化学数学（影印版）

定　价：¥78.00

作　者：	G.Doggeett,B.T.Sutcliffe
出版社：	Springer-Verlag
丛编项：
标　签：	暂缺

ISBN：	9787506242677	出版时间：	1999-06-01	包装：	平装
开本：	16开	页数：	286	字数：

内容简介

　　Chemistry is a practical subject， so why should mathematics now play such an important role in its understanding？ Coulson provided compelling answers to this question in his presidential address to the Institute of Mathematics and its Applications （Coulson， 1973）， when he reviewed the reactions of those involved in the development of chemical ideas one hundred years earlier. He reminds us， for example， that in 1878 Frankland wrote： 'I am convinced that further progress of chemistry as an exact science depends very much indeed upon the alliance with mathematics'. This prophetic view was not shared by most chemists of the time; and it was not until the development of the quantum theory in the late 1920s， and the consequent impact on our understanding of spectroscopy and electronic structure， that chemists started to develop the mathematical tools that were relevant to the needs of chemistry. There are many reasons for the growth of this symbiotic relationship， and it is helpful to examine some of them in putting the objectives of this book into the proper context.

作者简介

暂缺《化学数学（影印版）》作者简介

图书目录

Introduction
Mathematicsinthecontextofchemistry
Organizationofthetext
Acknowledgements
1Numbers,symbobandrules
1.1Numbers
Kindsofnumbers
Relationsinvolvingnumbers
Operationsonnumbers
Additionorsubtraction
Multiplication
Division
Exponentialnotation
Lawsofexponents
Rationalexponents
Realnumberexponents
Scientificnotation
1.2Symbolsandmorerules
1.3Simplepolynomialequations
1.4Afirstlookatcomplexnumbers
2Functionsofasinglevariable
2.1Theideaoffunction
Simplealgebraicfunctions
Theinversefunction
Moreonthedomain
Functionsasprescriptions
2.2Exponentialfunctions
2.3Thelogarithmfunction
2.4Trigonometricalfunctions
Inversetrigonometricalfunctions
Trigonometricalrelationsandidentifies
2.5Hyperbolicfunctions
Inversehyperbolicfunctions
3Limits,smallstepsandsmoothness
3.1Someexamplesoflimitingprocesses
3.2Definingthelimitingprocess
Functionsofanintegervariable
Functionsofarealvariable
Testingforcontinuity
3.3Someexamplesintheuseoflimits
4Ratesofchangeanddifferentiation
4.1Definingrateofchange
Averagerateofchange
Instantaneousrateofchange
4.2Differentiationofsomestandardfunctions
Differentiationofxn
Differentiationofsinxandcosx
Animportantlimit
Differentiatingtheexponentialandlogarithmfunctions
4.3Functionswithdiscontinuities
4.4Basicrulesfordifferentiation
Sums,products'andquotientsoffunctions
Thechainrule
4.5Higher-orderderivatives
4.6Maximaandminima
4.7Thedifferentiationoffunetiousoftwoormorevariables:
apreview
Thepartialderivative
5Differentials-smallandnotsosmallchanges
5.1Thetangentapproximation
5.2Somefurtherusesofthetangentapproximation
TheNewton-Raphsonmethod
Reformulatingthetangentapproximation
5.3Thedifferentialofafunctionoftwovariables:apreview
5.4Somediscussionoftheideaofadifferential
6Integration-undoingtheeffectsofdifferentiation
6.1TheantiderivativefunctionandtheIoperator
FurtherpropertiesoftheIoperator
6.2Methodsforevaluatingintegrals
Rearrangementoftheintegrand
6.3Thesubstitutionmethod
Ausefulresult
6.4Integralsinvolvingrationalpolynomialfunctions
Useofpartialfractions
6.5Integrationbyparts
6.6Thedefiniteintegral
6.7Improperintegrals
6.8Numericaldeterminationofdefiniteintegrals
7Powerseries:anewlookatfunctions
7.1TheMaclaurinseries
Testingforconvergence
7.2TheTaylorseries
7.3Manipulatingpowerseries
Limitsrevisited
8Complexnumbersrevisited
8.1Moremanipulationswithcomplexnumbers
8.2Cartesianandpolarrepresentationsofcomplexnumbers
8.3Euler'stheorem
8.4Powersofcomplexnumbers:thedeMoivretheorem
ExtensionofthedeMoivreresulttonegativeandrational
powers
8.5Rootsofcomplexnumbers
Logarithmsrevisited
9Thesolutionofsimpledifferentialequations-thenutsand
boltsofkinetics
9.1First-orderdifferentialequations
9.2Separationofvariablesforfirst-orderdifferentialequations
Asurfacechemistryexample
9.3First-orderlineardifferentialequations
Thesolutionofafirst-orderlineardifferentialequation
Sequentialfirst-orderreactionsrevisited
9.4Second-orderdifferentialequations
Simpleharmonicmotion
Inhomogeneoussecond-orderdifferentialequations
9.5Powerseriessolutionofdifferentialequations
Asimpleexample
10Functionsoftwoormorevariables-differentiationrevisited
10.1Therepresentationoffunctionsoftwoormorevariables
Coordinatesystemsforpropertiesdependingupontwo
variables
10.2Differentiationoffunctionsoftwoormorevariables
Thepartialderivative
Higher-orderpartialderivatives
Differentiatingundertheintegralsign-ausefulprocedure
Maxima,minimaandsaddlepoints
10.3Thedifferential,dz
10.4Applicationofdifferentialstoerrorcalculations
Formulaewithasinglemeasuredproperty
Formulaewithtwoormoremeasuredproperties
10.5Thechainruleandtheeffectsofchangingvariables
10.6Exactdifferentials
Findingthefunction,givenitsdifferential
10.7Thermodynamicapplications
11Multipleintegrals-integratingfunctionsofseveralvariables
11.1DoubleintegralsintermsofCartesiancoordinates
11.2Integrationovernon-rectangularregions
Integrationoveratriangularregion
Integrationoverasector
Integrationoveranannularregion
11.3Aspecialintegral
11.4Integralsinvolvingfunctionswithmorethantwovariables
12Statistics
12.1Statisticsinachemicalcontext
12.2Thetheoryoflinearregression
12.3Validatinglinearregression
Thedistributionofthemeasuredvalues
12.4Thenormaldistribution
Propertiesofcontinuousdistributions
12.5Samplingfromadistributionofmeasuredvalues
Propertiesofthenormaldistribution
Measuresofstatisticalconfidence
12.6Confidencelimitsonregressioncalculations
13Matrices-ausefultoolandaformofmathematicalshorthand
13.1Rulesformatrixcombination
13.2Specialformsofmatricesandoperationsonmatrices
Thenullmatrix
Theunitmatrix
Symmetricmatrices
Thetransposeofamatrix
Thetraceofamatrix
Thecomplexconjugateofamatrix
Theadjointofamatrix
Hermitianmatrices
Orthogonalmatrices
Unitarymatrices
13.3Isomorphismsinvolvingmatrices
Somepropertiesofgroups
Grouprepresentations
Thesymmetrypropertiesofozone-achemicalexample
Isomorphismsbetweengroups
14Determinants-functionsrevisitedandanewnotation
14.1Thedeterminantofasquarematrix
14.2Propertiesofdeterminants
14.3Determinantswithfunctionsaselements
14.4Notation
14.5Cofactorsofdeterminants
Expandingadeterminantintermsofcofactors
14.6Matricesrevisited
Theinversematrix
Solutionofsimultaneousequations
15Vectors-aformalismfordirectionalproperties
15.1Conventions
15.2Additionofvectors
15.3Basevectors
15.4Vectormultiplication
Thescalarproduct
Thevectorproduct
Thevectorproductinchemistry
15.5Geometryintwoandthreedimensions
Thestraightline
Theplane
Determinantsrevisited
15.6Differentiationrevisited
15.7Integrationrevisited
16Theeigenvalueproblem-animportantlinkbetweentheory
andexperiment
16.1Examplesofeigenvalueproblems
16.2Defininganeigenvalueproblem
16.3Solvingtheeigenvalueproblem
16.4Thecaseofrepeatedeigenvalues
Theprincipalaxistransformation
17Curvefitting-vectorsrevisited
17.1Basevectorsrevisited
Dealingwithndimensions
17.2Projectingavectorontoasubspace
17.3Curvefitting
Thestraightline
Thegeneralstraightline
Fittingasecond-degreepolynomial
17.4Conclusion
References
Appendix1
SIprefixesandsymbolsfornthpowersof10
Appendix2
Sometrigonometry
Appendix3
Derivativesofselectedfunctions
Answerstoproblems
Index