《傅里叶分析及其应用》电子书下载

傅里叶分析及其应用txt,chm,pdf,epub,mobi下载
作者:弗雷特布拉德
出版社: 科学出版社
出版年: 2011-6
页数: 269
定价: 69.00元
丛书: 国外数学名著系列
ISBN: 9787030313775

内容简介 · · · · · ·

《傅里叶分析及其应用(影印版)》内容简介：A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and comple...

目录 · · · · · ·

preface 1 introduction 1.1 the classical partial differential equations 1.2 well-posed problems 1.3 the one-dimensional wave equation 1.4 fourier's method 2 preparations 2.1 complex exponentials 2.2 complex-valued functions of a real variable 2.3 cesaro summation of series 2.4 positive summation kernels 2.5 the riemann-lebesgue lemma 2.6 *some simple distributions 2.7 *computing with δ 3 laplace and z transforms 3.1 the laplace transform 3.2 operations 3.3 applications to differential equations 3.4 convolution .3.5 *laplace transforms of distributions 3.6 the z transform 3.7 applications in control theory summary of chapter 3 4 fourier series 4.1 definitions 4.2 dirichlet's and fejer's kernels; uniqueness 4.3 differentiable functions 4.4 pointwise convergence 4.5 formulae for other periods 4.6 some worked examples 4.7 the gibbs phenomenon 4.8 *fourier series for distributions summary of chapter 4 5 l2 theory 5.1 linear spaces over the complex numbers 5.2 orthogonal projections 5.3 some examples 5.4 the fourier system is complete 5.5 legendre polynomials 5.6 other classical orthogonal polynomials summary of chapter 5 6 separation of variables 6.1 the solution of fourier's problem 6.2 variations on fourier's theme 6.3 the dirichlet problem in the unit disk 6.4 sturm-liouville problems 6.5 some singular sturm-liouville problems summary of chapter 6 7 fourier transforms 7.1 introduction 7.2 definition of the fourier transform 7.3 properties 7.4 the inversion theorem. 7.5 the convolution theorem 7.6 plancherel's formula 7.7 application i 7.8 application 2 7.9 application 3: the sampling theorem 7.10 *connection with the laplace transform 7.11 *distributions and fourier transforms summary of chapter 7 8 distributions 8.1 history 8.2 fuzzy points - test functions 8.3 distributions 8.4 properties 8.5 fourier transformation 8.6 convolution 8.7 periodic distributions and fourier series 8.8 fundamental solutions 8.9 back to the starting point summary of chapter 8 9 multi-dimensional fourier analysis 9.1 rearranging series 9.2 double series 9.3 multi-dimensional fourier series 9.4 multi-dimensional fourier transforms appendices a the ubiquitous convolution b the discrete fourier transform c formulae c.1 laplace transforms c.2 z transforms c.3 fourier series c.4 fourier transforms c.5 orthogonal polynomials d answers to selected exercises e literature index

preface 1 introduction 1.1 the classical partial differential equations 1.2 well-posed problems 1.3 the one-dimensional wave equation 1.4 fourier's method 2 preparations 2.1 complex exponentials 2.2 complex-valued functions of a real variable 2.3 cesaro summation of series 2.4 positive summation kernels 2.5 the riemann-lebesgue lemma 2.6 *some simple distributions 2.7 *computing with δ 3 laplace and z transforms 3.1 the laplace transform 3.2 operations 3.3 applications to differential equations 3.4 convolution .3.5 *laplace transforms of distributions 3.6 the z transform 3.7 applications in control theory summary of chapter 3 4 fourier series 4.1 definitions 4.2 dirichlet's and fejer's kernels; uniqueness 4.3 differentiable functions 4.4 pointwise convergence 4.5 formulae for other periods 4.6 some worked examples 4.7 the gibbs phenomenon 4.8 *fourier series for distributions summary of chapter 4 5 l2 theory 5.1 linear spaces over the complex numbers 5.2 orthogonal projections 5.3 some examples 5.4 the fourier system is complete 5.5 legendre polynomials 5.6 other classical orthogonal polynomials summary of chapter 5 6 separation of variables 6.1 the solution of fourier's problem 6.2 variations on fourier's theme 6.3 the dirichlet problem in the unit disk 6.4 sturm-liouville problems 6.5 some singular sturm-liouville problems summary of chapter 6 7 fourier transforms 7.1 introduction 7.2 definition of the fourier transform 7.3 properties 7.4 the inversion theorem. 7.5 the convolution theorem 7.6 plancherel's formula 7.7 application i 7.8 application 2 7.9 application 3: the sampling theorem 7.10 *connection with the laplace transform 7.11 *distributions and fourier transforms summary of chapter 7 8 distributions 8.1 history 8.2 fuzzy points - test functions 8.3 distributions 8.4 properties 8.5 fourier transformation 8.6 convolution 8.7 periodic distributions and fourier series 8.8 fundamental solutions 8.9 back to the starting point summary of chapter 8 9 multi-dimensional fourier analysis 9.1 rearranging series 9.2 double series 9.3 multi-dimensional fourier series 9.4 multi-dimensional fourier transforms appendices a the ubiquitous convolution b the discrete fourier transform c formulae c.1 laplace transforms c.2 z transforms c.3 fourier series c.4 fourier transforms c.5 orthogonal polynomials d answers to selected exercises e literature index
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