傅里叶分析及其应用-教辅教材-文化科教-太极之巅书单号

书刊介绍

傅里叶分析及其应用目录

preface1introduction1.1theclassicalpartialdifferentialequations1.2well-posedproblems1.3theone-dimensionalwaveequation1.4fourier'smethod2preparations2.1complexexponentials2.2complex-valuedfunctionsofarealvariable2.3cesarosummationofseries2.4positivesummationkernels2.5theriemann-lebesguelemma2.6*somesimpledistributions2.7*computingwithδ3laplaceandztransforms3.1thelaplacetransform3.2operations3.3applicationstodifferentialequations3.4convolution.3.5*laplacetransformsofdistributions3.6theztransform3.7applicationsincontroltheorysummaryofchapter34fourierseries4.1definitions4.2dirichlet'sandfejer'skernels;uniqueness4.3differentiablefunctions4.4pointwiseconvergence4.5formulaeforotherperiods4.6som

傅里叶分析及其应用内容简介

a carefully prepared account of thebasic ideas in fourier analysis and its applications to the studyof partial differential equations. the author succeeds to make hisexposition accessible to readers with a limited background, forexample, those not acquainted with the lebesgue integral. readersshould be familiar with calculus, linear algebra, and complexnumbers. at the same time, the author has managed to includediscussions of more advanced topics such as the gibbs phenomenon,distributions, sturm-liouville theory, cesaro summability andmulti-dimensional fourier analysis, topics which one usually doesnot find in books at this level. a variety of worked examples andexercises will help the readers to apply their newly acquiredknowledge.