北大数学物理方法(A)-复变函数教案01复变函数

Outline1˜ùEC¼ê®ŒÆÔnÆêÆÔn{‘§|2007cSC.S.Wu1˜ùEC¼êOutlineùLJ:1Eê9Ù$Ž5KEêµ½ÂEêAÛL«2EêSEêSS43EC¼ê½Â4†ëYá:C.S.Wu1˜ùEC¼êOutlineùLJ:1Eê9Ù$Ž5KEêµ½ÂEêAÛL«2EêSEêSS43EC¼ê½Â4†ëYá:C.S.Wu1˜ùEC¼êOutlineùLJ:1Eê9Ù$Ž5KEêµ½ÂEêAÛL«2EêSEêSS43EC¼ê½Â4†ëYá:C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableReferencesÇÂÁ§5êÆÔn{6§11Ùù&œ§5êÆÔn{6§§1.1,1.2nÎ!X1Á§5êÆÔn{6§§1.1C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableReferencesÇÂÁ§5êÆÔn{6§11Ùù&œ§5êÆÔn{6§§1.1,1.2nÎ!X1Á§5êÆÔn{6§§1.1C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableReferencesÇÂÁ§5êÆÔn{6§11Ùù&œ§5êÆÔn{6§§1.1,1.2nÎ!X1Á§5êÆÔn{6§§1.1C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationùLJ:1Eê9Ù$Ž5KEêµ½ÂEêAÛL«2EêSEêSS43EC¼ê½Â4†ëYá:C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEê½Âk˜ékS¢ê(a,b)§„le$Ž5Kµ\{(a1,b1)+(a2,b2)=(a1+a2,b1+b2)¦{(a,b)(c,d)=(ac−bd,ad+bc)K¡ù˜ékS¢ê(a,b)½Â˜‡Eêαα=(a,b)a¡α¢Ü§b¡αJÜa=Reαb=ImαC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEê½Âk˜ékS¢ê(a,b)§„le$Ž5Kµ\{(a1,b1)+(a2,b2)=(a1+a2,b1+b2)¦{(a,b)(c,d)=(ac−bd,ad+bc)K¡ù˜ékS¢ê(a,b)½Â˜‡Eêαα=(a,b)a¡α¢Ü§b¡αJÜa=Reαb=ImαC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEê½Âk˜ékS¢ê(a,b)§„le$Ž5Kµ\{(a1,b1)+(a2,b2)=(a1+a2,b1+b2)¦{(a,b)(c,d)=(ac−bd,ad+bc)K¡ù˜ékS¢ê(a,b)½Â˜‡Eêαα=(a,b)a¡α¢Ü§b¡αJÜa=Reαb=ImαC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEê½Âk˜ékS¢ê(a,b)§„le$Ž5Kµ\{(a1,b1)+(a2,b2)=(a1+a2,b1+b2)¦{(a,b)(c,d)=(ac−bd,ad+bc)K¡ù˜ékS¢ê(a,b)½Â˜‡Eêαα=(a,b)a¡α¢Ü§b¡αJÜa=Reαb=ImαC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEê½Âk˜ékS¢ê(a,b)§„le$Ž5Kµ\{(a1,b1)+(a2,b2)=(a1+a2,b1+b2)¦{(a,b)(c,d)=(ac−bd,ad+bc)K¡ù˜ékS¢ê(a,b)½Â˜‡Eêαα=(a,b)a¡α¢Ü§b¡αJÜa=Reαb=ImαC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEê´¢êí2(*¿)¢êaP(a,0)Ïdα=(a,b)=a(1,0)+b(0,1)C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEê´¢êí2(*¿)¢êaP(a,0)Ïdα=(a,b)=a(1,0)+b(0,1)C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEê´¢êí2(*¿)¢êaP(a,0)Ïdα=(a,b)=a(1,0)+b(0,1)C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEêªα=(a,b)=a(1,0)+b(0,1)¿ÂÛ¹EêƒVgüEêƒ⇐⇒¢Ü!JÜ©Oƒ#N`ü‡EêØEêØU'ŒœC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEêªα=(a,b)=a(1,0)+b(0,1)¿ÂÛ¹EêƒVgüEêƒ⇐⇒¢Ü!JÜ©Oƒ#N`ü‡EêØEêØU'ŒœC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEêªα=(a,b)=a(1,0)+b(0,1)¿ÂÛ¹EêƒVgüEêƒ⇐⇒¢Ü!JÜ©Oƒ#N`ü‡EêØEêØU'ŒœC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationEêªα=(a,b)=a(1,0)+b(0,1)¿ÂÛ¹EêƒVgüEêƒ⇐⇒¢Ü!JÜ©Oƒ#N`ü‡EêØEêØU'ŒœC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationAÏEê(0,0)——¢ê0(a,b)+(0,0)=(a,b)?ÛEê†(0,0)ƒ\§ÙŠØC(a,b)(0,0)=(0,0)?ÛEê†(0,0)ƒ¦§ð(0,0)C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationAÏEê(0,0)——¢ê0(a,b)+(0,0)=(a,b)?ÛEê†(0,0)ƒ\§ÙŠØC(a,b)(0,0)=(0,0)?ÛEê†(0,0)ƒ¦§ð(0,0)C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationAÏEê(0,0)——¢ê0(a,b)+(0,0)=(a,b)?ÛEê†(0,0)ƒ\§ÙŠØC(a,b)(0,0)=(0,0)?ÛEê†(0,0)ƒ¦§ð(0,0)C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationAÏEê(0,0)——¢ê0(a,b)+(0,0)=(a,b)?ÛEê†(0,0)ƒ\§ÙŠØC(a,b)(0,0)=(0,0)?ÛEê†(0,0)ƒ¦§ð(0,0)C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationAÏEê(0,0)——¢ê0(a,b)+(0,0)=(a,b)?ÛEê†(0,0)ƒ\§ÙŠØC(a,b)(0,0)=(0,0)?ÛEê†(0,0)ƒ¦§ð(0,0)C.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationAÏEê(1,0)——¢ê1(1,0)(a,b)=(a,b)?ÛEê†(1,0)ƒ¦§ÙŠØCC.S.Wu1˜ùEC¼êComplexNumbers&ComplexAlgebraComplexSequenceFunctionofaComplexVariableComplexNumbers:DefinitionGeometricRepresentationAÏEê(1,0)——¢ê1(1,0)(a,b)=(a,b)?ÛEê†(1,0)ƒ¦§ÙŠØCC.S.