| 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 |
|
