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Principles of Applied Mathematics Transformation and Approximation

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ISBN-10: 0201483637

ISBN-13: 9780201483635

Edition: 1995

Authors: James P. Keener

List price: $88.00
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Book details

List price: $88.00
Copyright year: 1995
Publisher: CRC Press LLC
Publication date: 1/21/1995
Binding: Paperback
Pages: 576
Size: 6.25" wide x 9.00" long x 1.25" tall
Weight: 1.584
Language: English

Preface to First Edition
Preface to Second Edition
Finite Dimensional Vector Spaces
Linear Vector Spaces
Spectral Theory for Matrices
Geometrical Significance of Eigenvalues
Fredholm Alternative Theorem
Least Squares Solutions-Pseudo Inverses
The Problem of Procrustes
Applications of Eigenvalues and Eigenfunctions
Exponentiation of Matrices
The Power Method and Positive Matrices
Iteration Methods
Further Reading
Problems for Chapter 1
Function Spaces
Complete Vector Spaces
Sobolev Spaces
Approximation in Hilbert Spaces
Fourier Series and Completeness
Orthogonal Polynomials
Trigonometric Series
Discrete Fourier Transforms
Sinc Functions
Finite Elements
Further Reading
Problems for Chapter 2
Integral Equations
Bounded Linear Operators in Hilbert Space
Compact Operators
Spectral Theory for Compact Operators
Resolvent and Pseudo-Resolvent Kernels
Approximate Solutions
Singular Integral Equations
Further Reading
Problems for Chapter 3
Differential Operators
Distributions and the Delta Function
Green's Functions
Differential Operators
Domain of an Operator
Adjoint of an Operator
Inhomogeneous Boundary Data
The Fredholm Alternative
Least Squares Solutions
Eigenfunction Expansions
Trigonometric Functions
Orthogonal Polynomials
Special Functions
Discretized Operators
Further Reading
Problems for Chapter 4
Calculus of Variations
The Euler-Lagrange Equations
Constrained Problems
Several Unknown Functions
Higher Order Derivatives
Variable Endpoints
Several Independent Variables
Hamilton's Principle
The Swinging Pendulum
The Vibrating String
The Vibrating Rod
Nonlinear Deformations of a Thin Beam
A Vibrating Membrane
Approximate Methods
Eigenvalue Problems
Optimal Design of Structures
Further Reading
Problems for Chapter 5
Complex Variable Theory
Complex Valued Functions
The Calculus of Complex Functions
Differentiation-Analytic Functions
Cauchy Integral Formula
Taylor and Laurent Series
Fluid Flow and Conformal Mappings
Laplace's Equation
Conformal Mappings
Free Boundary Problems
Contour Integration
Special Functions
The Gamma Function
Bessel Functions
Legendre Functions
Sinc Functions
Further Reading
Problems for Chapter 6
Transform and Spectral Theory
Spectrum of an Operator
Fourier Transforms
Transform Pairs
Completeness of Hermite and Laguerre Polynomials
Sinc Functions
Windowed Fourier Transforms
Related Integral Transforms
Laplace Transform
Mellin Transform
Hankel Transform
Z Transforms
Scattering Theory
Scattering Examples
Spectral Representations
Further Reading
Problems for Chapter 7
Fourier Transform Pairs
Partial Differential Equations
Poisson's Equation
Fundamental Solutions
The Method of Images
Transform Methods
Hilbert Transforms
Boundary Integral Equations
The Wave Equation
Fundamental Solutions
Diffraction Patterns
The Heat Equation
Fundamental Solutions
Transform Methods
Differential-Difference Equations
Transform Methods
Numerical Methods
Further Reading
Problems for Chapter 8
Inverse Scattering Transform
Inverse Scattering
Isospectral Flows
Korteweg-deVries Equation
The Toda Lattice
Further Reading
Problems for Chapter 9
Asymptotic Expansions
Definitions and Properties
Integration by Parts
Laplace's Method
Method of Steepest Descents
Method of Stationary Phase
Further Reading
Problems for Chapter 10
Regular Perturbation Theory
The Implicit Function Theorem
Perturbation of Eigenvalues
Nonlinear Eigenvalue Problems
Lyapunov-Schmidt Method
Oscillations and Periodic Solutions
Advance of the Perihelion of Mercury
Van der Pol Oscillator
Knotted Vortex Filaments
The Melnikov Function
Hopf Bifurcations
Further Reading
Problems for Chapter 11
Singular Perturbation Theory
Initial Value Problems I
Van der Pol Equation
Adiabatic Invariance
Homogenization Theory
Initial Value Problems II
Operational Amplifiers
Enzyme Kinetics
Slow Selection in Population Genetics
Boundary Value Problems
Matched Asymptotic Expansions
Flame Fronts
Relaxation Dynamics
Exponentially Slow Motion
Further Reading
Problems for Chapter 12
Selected Hints and Solutions