| Description |
1 online resource : illustrations |
| Contents |
Cover; Title Page; Copyright Page; Dedication; Table of Contents; 1 Finite Dimensional Vector Spaces; 1.1 Linear Vector Spaces; 1.2 Spectral Theory for Matrices; 1.3 Geometrical Significance of Eigenvalues; 1.4 Fredholm Alternative Theorem; 1.5 Least Squares Solutionsâ#x80;#x94;Pseudo Inverses; 1.6 Numerical Considerations; Further Reading; Problems for Chapter 1; 1.7 Appendix: Jordan Canonical Form; 2 Function Spaces; 2.1 Complete Metric Spaces; 2.1.1 Sobolev Spaces; 2.2 Approximation in Hilbert Spaces; 2.2.1 Fourier Series and Completeness; 2.2.2 Orthogonal Polynomials; 2.2.3 Trigonometric Series |
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2.2.4 Discrete Fourier Transforms2.2.5 Walsh Functions and Walsh Transforms; 2.2.6 Finite Elements; 2.2.7 Sine Functions; Further Reading; Problems for Chapter 2; 3 Integral Equations; 3.1 Introduction; 3.2 The Fredholm Alternative; 3.3 Compact Operatorsâ#x80;#x94;Hilbert Schmidt Kernels; 3.4 Spectral Theory for Compact Operators; 3.5 Resolvent and Pseudo-Resolvent Kernels; 3.6 Approximate Solutions; 3.7 Singular Integral Equations; Further Reading; Problems for Chapter 3; 4 Differential Operators; 4.1 Distributions and the Delta Function; 4.2 Greenâ#x80;#x99;s Functions; 4.3 Differential Operators |
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4.3.1 Domain of an Operator4.3.2 Adjoint of an Operator; 4.3.3 The Extended Definition of an Operator; 4.3.4 Inhomogeneous Boundary Data; 4.3.5 The Fredholm Alternative; 4.4 Least Squares Solutions; 4.5 Eigenfunction Expansions; 4.5.1 Trigonometric Functions; 4.5.2 Orthogonal Polynomials; 4.5.3 Special Functions; 4.5.4 Discretized Operators; Further Reading; Problems for Chapter 4; 5 Calculus of Variations; 5.1 Euler-Lagrange Equations; 5.1.1 Constrained Problems; 5.1.2 Several Unknown Functions; 5.1.3 Higher Order Derivatives; 5.1.4 Variable Endpoints; 5.1.5 Several Independent Variables |
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5.2 Hamiltonâ#x80;#x99;s Principle5.3 Approximate Methods; 5.4 Eigenvalue Problems; Further Reading; Problems for Chapter 5; 6 Complex Variable Theory; 6.1 Complex Valued Functions; 6.2 The Calculus of Complex Functions; 6.2.1 Differentiationâ#x80;#x94;Analytic Functions; 6.2.2 Integration; 6.2.3 Cauchy Integral Formula; 6.2.4 Taylor and Laurent Series; 6.3 Fluid Flow and Conformal Mappings; 6.3.1 Laplaceâ#x80;#x99;s Equation; 6.3.2 Conformal Mappings; 6.3.3 Free Boundary Problemsâ#x80;#x94;Hodograph Transformation; 6.4 Contour Integration; 6.5 Special Functions; 6.5.1 The Gamma Function; 6.5.2 Bessel Functions |
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6.5.3 Legendre Functions6.5.4 Sine Functions; Further Reading; Problems for Chapter 6; 7 Transform and Spectral Theory; 7.1 Spectrum of an Operator; 7.2 Fourier Transforms; 7.2.1 Transform Pairs; 7.2.2 Completeness of Hermite and Laguerre Polynomials; 7.2.3 Sine Functions; 7.3 Laplace, Mellin and Hankel Transforms; 7.4 Z Transforms; 7.5 Scattering Theory; Further Reading; Problems for Chapter 7; 8 Partial Differential Equations; 8.1 Poissonâ#x80;#x99;s Equation; 8.1.1 Fundamental solutions; 8.1.2 The Method of Images; 8.1.3 Transform Methods; 8.1.4 Eigenfunctions; 8.2 The Wave Equation |
| Summary |
This book is written for beginning graduate students in applied mathematics, science, and engineering, and is appropriate as a one-year course in applied mathematical techniques (although I have never been able to cover all of this material in one year) We assume that the students have studied at an introductory undergraduate level material on linear algebra, ordinary and partial differential equations, and complex variables. The emphasis of the book is a working, systematic understanding of classical techniques in a modern context. Along the way, students are exposed to models from a variety of disciplines. It is hoped that this course will prepare students for further study of modern techniques and in-depth modeling in their own specific discipline |
| Notes |
Originally published 1988 by Perseus Books Publishing |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed March 23, 2018) |
| Subject |
Transformations (Mathematics)
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Asymptotic expansions.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Asymptotic expansions
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Transformations (Mathematics)
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| Form |
Electronic book
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| ISBN |
9780429493263 |
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0429493266 |
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9780429972898 |
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042997289X |
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9780429961816 |
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0429961812 |
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9780429983979 |
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0429983972 |
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