mathematical methods for physics and engineering [riley]

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1、ContentsPrefacetothesecondeditionxixPrefacetothefirsteditionxxi1Preliminaryalgebra11.1Simplefunctionsandequations1Polynomialequations;factorisation;propertiesofroots1.2Trigonometricidentities10Singleangle;compound-angles;double-andhalf-angleidentities1.3Coordina

2、tegeometry151.4Partialfractions18Complicationsandspecialcases;complexroots;repeatedroots1.5Binomialexpansion251.6Propertiesofbinomialcoefficients271.7Someparticularmethodsofproof30Methodsofproof;byinduction;bycontradiction;necessaryandsufficientconditions1.8Exercis

3、es361.9Hintsandanswers392Preliminarycalculus422.1Differentiation42Differentiationfromfirstprinciples;products;thechainrule;quotients;implicitdifferentiation;logarithmicdifferentiation;Leibniz’theorem;specialpointsofafunction;theoremsofdifferentiationvCONTENTS2.2Integ

4、ration60Integrationfromfirstprinciples;theinverseofdifferentiation;integrationbyinspection;sinusoidalfunctions;logarithmicintegration;integrationusingpartialfractions;substitutionmethod;integrationbyparts;reductionformulae;infiniteandimproperintegrals;planepolarco

5、ordinates;integralinequalities;applicationsofintegration2.3Exercises772.4Hintsandanswers823Complexnumbersandhyperbolicfunctions863.1Theneedforcomplexnumbers863.2Manipulationofcomplexnumbers88Additionandsubtraction;modulusandargument;multiplication;complexconjug

6、ate;division3.3Polarrepresentationofcomplexnumbers95Multiplicationanddivisioninpolarform3.4deMoivre’stheorem98trigonometricidentities;findingthenthrootsofunity;solvingpolynomialequations3.5Complexlogarithmsandcomplexpowers1023.6Applicationstodifferentiationandint

7、egration1043.7Hyperbolicfunctions105Definitions;hyperbolic–trigonometricanalogies;identitiesofhyperbolicfunctions;solvinghyperbolicequations;inversesofhyperbolicfunctions;calculusofhyperbolicfunctions3.8Exercises1123.9Hintsandanswers1164Seriesandlimits1184.1Seri

8、es1184.2Summationofseries119Arithmeticseries;geometricseries;arithmetico-geometricseries;thedifferencemethod;seriesinvolvingnaturalnumbers;transformationofseries4.3Convergenc