math_method_for_phy_eng

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1、ContentsPrefacetothesecondeditionxixPrefacetothefirsteditionxxi1Preliminaryalgebra11.1Simplefunctionsandequations1Polynomialequations;factorisation;propertiesofroots1.2Trigonometricidentities10Singleangle;compound-angles;double-andhalf-angleidentities1.3Coordinategeometry151.4Partialfractions1

2、8Complicationsandspecialcases;complexroots;repeatedroots1.5Binomialexpansion251.6Propertiesofbinomialcoefficients271.7Someparticularmethodsofproof30Methodsofproof;byinduction;bycontradiction;necessaryandsufficientconditions1.8Exercises361.9Hintsandanswers392Preliminarycalculus422.1Differentiation4

3、2Differentiationfromfirstprinciples;products;thechainrule;quotients;implicitdifferentiation;logarithmicdifferentiation;Leibniz’theorem;specialpointsofafunction;theoremsofdifferentiationvCONTENTS2.2Integration60Integrationfromfirstprinciples;theinverseofdifferentiation;integrationbyinspection;sinusoi

4、dalfunctions;logarithmicintegration;integrationusingpartialfractions;substitutionmethod;integrationbyparts;reductionformulae;infiniteandimproperintegrals;planepolarcoordinates;integralinequalities;applicationsofintegration2.3Exercises772.4Hintsandanswers823Complexnumbersandhyperbolicfunctions8

5、63.1Theneedforcomplexnumbers863.2Manipulationofcomplexnumbers88Additionandsubtraction;modulusandargument;multiplication;complexconjugate;division3.3Polarrepresentationofcomplexnumbers95Multiplicationanddivisioninpolarform3.4deMoivre’stheorem98trigonometricidentities;findingthenthrootsofunity;s

6、olvingpolynomialequations3.5Complexlogarithmsandcomplexpowers1023.6Applicationstodifferentiationandintegration1043.7Hyperbolicfunctions105Definitions;hyperbolic–trigonometricanalogies;identitiesofhyperbolicfunctions;solvinghyperbolicequations;inversesofhyperbolicfunctions;calculusofhyperbolicfu

7、nctions3.8Exercises1123.9Hintsandanswers1164Seriesandlimits1184.1Series1184.2Summationofseries119Arithmeticseries;geometricseries;arithmetico-geometricseries;thedifferencemethod;seriesinvolvingnaturalnumbers;transformationofseries4.3Convergenc