Cover |
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SCHAUM'S OUTLINE OF THEORY AND PROBLEMS of FOURIER ANALYSIS with Applications to Boundary Value Problems |
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Copyright Page |
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Preface |
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CONTENTS |
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Chapter 1 Boundary Value Problems |
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Mathematical Formulation and Solution of Physical Problems |
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Definitions Pertaining to Partial Differential Equations |
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Linear Partial Differential Equations |
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Some Important Partial Differential Equations |
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The Laplacian in Different Coordinate Systems |
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Methods of Solving Boundary Value Problems |
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Chapter 2 Fourier Series and Applications |
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The Need for Fourier Series |
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Periodic Functions |
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Piecewise Continuous Functions |
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Definition of Fourier Series |
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Dirichlet Conditions |
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Odd and Even Functions |
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Half-Range Fourier Sine or Cosine Series |
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Parseval's Identity |
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Uniform Convergence |
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Integration and Differentiation of Fourier Series |
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Complex Notation for Fourier Series |
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Double Fourier Series |
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Applications of Fourier Series |
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Chapter 3 Orthogonal Functions |
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Definitions Involving Orthogonal Functions. Orthonormal Sets |
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Orthogonality with Respect to a Weight Function |
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Expansion of Functions in Orthonormal Series |
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Approximations in the Least-Squares Sense |
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The Fourier Integral |
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Equivalent Forms of Fourier's Integral Theorem |
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Fourier Transforms |
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Fourier Sine and Cosine Transforms |
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Parseval's Identities for Fourier Integrals |
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The Convolution Theorem for Fourier Transforms |
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Applications of Fourier Integrals and Transforms |
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Chapter 6 Bessel Functions and Applications |
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Bessel's Differential Equation |
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The Method of Frobenius |
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Bessel Functions of the First Kind |
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Bessel Functions of the Second Kind |
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Generating Function for Jn(x) |
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Recurrence Formulas |
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Functions Related to Bessel Functions |
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Equations Transformable into Bessel's Equation |
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Asymptotic Formulas for Bessel Functions |
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Zeros of Bessel Functions |
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Orthogonality of Bessel Functions of the First Kind |
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Series of Bessel Functions of the First Kind |
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Orthogonality and Series of Bessel Functions of the Second Kind |
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Solutions to Boundary Value Problems Using Bessel Functions |
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Chapter 7 Legendre Functions and Applications |
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Legendre's Differential Equation |
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Legendre Polynomials |
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Generating Function for Legendre Polynomials |
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Legendre Functions of the Second Kind |
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Cover |
|
SCHAUM'S OUTLINE OF THEORY AND PROBLEMS of FOURIER ANALYSIS with Applications to Boundary Value Problems |
|
Copyright Page |
|
Preface |
|
CONTENTS |
|
Chapter 1 Boundary Value Problems |
|