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| 001 | 9780429437878 | ||
| 003 | FlBoTFG | ||
| 005 | 20220724194527.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 181101s2019 flua ob 001 0 eng d | ||
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_a9780429437878 _qelectronic book |
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_a9780429795336 _q(electronic bk. : Mobipocket) |
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_a0429795335 _q(electronic bk. : Mobipocket) |
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| 020 | _z9781138345430 | ||
| 020 | _z1138345431 | ||
| 035 | _a(OCoLC)1060524545 | ||
| 035 | _a(OCoLC-P)1060524545 | ||
| 050 | 4 |
_aQA372 _b.G84 2019 |
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| 072 | 7 |
_aMAT _x005000 _2bisacsh |
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_a515/.352 _223 |
| 100 | 1 |
_aGuenther, Ronald B., _eauthor. |
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| 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] |
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| 300 | _a1 online resource (xiii, 406 pages). | ||
| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 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 |
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| 650 | 7 |
_aMATHEMATICS / Mathematical Analysis _2bisacsh |
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| 650 | 7 |
_aMATHEMATICS / Applied _2bisacsh |
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| 650 | 7 |
_aMATHEMATICS / Differential Equations _2bisacsh |
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| 650 | 7 |
_aMATHEMATICS / Geometry / General _2bisacsh |
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| 700 | 1 |
_aLee, John W., _d1942- _eauthor. |
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| 856 | 4 | 0 |
_3Read Online _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 |
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_2lcc _cEBK |
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| 999 |
_c18620 _d18620 |
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