQUATIONS f
Page 431 and 432:
SIMPLE LINEAR INTEGRAL EQUATIONS Th
Page 433 and 434:
SIMPLE LINEAR INTEGRAL EQUATIONS wh
Page 435 and 436:
SIMPLE LINEAR INTEGRAL EQUATIONS in
Page 437 and 438:
SIMPLE LINEAR INTEGRAL EQUATIONS A
Page 439 and 440:
SIMPLE LINEAR INTEGRAL EQUATIONS no
Page 441 and 442:
SIMPLE LINEAR INTEGRAL EQUATIONS Th
Page 443 and 444:
SIMPLE LINEAR INTEGRAL EQUATIONS wh
Page 445 and 446:
12 Elements of group theory Group t
Page 447 and 448:
ELEMENTS OF GROUP THEORY The same s
Page 449 and 450:
ELEMENTS OF GROUP THEORY Figure 12.
Page 451 and 452:
ELEMENTS OF GROUP THEORY Table 12.3
Page 453 and 454:
ELEMENTS OF GROUP THEORY Obviously
Page 455 and 456:
ELEMENTS OF GROUP THEORY This can b
Page 457 and 458:
ELEMENTS OF GROUP THEORY Group repr
Page 459 and 460:
ELEMENTS OF GROUP THEORY (1) A matr
Page 461 and 462:
ELEMENTS OF GROUP THEORY Equation (
Page 463 and 464:
ELEMENTS OF GROUP THEORY Table 12.6
Page 465 and 466:
ELEMENTS OF GROUP THEORY met. In qu
Page 467 and 468:
ELEMENTS OF GROUP THEORY 0 1 1 0 0
Page 469 and 470:
ELEMENTS OF GROUP THEORY Figure 12.
Page 471 and 472:
ELEMENTS OF GROUP THEORY We can exp
Page 473 and 474:
ELEMENTS OF GROUP THEORY Next, we a
Page 475 and 476:
NUMERICAL METHODS is rather tedious
Page 477 and 478:
NUMERICAL METHODS Figure 13.2. cour
Page 479 and 480:
NUMERICAL METHODS and take g…x†
Page 481 and 482:
NUMERICAL METHODS Solution: Here f
Page 483 and 484:
NUMERICAL METHODS where y i ˆ f
Page 485 and 486:
NUMERICAL METHODS The ®rst-order o
Page 487 and 488:
NUMERICAL METHODS approximate value
Page 489 and 490:
NUMERICAL METHODS Runge±Kutta meth
Page 491 and 492:
NUMERICAL METHODS Equations of high
Page 493 and 494:
NUMERICAL METHODS We now illustrate
Page 495 and 496:
NUMERICAL METHODS 13.14. Find to th
Page 497 and 498:
INTRODUCTION TO PROBABILITY THEORY
Page 499 and 500:
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
Page 507 and 508:
Page 509 and 510:
Page 511 and 512:
Page 513 and 514:
Page 515 and 516:
Page 517 and 518:
Page 519 and 520:
Page 521 and 522:
Appendix 1 Preliminaries (review of
Page 523 and 524:
APPENDIX 1 PRELIMINARIES Problem A1
Page 525 and 526:
Page 527 and 528:
APPENDIX 1 PRELIMINARIES Example A1
Page 529 and 530:
APPENDIX 1 PRELIMINARIES Since the
Page 531 and 532:
APPENDIX 1 PRELIMINARIES Figure A1.
Page 533 and 534:
APPENDIX 1 PRELIMINARIES How do we
Page 535 and 536:
Page 537 and 538:
APPENDIX 1 PRELIMINARIES This follo
Page 539 and 540:
APPENDIX 1 PRELIMINARIES Theorems o
Page 541 and 542:
APPENDIX 1 PRELIMINARIES This is th
Page 543 and 544:
APPENDIX 1 PRELIMINARIES (d) Find t
Page 545 and 546:
APPENDIX 1 PRELIMINARIES Divide the
Page 547 and 548:
APPENDIX 1 PRELIMINARIES Example A1
Page 549 and 550:
APPENDIX 1 PRELIMINARIES Di€erent
Page 551 and 552:
APPENDIX 1 PRELIMINARIES derivative
Page 553 and 554:
Appendix 2 Determinants The determi
Page 555 and 556:
APPENDIX 2 DETERMINANTS where a 11
Page 557 and 558:
APPENDIX 2 DETERMINANTS D ˆ a i1 C
Page 559 and 560:
APPENDIX 2 DETERMINANTS Example A2.
Page 561 and 562:
APPENDIX 2 DETERMINANTS Proof: Expa
Page 563 and 564:
Appendix 3 Table of * F…x† ˆp
Page 565 and 566:
Index Abel's integral equation, 426
Page 567 and 568:
INDEX group theory (contd) symmetry
Page 569:
INDEX series solution of di€erent
show all

Mathematical Methods for Physicists: A concise introduction - Site Map

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?