纯数学教程（英文版·第10版）
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| 新书城图书编号：960 |
| 图书ISBN：711113785X |
| 出版时间：2004-2-10 |
| 出版社：机械工业出版社 |
| 作者：（英）哈代 著 |
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市场价格：￥65 |
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【图书简介】
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There can be few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigour of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit
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【图书目录】
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CONTENTS
(Entriesinsmallprintattheendofthecontentsofeachchapter
refertosubjectsdiscussedincidentallyintheexamples)
CHAPTERI
REALVARIABLES
SECT.
1-2.Rationalnumbers
3-7.Irrationalnumbers
8.Realnumbers
9.Relationsofmagnitudebetweenrealnumbers
10-11.Algebraicaloperationswithrealnumbers
12.Thenumber2
13-14.Quadraticsurds
15.Thecontinum
16.Thecontinuousrealvariable
17.Sectionsoftherealnumbers.Dedekind'stheorem
18.Pointsofaccumulation
19.Weierstrass'stheorem.
Miscellaneousexamples
CHAPTERII
FUNCTIONSOFREALVARIABLES
20.Theideaofafunction
21.Thegraphicalrepresentationoffunctions.Coordinates
22.Polarcoordinates
23.Polynomias
24-25.Rationalfunctions
26-27.Aigebraicalfunctious
28-29.Transcendentalfunctions
30.Graphicalsolutionofequations
31.Functionsoftwovariablesandtheirgraphicalrepre-
sentation
32.Curvesinaplane
33.Lociinspace
Miscellaneousexamples
CHAPTERIII
COMPLEXNUMBERS
SECT.
34-38.Displacements
39-42.Complexnumbers
43.Thequadraticequationwithrealcoefficients
44.Argand'sdiagram
45.DeMoivre'stheorem
46.Rationalfunctionsofacomplexvariable
47-49.Rootsofcomplexnumbers
Miscellaneousexamples
CHAPTERIV
LIMITSOFFUNCTIONSOFAPOSITIVEINTEGRALVARIABLE
50.Functionsofapositiveintegralvariable
51.Interpolation
52.Finiteandinfiniteclasses
53-57.Propertiespossessedbyafunctionofnforlargevalues
ofn
58-61.Definitionofalimitandotherdefinitions
62.Oscillatingfunctions
63-68.Generaltheoremsconcerninglimits
69-70.Steadilyincreasingordecreasingfunctions
71.AlternativeproofofWeierstrass'stheorem
72.Thelimitofxn
73.Thelimitof(1+
74.Somealgebraicallemmas
75.Thelimitofn(nX-1)
76-77.Infiniteseries
78.Theinfinitegeometricalseries
79.Therepresentationoffunctionsofacontinuousreal
variablebymeansoflimits
80.Theboundsofaboundedaggregate
81.Theboundsofaboundedfunction
82.Thelimitsofindeterminationofaboundedfunction
83-84.Thegeneralprincipleofconvergence
85-86.Limitsofcomplexfunctionsandseriesofcomplexterms
87-88.Applicationstoznandthegeometricalseries
89.ThesymbolsO,o,
Miscellaneousexamples
CHAPTERV
LIMITSOFFUNCTIONSOFACONTINUOUSVARIABLE.CONTINUOUS
ANDDISCONTINUOUSFUNCTIONS
90-92.Limitsasx--orx---
93-97.Limitsasz-,a
98.ThesymbolsO,o,～:ordersofsmallnessandgreatness
99-100.Continuousfunctionsofarealvariable
101-105.Propertiesofcontinuousfunctions.Boundedfunctions.
Theoscillationofafunctioninaninterval
106-107.Setsofintervalsonaline.TheHeine-Boreltheorem
108.Continuousfunctionsofseveralvariables
109-110.Implicitandinversefunctions
Miscellaneousexamples
CHAPTERVI
DERIVATIVESANDINTEGRALS
111-113.Derivatives
114.Generalrulesfordifferentiation
115.Derivativesofcomplexfunctions
116.Thenotationofthedifferentialcalculus
117.Differentiationofpolynomials
118.Differentiationofrationalfunctions
119.Differentiationofalgebraicalfunctions
120.Differentiationoftranscendentalfunctions
121.Repeateddifferentiation
122.Generaltheoremsconcerningderivatives,Rolle's
theorem
123-125.Maximaandminima
126-127.Themeanvaluetheorem
128.Cauchy'smeanvaluetheorem
SECT.
129.AtheoremofDarboux
130-131.Integration.Thelogarithmicfunction
132.Integrationofpolynomials
133-134.Integrationofrationalfunctions
135-142.Integrationofalgebraicalfunctions.Integrationby
rationalisation.Integrationbyparts
143-147.Integrationoftranscendentalfunctions
148.Areasofplanecurves
149.Lengthsofplanecurve
Miscellaneousexamples
CHAPTERVII
ADDITIONALTHEOREMSINTHEDIFFERENTIALANDINTEGRALCALCULUS
150-151.Taylor'stheorem
152.Taylor'sseries
153.ApplicationsofTaylor'stheoremtomaximaand
minima
154.Thecalculationofcertainlimits
155.Thecontactofplanecurves
156-158.Differentiationoffunctionsofseveralvariables
159.Themeanvaluetheoremforfunctionsoftwovariables
160.Differentials
161-162.Definiteintegrals
163.Thecircularfunctions
164.Calculationofthedefiniteintegralasthelimitofasum
165.Generalpropertiesofthedefiniteintegral
166.Integrationbypartsandbysubstitution
167.AlternativeproofofTaylor'stheorem
168.Applicationtothebinomialseries
169.Approximateformulaefordefiniteintegrals.Simpson's
rule
170.Integralsofcomplexfunctions
Miscellaneousexamples
CHAPTERVIII
THECONVERGENCEOFINFINITESERIESANDINFINITEINTEGRALS
SECT.PAGE
171-174.Seriesofpositiveterms.Cauchy'sandd'Alembert's
testsofconvergence
175.Ratiotests
176.Dirichlet'stheorem
177.Multiplicationofseriesofpositiveterms
178-180.Furthertestsforconvergence.Abel'stheorem.Mac-
laurin'sintegraltest
181.Theseriesn-s
182.Cauchy'scondensationtest
183.Furtherratiotests
184-189.Infiniteintegrals
190.Seriesofpositiveandnegativeterms
191-192.Absolutelyconvergentseries
193-194.Conditionallyconvergentseries
195.Alternatingseries
196.Abel'sandDirichlet'stestsofconvergence
197.Seriesofcomplexterms
198-201.Powerseries
202.Multiplicationofseries
203.Absolutelyandconditionallyconvergentinfinite
integrals
Miscellaneousexamples
CHAPTERIX
THELOGARITHMIC,EXPONENTIAL,ANDCIRCULARFUNCTIONS
OFAREALVARIABLE
204-205.Thelogarithmicfunction
206.Thefunctionalequationsatisfiedbylogx
207-209.Thebehaviouroflogxasxtendstoinfinityortozero
210.Thelogarithmicscaleofinfinity
211.Thenumbere
212-213.Theexponentialfunction
214.Thegeneralpowerax
215.Theexponentiallimit
216.Thelogarithmiclimit
SECT.
217.Commonlogarithms
218.Logarithmictestsofconvergence
219.Theexponentialseries
220.Thelogarithmicseries
221.Theseriesforarctanx
222.Thebinomialseries
223.Alternativedevelopmentofthetheory
224-226.Theanalyticaltheoryofthecircularfunctions
Miscellaneousexamples
CHAPTERX
THEGENERALTHEORYOFTHELOGARITHMIC,EXPONENTIAL,
ANDCIRCULARFUNCTIONS
227-228.Functionsofacomplexvariable
229.Curvilinearintegrals
230.Definitionofthelogarithmicfunction
231.Thevaluesofthelogarithmicfunction
232-234.Theexponentialfunction
235-236.Thegeneralpowera
237-240.Thetrigonometricalandhyperbolicfunctions
241.Theconnectionbetweenthelogarithmicandinverse
trigonometricalfunctions
242.Theexponentialseries
243.Theseriesforcoszandsinz
244-245.Thelogarithmicseries
246.Theexponentiallimit
247.Thebinomialseries
Miscellaneousexamples
ThefunctionalequationsatisfiedbyLogz,454.Thefunctione,460.
Logarithmstoanybase,461.Theinversecosine,sine,andtangentofa
complexnumber,464.Trigonometricalseries,470,472-474,484,485.
Rootsoftranscendentalequations,479,480.Transformations,480-483.
Stereographicprojection,482.Mercator'sprojection,482.Levelcurves,
484-485.Definiteintegrals,486.
APPENDIXI.Theproofthateveryequationhasaroot
APPENDIXII.Anoteondoublelimitproblems
APPENDIXIII.Theinfiniteinanalysisandgeometry
APPENDIXIV.Theinfiniteinanalysisandgeometry
INDEX
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