Fourier Series and Systems of Differential...

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1、FourierSeriesandSystemsofDifferential...LeifMejlbroDownloadfreebooksatLeifMejlbroFourierSeriesandSystemsofDifferentialEquationsandEigenvalueProblemsGuidelinesforSolutionsofProblemsCalculus4bDownloadfreeeBooksatbookboon.comFourierSeriesandSystemsofDifferentialEquationsandEigenvalueProblems–Guidelin

2、esforSolutionsofProblems–Calculus4b©2007LeifMejlbro&VentusPublishingApsISBN978-87-7681-242-3DownloadfreeeBooksatbookboon.comCalculus4bContentsContentsPreface61Reviewofsomeimportanttrigonometricformulæ71.1Trigonometricformulæ71.2Integrationoftrigonometricpolynomials72Fourierseries;methodsofcalculat

3、ion112.1General112.2Standardprocedure142.3StandardFourierseries182.4Thesquarefunction182.5Theidenticalfunctionin]-π;π[192.6Thefirstsawtoothfunction192.7Thesecondsawtoothfunction212.8Expansionofcosineinasinusseriesoverahalfperiod222.9Symmetricparabolicarcin[-π;π]360°232.10Hyperboliccosinein[-π;π]232

4、.11Exponentialfunctionover]-π;π]thinking.253AlistofproblemsintheTheoryofFourierseries273.1Apiecewiseconstantfunction27360°thinking.360°thinking.Discoverthetruthatwww.deloitte.ca/careersDiscoverthetruthatwww.deloitte.ca/careers©Deloitte&ToucheLLPandaffiliatedentities.Discoverthetruthatwww.deloitte.

5、ca/careers©Deloitte&ToucheLLPandaffiliatedentities.©Deloitte&ToucheLLPandaffiliatedentities.Discoverthetruthatwww.deloitte.ca/careers4ClickontheadtoreadmoreDownloadfreeeBooksatbookboon.com©Deloitte&ToucheLLPandaffiliatedentities.Calculus4bContents3.2Piecewiselinearfunctions323.3Apiecewisepolynomia

6、lofseconddegree373.4Apiecewisepolynomialofthirddegree473.5Apiecewisepolynomialoffourthdegree493.6Piecewisesinus503.7Piecewisecosine573.8Mixedsinusandcosine643.9Apiecewisepolynomialtimesatrigonometricfunction663.10Theexponentialfunctionoccurs723.11Theproblemoftheassumptionofnoverticalhalftangent774

7、Systemsoflineardierentialequations;methods804.1TheExistenceandUniquenessTheorem804.2ConstantsystemmatrixA804.3Eigenvaluemethod,realeigenvalues,Aaconstant(2x2)-matrix824.4Theeigenvaluemethod,complexconjugatedeigen