Mathematical Physics: A Modern Introduction to Its FoundationsSpringer Science & Business Media, 8 בפבר׳ 2002 - 1026 עמודים This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained. The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws. Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids. |
תוכן
IV | 1 |
VII | 4 |
VIII | 7 |
IX | 10 |
X | 12 |
XI | 14 |
XII | 17 |
XIII | 19 |
CXVII | 451 |
CXVIII | 453 |
CXIX | 457 |
CXX | 458 |
CXXI | 464 |
CXXII | 467 |
CXXIII | 473 |
CXXIV | 480 |
XIV | 23 |
XV | 32 |
XVI | 41 |
XVII | 43 |
XVIII | 49 |
XX | 56 |
XXI | 61 |
XXII | 63 |
XXIII | 67 |
XXIV | 70 |
XXV | 76 |
XXVI | 82 |
XXVIII | 87 |
XXIX | 89 |
XXX | 91 |
XXXI | 93 |
XXXII | 101 |
XXXIII | 103 |
XXXIV | 109 |
XXXVI | 112 |
XXXVII | 114 |
XXXVIII | 117 |
XXXIX | 125 |
XL | 129 |
XLI | 130 |
XLII | 138 |
XLIII | 143 |
XLIV | 145 |
XLVI | 150 |
XLVII | 157 |
XLVIII | 159 |
L | 165 |
LI | 169 |
LII | 172 |
LV | 175 |
LVI | 176 |
LVII | 179 |
LVIII | 186 |
LIX | 189 |
LX | 190 |
LXI | 196 |
LXII | 208 |
LXIII | 220 |
LXIV | 225 |
LXV | 227 |
LXVII | 228 |
LXVIII | 236 |
LXIX | 241 |
LXX | 248 |
LXXI | 252 |
LXXII | 263 |
LXXIII | 270 |
LXXIV | 273 |
LXXV | 275 |
LXXVI | 290 |
LXXVII | 293 |
LXXX | 295 |
LXXXI | 302 |
LXXXII | 309 |
LXXXIII | 312 |
LXXXIV | 319 |
LXXXV | 325 |
LXXXVI | 327 |
LXXXVII | 331 |
LXXXVIII | 334 |
LXXXIX | 338 |
XC | 346 |
XCI | 348 |
XCII | 349 |
XCIII | 350 |
XCIV | 352 |
XCV | 355 |
XCVI | 364 |
XCVII | 367 |
XCVIII | 376 |
XCIX | 380 |
C | 382 |
CI | 383 |
CII | 394 |
CIII | 400 |
CIV | 401 |
CV | 404 |
CVI | 410 |
CVII | 413 |
CVIII | 419 |
CIX | 426 |
CX | 433 |
CXI | 434 |
CXII | 437 |
CXIII | 438 |
CXIV | 443 |
CXV | 445 |
CXVI | 449 |
CXXV | 485 |
CXXVI | 488 |
CXXVII | 494 |
CXXVIII | 505 |
CXXIX | 507 |
CXXX | 513 |
CXXXI | 517 |
CXXXII | 522 |
CXXXIII | 524 |
CXXXIV | 540 |
CXXXV | 545 |
CXXXVI | 551 |
CXXXVII | 553 |
CXXXVIII | 554 |
CXXXIX | 557 |
CXL | 565 |
CXLI | 577 |
CXLII | 580 |
CXLIII | 583 |
CXLIV | 584 |
CXLV | 592 |
CXLVI | 596 |
CXLVII | 600 |
CXLVIII | 603 |
CXLIX | 610 |
CL | 613 |
CLI | 621 |
CLII | 626 |
CLIII | 628 |
CLIV | 636 |
CLV | 641 |
CLVI | 649 |
CLVII | 651 |
CLVIII | 652 |
CLIX | 656 |
CLX | 663 |
CLXI | 664 |
CLXII | 669 |
CLXIII | 673 |
CLXIV | 680 |
CLXV | 685 |
CLXVI | 687 |
CLXVII | 692 |
CLXIX | 695 |
CLXX | 699 |
CLXXI | 701 |
CLXXII | 707 |
CLXXIII | 723 |
CLXXIV | 728 |
CLXXV | 729 |
CLXXVI | 736 |
CLXXVII | 739 |
CLXXVIII | 749 |
CLXXIX | 756 |
CLXXX | 758 |
CLXXXI | 763 |
CLXXXII | 770 |
CLXXXIII | 776 |
CLXXXIV | 780 |
CLXXXV | 791 |
CLXXXVI | 801 |
CLXXXVII | 808 |
CLXXXVIII | 813 |
CLXXXIX | 815 |
CXCII | 826 |
CXCIII | 832 |
CXCIV | 833 |
CXCV | 845 |
CXCVI | 856 |
CXCVII | 859 |
CXCVIII | 876 |
CXCIX | 882 |
CC | 883 |
CCI | 887 |
CCII | 897 |
CCIII | 908 |
CCIV | 913 |
CCV | 918 |
CCVI | 932 |
CCVII | 936 |
CCVIII | 941 |
CCIX | 951 |
CCX | 956 |
CCXI | 964 |
CCXII | 970 |
CCXIII | 973 |
CCXIV | 988 |
CCXV | 992 |
CCXVI | 997 |
CCXVII | 1000 |
1003 | |
1007 | |
מהדורות אחרות - הצג הכל
Mathematical Physics: A Modern Introduction to Its Foundations <span dir=ltr>Sadri Hassani</span> אין תצוגה מקדימה זמינה - 2012 |
מונחים וביטויים נפוצים
analytic arbitrary basis Bessel called Cauchy Chapter coefficients commute compact complex numbers components conjugacy classes consider constant contour convergence coordinates corresponding curve defined definition denoted derivative differential equation dimensions eigenvalues eigenvectors elements evaluate Example expansion finite finite-dimensional Fourier given Green's function hermitian hermitian operator Hilbert space identity infinite inner product inner product space integral invariant inverse irreducible representations isomorphism lemma Lie algebra Lie group linear operator manifold mathematics matrix multiplication nonzero obtain orthogonal orthonormal permutation physics polynomials problem proof Proposition reader real numbers relation result rotation Schrödinger equation Show singular solution subgroup subset subspace Substituting symmetric tensor Theorem theory transformation unitary vanishes variables vector field vector space verify write yields zero ди дх
הפניות לספר זה
Mathematical Methods: For Students of Physics and Related Fields <span dir=ltr>Sadri Hassani</span> תצוגה מקדימה מוגבלת - 2000 |
Mathematical Methods Using Mathematica®: For Students of Physics and Related ... <span dir=ltr>Sadri Hassani</span> אין תצוגה מקדימה זמינה - 2003 |