Peter V. O'Neil
Partial DE 3e SM
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Peter V. O'Neil
Partial DE 3e SM
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Solutions Manual to Accompany Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe s pendulum and Kepler s problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe s pendulum and Kepler s problem in astronomy.
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Solutions Manual to Accompany Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe s pendulum and Kepler s problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe s pendulum and Kepler s problem in astronomy.
Produktdetails
- Produktdetails
- Wiley Series in Pure and Applied Mathematics .1
- Verlag: Wiley & Sons
- Artikelnr. des Verlages: 1W118630090
- 3. Aufl.
- Seitenzahl: 128
- Erscheinungstermin: 1. Oktober 2014
- Englisch
- Abmessung: 229mm x 152mm x 7mm
- Gewicht: 186g
- ISBN-13: 9781118630099
- ISBN-10: 1118630092
- Artikelnr.: 40693830
- Wiley Series in Pure and Applied Mathematics .1
- Verlag: Wiley & Sons
- Artikelnr. des Verlages: 1W118630090
- 3. Aufl.
- Seitenzahl: 128
- Erscheinungstermin: 1. Oktober 2014
- Englisch
- Abmessung: 229mm x 152mm x 7mm
- Gewicht: 186g
- ISBN-13: 9781118630099
- ISBN-10: 1118630092
- Artikelnr.: 40693830
Peter V. O'Neil, PhD, is Professor Emeritus in the Department of Mathematics at The University of Alabama at Birmingham. Dr. O'Neil has over forty years of academic experience and is the recipient of the Lester R. Ford Award from the Mathematical Association of America. He is a member of the American Mathematical Society, the Society for Industrial and Applied Mathematics, and the American Association for the Advancement of Science.
Preface vii 1 First Ideas 1 1.1 Two Partial Differential Equations 1 1.2
Fourier Series 4 1.3 Two Eigenvalue Problems 12 1.4 A Proof of the
Convergence Theorem 14 2 Solutions of the Heat Equation 15 2.1 Solutions on
an Interval [0, L] 15 2.2 A Nonhomogeneous Problem 19 3 Solutions of the
Wave Equation 25 3.1 Solutions on Bounded Intervals 25 3.2 The Cauchy
Problem 32 3.2.1 d'Alembert's Solution 32 3.2.2 The Cauchy Problem on a
Half Line 36 3.2.3 Characteristic Triangles and Quadrilaterals 41 3.2.4 A
Cauchy Problem with a Forcing Term 41 3.2.5 String with Moving Ends 42 3.3
The Wave Equation in Higher Dimensions 46 3.3.1 Vibrations in a Membrane
with Fixed Frame 46 3.3.2 The Poisson Integral Solution 47 3.3.3 Hadamard's
Method of Descent 47 4 Dirichlet and Neumann Problems 49 4.1 Laplace's
Equation and Harmonic Functions 49 4.2 The Dirichlet Problem for a
Rectangle 50 4.3 The Dirichlet Problem for a Disk 52 4.4 Properties of
Harmonic Functions 57 4.4.1 Topology of Rn 57 4.4.2 Representation Theorems
58 4.4.3 The Mean Value Theorem and the Maximum Principle 60 4.5 The
Neumann Problem 61 4.5.1 Uniqueness and Existence 61 4.5.2 Neumann Problem
for a Rectangle 62 4.5.3 Neumann Problem for a Disk 63 4.6 Poisson's
Equation 64 4.7 An Existence Theorem for the Dirichlet Problem 65 5 Fourier
Integral Methods of Solution 67 5.1 The Fourier Integral of a Function 67
5.2 The Heat Equation on the Real Line 70 5.3 The Debate Over the Age of
the Earth 73 5.4 Burgers' Equation 73 5.5 The Cauchy Problem for the Wave
Equation 74 5.6 Laplace's Equation on Unbounded Domains 76 6 Solutions
Using Eigenfunction Expansions 79 6.1 A Theory of Eigenfunction Expansions
79 6.2 Bessel Functions 83 6.3 Applications of Bessel Functions 87 6.3.1
Temperature Distribution in a Solid Cylinder 87 6.3.2 Vibrations of a
Circular Drum 87 6.4 Legendre Polynomials and Applications 90 7 Integral
Transform Methods of Solution 97 7.1 The Fourier Transform 97 7.2 Heat and
Wave Equations 101 7.3 The Telegraph Equation 104 7.4 The Laplace Transform
106 8 First-Order Equations 109 8.1 Linear First-Order Equations 109 8.2
The Significance of Characteristics 111 8.3 The Quasi-Linear Equation 114
Series List 117
Fourier Series 4 1.3 Two Eigenvalue Problems 12 1.4 A Proof of the
Convergence Theorem 14 2 Solutions of the Heat Equation 15 2.1 Solutions on
an Interval [0, L] 15 2.2 A Nonhomogeneous Problem 19 3 Solutions of the
Wave Equation 25 3.1 Solutions on Bounded Intervals 25 3.2 The Cauchy
Problem 32 3.2.1 d'Alembert's Solution 32 3.2.2 The Cauchy Problem on a
Half Line 36 3.2.3 Characteristic Triangles and Quadrilaterals 41 3.2.4 A
Cauchy Problem with a Forcing Term 41 3.2.5 String with Moving Ends 42 3.3
The Wave Equation in Higher Dimensions 46 3.3.1 Vibrations in a Membrane
with Fixed Frame 46 3.3.2 The Poisson Integral Solution 47 3.3.3 Hadamard's
Method of Descent 47 4 Dirichlet and Neumann Problems 49 4.1 Laplace's
Equation and Harmonic Functions 49 4.2 The Dirichlet Problem for a
Rectangle 50 4.3 The Dirichlet Problem for a Disk 52 4.4 Properties of
Harmonic Functions 57 4.4.1 Topology of Rn 57 4.4.2 Representation Theorems
58 4.4.3 The Mean Value Theorem and the Maximum Principle 60 4.5 The
Neumann Problem 61 4.5.1 Uniqueness and Existence 61 4.5.2 Neumann Problem
for a Rectangle 62 4.5.3 Neumann Problem for a Disk 63 4.6 Poisson's
Equation 64 4.7 An Existence Theorem for the Dirichlet Problem 65 5 Fourier
Integral Methods of Solution 67 5.1 The Fourier Integral of a Function 67
5.2 The Heat Equation on the Real Line 70 5.3 The Debate Over the Age of
the Earth 73 5.4 Burgers' Equation 73 5.5 The Cauchy Problem for the Wave
Equation 74 5.6 Laplace's Equation on Unbounded Domains 76 6 Solutions
Using Eigenfunction Expansions 79 6.1 A Theory of Eigenfunction Expansions
79 6.2 Bessel Functions 83 6.3 Applications of Bessel Functions 87 6.3.1
Temperature Distribution in a Solid Cylinder 87 6.3.2 Vibrations of a
Circular Drum 87 6.4 Legendre Polynomials and Applications 90 7 Integral
Transform Methods of Solution 97 7.1 The Fourier Transform 97 7.2 Heat and
Wave Equations 101 7.3 The Telegraph Equation 104 7.4 The Laplace Transform
106 8 First-Order Equations 109 8.1 Linear First-Order Equations 109 8.2
The Significance of Characteristics 111 8.3 The Quasi-Linear Equation 114
Series List 117
Preface vii 1 First Ideas 1 1.1 Two Partial Differential Equations 1 1.2
Fourier Series 4 1.3 Two Eigenvalue Problems 12 1.4 A Proof of the
Convergence Theorem 14 2 Solutions of the Heat Equation 15 2.1 Solutions on
an Interval [0, L] 15 2.2 A Nonhomogeneous Problem 19 3 Solutions of the
Wave Equation 25 3.1 Solutions on Bounded Intervals 25 3.2 The Cauchy
Problem 32 3.2.1 d'Alembert's Solution 32 3.2.2 The Cauchy Problem on a
Half Line 36 3.2.3 Characteristic Triangles and Quadrilaterals 41 3.2.4 A
Cauchy Problem with a Forcing Term 41 3.2.5 String with Moving Ends 42 3.3
The Wave Equation in Higher Dimensions 46 3.3.1 Vibrations in a Membrane
with Fixed Frame 46 3.3.2 The Poisson Integral Solution 47 3.3.3 Hadamard's
Method of Descent 47 4 Dirichlet and Neumann Problems 49 4.1 Laplace's
Equation and Harmonic Functions 49 4.2 The Dirichlet Problem for a
Rectangle 50 4.3 The Dirichlet Problem for a Disk 52 4.4 Properties of
Harmonic Functions 57 4.4.1 Topology of Rn 57 4.4.2 Representation Theorems
58 4.4.3 The Mean Value Theorem and the Maximum Principle 60 4.5 The
Neumann Problem 61 4.5.1 Uniqueness and Existence 61 4.5.2 Neumann Problem
for a Rectangle 62 4.5.3 Neumann Problem for a Disk 63 4.6 Poisson's
Equation 64 4.7 An Existence Theorem for the Dirichlet Problem 65 5 Fourier
Integral Methods of Solution 67 5.1 The Fourier Integral of a Function 67
5.2 The Heat Equation on the Real Line 70 5.3 The Debate Over the Age of
the Earth 73 5.4 Burgers' Equation 73 5.5 The Cauchy Problem for the Wave
Equation 74 5.6 Laplace's Equation on Unbounded Domains 76 6 Solutions
Using Eigenfunction Expansions 79 6.1 A Theory of Eigenfunction Expansions
79 6.2 Bessel Functions 83 6.3 Applications of Bessel Functions 87 6.3.1
Temperature Distribution in a Solid Cylinder 87 6.3.2 Vibrations of a
Circular Drum 87 6.4 Legendre Polynomials and Applications 90 7 Integral
Transform Methods of Solution 97 7.1 The Fourier Transform 97 7.2 Heat and
Wave Equations 101 7.3 The Telegraph Equation 104 7.4 The Laplace Transform
106 8 First-Order Equations 109 8.1 Linear First-Order Equations 109 8.2
The Significance of Characteristics 111 8.3 The Quasi-Linear Equation 114
Series List 117
Fourier Series 4 1.3 Two Eigenvalue Problems 12 1.4 A Proof of the
Convergence Theorem 14 2 Solutions of the Heat Equation 15 2.1 Solutions on
an Interval [0, L] 15 2.2 A Nonhomogeneous Problem 19 3 Solutions of the
Wave Equation 25 3.1 Solutions on Bounded Intervals 25 3.2 The Cauchy
Problem 32 3.2.1 d'Alembert's Solution 32 3.2.2 The Cauchy Problem on a
Half Line 36 3.2.3 Characteristic Triangles and Quadrilaterals 41 3.2.4 A
Cauchy Problem with a Forcing Term 41 3.2.5 String with Moving Ends 42 3.3
The Wave Equation in Higher Dimensions 46 3.3.1 Vibrations in a Membrane
with Fixed Frame 46 3.3.2 The Poisson Integral Solution 47 3.3.3 Hadamard's
Method of Descent 47 4 Dirichlet and Neumann Problems 49 4.1 Laplace's
Equation and Harmonic Functions 49 4.2 The Dirichlet Problem for a
Rectangle 50 4.3 The Dirichlet Problem for a Disk 52 4.4 Properties of
Harmonic Functions 57 4.4.1 Topology of Rn 57 4.4.2 Representation Theorems
58 4.4.3 The Mean Value Theorem and the Maximum Principle 60 4.5 The
Neumann Problem 61 4.5.1 Uniqueness and Existence 61 4.5.2 Neumann Problem
for a Rectangle 62 4.5.3 Neumann Problem for a Disk 63 4.6 Poisson's
Equation 64 4.7 An Existence Theorem for the Dirichlet Problem 65 5 Fourier
Integral Methods of Solution 67 5.1 The Fourier Integral of a Function 67
5.2 The Heat Equation on the Real Line 70 5.3 The Debate Over the Age of
the Earth 73 5.4 Burgers' Equation 73 5.5 The Cauchy Problem for the Wave
Equation 74 5.6 Laplace's Equation on Unbounded Domains 76 6 Solutions
Using Eigenfunction Expansions 79 6.1 A Theory of Eigenfunction Expansions
79 6.2 Bessel Functions 83 6.3 Applications of Bessel Functions 87 6.3.1
Temperature Distribution in a Solid Cylinder 87 6.3.2 Vibrations of a
Circular Drum 87 6.4 Legendre Polynomials and Applications 90 7 Integral
Transform Methods of Solution 97 7.1 The Fourier Transform 97 7.2 Heat and
Wave Equations 101 7.3 The Telegraph Equation 104 7.4 The Laplace Transform
106 8 First-Order Equations 109 8.1 Linear First-Order Equations 109 8.2
The Significance of Characteristics 111 8.3 The Quasi-Linear Equation 114
Series List 117