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040 _aOCoLC-P
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020 _a9780429437878
_qelectronic book
020 _a0429437870
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020 _a9780429795343
_qelectronic book
020 _a0429795343
_qelectronic book
020 _a9780429795350
_qelectronic book
020 _a0429795351
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020 _a9780429795336
_q(electronic bk. : Mobipocket)
020 _a0429795335
_q(electronic bk. : Mobipocket)
020 _z9781138345430
020 _z1138345431
035 _a(OCoLC)1060524545
035 _a(OCoLC-P)1060524545
050 4 _aQA372
_b.G84 2019
072 7 _aMAT
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072 7 _aMAT
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072 7 _aMAT
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072 7 _aMAT
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072 7 _aMAT
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072 7 _aPB
_2bicssc
082 0 4 _a515/.352
_223
100 1 _aGuenther, Ronald B.,
_eauthor.
245 1 0 _aSturm-Liouville problems :
_btheory and numerical implementation /
_cRonald B. Guenther, John W. Lee (Department of Mathematics, Oregon State University, Corvallis).
264 1 _aBoca Raton, FL :
_bCRC Press, Taylor & Francis Group,
_c[2019]
300 _a1 online resource (xiii, 406 pages).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aMonographs and research notes in mathematics
505 0 _aCover; Half Title; Title Page; Copyright Page; Contents; Preface; 1. Setting the Stage; 1.1 Euler Buckling; 1.2 Hanging Chain; 1.3 Separation of Variables; 1.4 Vibration Problems; 1.4.1 Vibrations of a String; 1.4.2 Vibrations of a Circular Membrane; 1.4.3 Spherically Symmetric Vibrations in a Ball; 1.5 Diffusion Problems; 1.5.1 Chemical Transport; 1.5.2 Heat Conduction in a Rod; 1.5.3 Heat Conduction in a Disk; 1.6 Steady State Regimes; 1.6.1 Heat Conduction in a Rectangular Plate; 1.6.2 Heat Conduction in a Circular Plate; 1.7 On Models; 1.8 Sturm-Liouville Boundary Value Problems
505 8 _a1.9 Calculus of Variations1.10 Green's Functions; 1.11 The Path Ahead; 1.11.1 Thread I; 1.11.2 Thread II; 1.11.3 Finding Eigenvalues and Eigenfunctions; 1.12 Intrinsic Interest of Eigenvalues; 1.13 Real Versus Complex Solutions; 2. Preliminaries; 2.1 Euclidean Spaces; 2.1.1 Real Euclidean Spaces; 2.1.2 Complex Euclidean Spaces; 2.1.3 Elements of Convergence; 2.1.4 Upper Bounds and Sups; 2.1.5 Closed and Compact Sets; 2.2 Calculus and Analysis; 2.2.1 Continuity; 2.2.2 Differential Calculus; 2.2.3 Integral Calculus; 2.2.4 Sequences and Series of Functions; 2.3 Matrix and Linear Algebra
505 8 _a2.3.1 Determinants2.3.2 Systems of Linear Algebraic Equations; 2.3.3 Linear Dependence and Linear Independence; 2.3.4 Eigenvalues and Eigenvectors; 2.3.5 Self-Adjoint and Symmetric Matrices; 2.3.6 Principal Axis Theorem; 2.3.7 Matrices as Linear Transformations; 2.4 Interpolation and Approximation; 2.4.1 Tchebycheff Systems; 2.4.2 Total Positivity; 2.5 Linear Spaces and Function Spaces; 2.5.1 Linear Spaces; 2.5.2 Normed Linear Spaces; 2.5.3 Inner Product Spaces; 2.5.3.1 Gram-Schmidt Process; 2.6 Completeness and Completion; 2.7 Compact Sets in C[a, b]; 2.8 Contraction Mapping Theorem
505 8 _a2.9 Bisection and Newton-Raphson Methods2.9.1 Bisection Method; 2.9.2 Newton-Raphson Method; 2.10 Maximum Principle; 3. Integral Equations; 3.1 Integral Operators; 3.2 More General Domains; 3.3 Eigenvalues of Operators and Kernels; 3.4 Self-Adjoint Operators and Kernels; 3.4.1 Hilbert-Schmidt Theorem; 3.4.2 Mercer's Theorem; 3.5 Nonnegative Kernels; 3.5.1 Positive Kernels; 3.5.2 Kernels Positive on the Open Diagonal; 3.5.3 Summary of Results; 3.6 Kellogg Kernels and Total Positivity; 3.6.1 Compound Kernels; 3.6.2 Spectral Properties of Compound Kernels
505 8 _a3.6.3 Spectral Properties of Kellogg Kernels3.7 Singular Kellogg Kernels; 3.7.1 Compound Kernels; 3.7.2 Spectral Properties of Compound Kernels; 3.7.3 Spectral Properties of Kellogg Kernels; 4. Regular Sturm-Liouville Problems; 4.1 Sturm-Liouville Form; 4.2 Sturm-Liouville Differential Equations; 4.3 Initial Value Problems; 4.3.1 Basis of Solutions; 4.3.2 Variation of Parameters; 4.3.3 Continuous Dependence; 4.4 BVPs and EVPs -- Examples; 4.5 BVPs and EVPs -- Notation; 4.6 Green's Functions; 4.6.1 Separated Boundary Conditions; 4.6.2 Mixed Boundary Conditions; 4.7 Adjoint Operators and Problems
520 _aSturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified way, the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.
588 _aOCLC-licensed vendor bibliographic record.
650 0 _aSturm-Liouville equation.
650 0 _aDifferential equations.
650 0 _aEigenvalues.
650 7 _aMATHEMATICS / Calculus
_2bisacsh
650 7 _aMATHEMATICS / Mathematical Analysis
_2bisacsh
650 7 _aMATHEMATICS / Applied
_2bisacsh
650 7 _aMATHEMATICS / Differential Equations
_2bisacsh
650 7 _aMATHEMATICS / Geometry / General
_2bisacsh
700 1 _aLee, John W.,
_d1942-
_eauthor.
856 4 0 _3Taylor & Francis
_uhttps://www.taylorfrancis.com/books/9780429437878
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
999 _c130515
_d130515