mathematical methods for physics and engineering

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1、ContentsPrefacetothesecondeditionxixPrefacetothefirsteditionxxi1Preliminaryalgebra11.1Simplefunctionsandequations1Polynomialequations;factorisation;propertiesofroots1.2Trigonometricidentities10Singleangle;compound-angles;double-andhalf-angleidentities1.3Coordinategeometry151.4Partialfract

2、ions18Complicationsandspecialcases;complexroots;repeatedroots1.5Binomialexpansion251.6Propertiesofbinomialcoefficients271.7Someparticularmethodsofproof30Methodsofproof;byinduction;bycontradiction;necessaryandsufficientconditions1.8Exercises361.9Hintsandanswers392Preliminarycalculus422.1Differ

3、entiation42Differentiationfromfirstprinciples;products;thechainrule;quotients;implicitdifferentiation;logarithmicdifferentiation;Leibniz’theorem;specialpointsofafunction;theoremsofdifferentiationvCONTENTS2.2Integration60Integrationfromfirstprinciples;theinverseofdifferentiation;integrationbyins

4、pection;sinusoidalfunctions;logarithmicintegration;integrationusingpartialfractions;substitutionmethod;integrationbyparts;reductionformulae;infiniteandimproperintegrals;planepolarcoordinates;integralinequalities;applicationsofintegration2.3Exercises772.4Hintsandanswers823Complexnumbersand

5、hyperbolicfunctions863.1Theneedforcomplexnumbers863.2Manipulationofcomplexnumbers88Additionandsubtraction;modulusandargument;multiplication;complexconjugate;division3.3Polarrepresentationofcomplexnumbers95Multiplicationanddivisioninpolarform3.4deMoivre’stheorem98trigonometricidentities;fi

6、ndingthenthrootsofunity;solvingpolynomialequations3.5Complexlogarithmsandcomplexpowers1023.6Applicationstodifferentiationandintegration1043.7Hyperbolicfunctions105Definitions;hyperbolic–trigonometricanalogies;identitiesofhyperbolicfunctions;solvinghyperbolicequations;inversesofhyperbolicfu

7、nctions;calculusofhyperbolicfunctions3.8Exercises1123.9Hintsandanswers1164Seriesandlimits1184.1Series1184.2Summationofseries119Arithmeticseries;geometricseries;arithmetico-geometricseries;thedifferencemethod;seriesinvolvingnaturalnumbers;transformationofseries4.3Convergenc