Introduction to Mathematical Physics Prentice-Hall of india Private Limited New Dethi-110001 1995 ‘The Sta Indian Reprint fs, 69. {Grins US Catone he 10100) INTRODUCTION To MATHEMATICAL PHYSICS ty Chace Horpar PAENTICE-HALL INTERNATIONAL, INC, Englaword Cals, PHENTICE HALL BITEFNATIONAL (UK) LBMITED, Londen. PRENTICE-HALL OF AUSTRALIA PIY. UMITED, Shey, PHENTICE HALL CANADA, NG. Tareto. PRENTICE-HALL HISPANGAMEAIGANA, S.A, Maco PRENTICE-HALL OF JAPAN, ING, Tolyo SIMON & SCHUSTER ASIA PTE. LTD, Singapore EDITORA PRENTICEHALL OO BRASIL LTDR, Flo de lai, (© 1976 by Prentice Hat, In. Englowaod Cif, NL. U.S.A. Al gh Tesotwed. No part ct thi book miy be reproducad In any form by Ininaogyaph of any chr meant, waht perrnilan In wig rah the pushes. WeENT-700-0252-1 “The expat ght af thie book are vec ecely withthe pubahe, “Tie Egttem Ezonory Eston je the onky authorized, compete and Unabridged photortest reproduction ofthe latest Ameroen ton ‘Specialy publahod and paced for aale ony ie Barglacoch, Sura. Canbodia, Ching, Fp. Hong Kong, India, indonesia, Laos, aleve, Nepal Pasar, Priggnee Singapore, Sou Kors, Siang, Tan, “Thaland, and Vistas Roprctd In Ina by spacal arangement with Prentice Hal, fn. Engoveod Gifts, Nal, USA bch Printing o cee uty, 1995 Published by Prenion-Hal of India Private Linded, M97, Connaught ‘Grou New Gets 10001 sid Printed by VK. Bate at Pend Ofek Prata Privme Limited, New Dal-110016 Dedicated ta the memory of Se Contents Preface xe 1 Vector Analysis 1 Li simopuenes UHC Deleon of tee 112 Funeanenal Coeere and Notions? 1 Vstor adding wihon Coornass 12 Tm camreman semi o nase vecrane 4 E3 Redon Vector adr cen) 5 URE Renaranar Reign ote ator 5 TXe Dieoton Covaee TRS Vastur alba ih Cosas 7 1 mirgemmenarion op vernon PENEIONS OD 1s 16 ay aa 22 23 uu as Soe SEFDL RELATIONS NvOLUING VECTORS. 30 E51 Reutions involving the? Opcioe 30 ‘GevERALsZe0 COORDINATES 4 FS Ohomonl Cuvitna Conran 35 145 The Lanes ie Gros) Corina Coton TAG Mane PlerCootnater 38 NAP Rig Cher yndial Coons 36 TiGk Spheta! Plann 38 Proms 38 2 Operntor and Matrix Analysis 2 omopLcHon 42 supers OF YoCroR space 43 ZBL Daina of Yet Seace 322 Lone 224 Inoer Buel de 324 Hite Smee 3 226 Leer oom 45 ATR ANALYSE AND NerATIONS — 46 warmx opsnarions 48 EAL Addon Sahencton) 6 242 Mataton 243 Don 2 BAS Themen ote Manis 9 EES tacilnaed Mvices 5? PRUPERUIES OF ARSTOURY MATRICES SL FE Trenmne Maus SL 252 Coles Conn ounae $f SS Heemtian Cones 3 28 swemsquenenvuncis 2 261 Cnt Sinule 32 Ede Reade weete 34 2d Syancte Sar 265 Adliyaule show Male 56 27 SOLON OF A SIDE Or Can EQLAIONS ST 2B WeMOENvaLLe MLE 8 2.9 cuonuinare uaseicanrons 60 2.40 prone 63 Ammesnis: Remi WF DETERSINAKTS G7 3 Funevions of « Complex Variable 72 wsmopvenid 72 COMPLEX VARUOLLS JSD REEEUSENUATIONS TS B21 alponiepestion 7 WOE Commie coat 73 222 Eales Fors 77 B25 beMehes Timon 78 {33 anata e ronerions oF cxmmmume vaRIAnLE 80 SLD Meburnadec of /CZ an Ay 30 34 suuatsmeransost HT romans 95 AveIIUSE-AIMENTS OF SERS — 9B a 4a 49 sa 52 54 4. Caleatys of Residoes 101 rene 101 soLaren aveRTAR Fons 182. EALRHON OF RERDTES 104 Si metre tle hh Senevee aos ie caucHY arc neem 10 ae cane venvemat vate SLL anwar or Dias ninoRACS 112 4:6 Tero he Foon: [Vln dcos he 222 2 megmb of no Roma: 7_flente 1¢ 46e tert of the en: [700 de merernen RELATIONS 118 cuoasmice mepmusarcasios 120 482, Coolers! Bsecnmatin (upping) 120 proscase 124 8 Dilfereotal Fuustions 127 pemepuccen 127 DkORARY DIFFERITTAL ATEN 2B 522 Thefigerpcnn Pipe 144 ELT Secondidet Hourroses Hato wth Coosa? Coe $24, Seoul. alee Nastesgnesoh Eaves ih ant 12.5. Seund.iter NonhomgamousFaptors wk Varia Eeetirts a? 4126 SeconkOUh one: Egan tk Yai Cones SATIAL DIFFERENTIAL ORATIONG. 148 Sac Soe frporact Pt Pisa Kowa Roa 42 589 Aniline of Ue Sete of iver fetes 282 Sood of Spation of Wares 282 Bs 63 64 66 ul 1a 1a 14 4s 16 comer 6 Special Funetinas of Mathematical Physics 163 memonuctios 163 TUTLeTE FOLYSOMLALS 164 S24 hae Hatnbous of Monin Mechanes 64 622 Motuebineauil Laser Baonie Onalatar 165 G25 TaeSokiencl Morales Dutectal Faun 168 ERRRNORE AND ASOEIATE LPCUDAE OEYNOMIATS ATE 683 Lagendce Foooauals 223 Oe canensL vowuvnunaM 182 {643 Two Byulions Refuchle to Toppers guntion AS eRe TECHONS 186 ESE TheSoldion otal Equation 285 C13 Meehan Sie oF Bea Egon 8 835 intel Moredore CAG Modes Borel Futons — 104 237 Sahel Bend Bons 350 mowsys 202 AYPLRDIN: TL RLLATION REFWFEN POOP) AND POOP) 208 7 Fuwies Series 207 puraoucued 207 IS Powder eget 29. JE Conlon roe te Foe Sis 210 SUMACATION OF TNE FOURUR RAIS 219 i cages enon 221 SISWOARY OF 90M FROPERTO OF FOUTUER SEES 23 mons 223