000			06514nam a2200253 i 4500
008			130716s2013 si m b a001 0 eng d
020			_a9789814407564
020			_a9814407569
040			_aBAUN _beng _cBAUN _erda
049			_aBAUN_MERKEZ
050	0	4	_aQA374 _b.H38 2013
100	1		_aHattori, Harumi.
245	1	0	_aPartial differential equations : _bmethods, applications and theories / _cHarumi Hattori.
264		1	_aSingapore : _bWorld Scientific Publishing, _c2013.
300			_a375 pages : _billustrations ; _c26 cm.
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
504			_aIncludes bibliographical references (pages 369-370) and index.
505	0	0	_tTable Of Contents: _tPreface _t1 First and Second Order Linear Equations - Preparation _t1.1 Terminologies _t1.2 Linearity _t1.2.1 Superposition Principle _t1.2.2 Linear Independence _t1.3 First Order Linear Equations _t1.3.1 Initial Value Problems _t1.3.2 General Solutions _t1.4 Classification of Second Order Linear Equations _t1.5 Well-posedness _t2 Heat Equation _t2.1 Derivation of the Heat Equation _t2.1.1 One-dimensional Case _t2.1.2 Divergence Theorem _t2.1.3 Multi-dimensional Case _t2.2 Initial Boundary Value Problems _t2.3 Homogeneous Boundary Conditions _t2.3.1 Temperature is Fixed at Zero at Both Ends _t2.3.2 Brief Discussion of the Fourier Series _t2.3.3 Both Ends are Insulated _t2.3.4 Temperature of One End is Zero and the Other End is Insulated _t2.4 Non-homogeneous Boundary Conditions _t2.4.1 Steady State Solutions _t2.4.2 Non-homogeneous Boundary Conditions _t2.5 Robin Boundary Conditions _t2.6 Infinite Domain Problems _t2.6.1 Initial Value Problems _t2.6.2 Initial Value Problems via Fourier Transform _t2.6.3 Semi-infinite Domains _t2.7 Maximum Principle, Energy Method, and Uniqueness of Solutions _t2.7.1 Maximum Principle _t2.7.2 Energy Method _t3 Wave Equation _t3.1 Derivation of Wave Equation _t3.1.1 One-dimensional Case _t3.1.2 Multi-dimensional Case _t3.2 Initial Value Problems _t3.2.1 Homogeneous Wave Equation _t3.2.2 Non-homogeneous Wave Equation _t3.3 Wave Reflection Problems _t3.3.1 Homogeneous Boundary Conditions _t3.3.2 Non-homogeneous Boundary Conditions _t3.4 Initial Boundary Value Problems _t3.5 Energy Method _t4 Laplace Equation _t4.1 Motivations _t4.2 Boundary Value Problems - Separation of Variables _t4.2.1 Laplace Equation on a Rectangular Domain _t4.2.2 Laplace Equation on a Circular Disk _t4.3 Fundamental Solution _t4.3.1 Green's Identity _t4.3.2 Derivation of Fundamental Solution _t4.3.3 Green's Identity and Fundamental Solution _t4.4 Green's Function _t4.4.1 Definition _t4.4.2 Green's Function for a Half Space _t4.4.3 Green's Function for a Ball _t4.4.4 Symmetry of Green's Function _t4.5 Properties of Harmonic Functions _t4.5.1 Mean Value Property _t4.5.2 The Maximum Principle and Uniqueness _t4.6 Well-posedness Issues _t4.6.1 Laplace Equation _t4.6.2 Wave Equation _t5 First Order Equations Revisited _t5.1 First Order Quasilinear Equations _t5.2 An Application of Quasilinear Equations _t5.2.1 Scalar Conservation Law _t5.2.2 Rankine-Hugoniot Condition _t5.2.3 Weak Solutions _t5.2.4 Entropy Condition and Admissibility Criterion _t5.2.5 Traffic Flow Problem _t5.3 First Order Nonlinear Equations _t5.4 An Application of Nonlinear Equations - Optimal Control Problem _t5.5 Systems of First Order Equations _t5.5.1 2 x 2 System _t5.5.2 n x n System _t6 Fourier Series and Eigenvalue Problems _t6.1 Even, Odd, and Periodic Functions _t6.1.1 Even and Odd Functions _t6.1.2 Periodic Functions _t6.2 Fourier Series _t6.2.1 Fourier Series _t6.2.2 Fourier Sine and Cosine Series _t6.3 Fourier Convergence Theorems _t6.3.1 Mean-square Convergence _t6.3.2 Pointwise Convergence _t6.3.3 Uniform Convergence _t6.4 Derivatives of Fourier Series _t6.5 Eigenvalue Problems _t6.5.1 The Sturm-Liouville Problems _t6.5.2 Proofs _t7 Separation of Variables in Higher Dimensions _t7.1 Rectangular Domains _t7.2 Eigenvalue Problems _t7.2.1 Multidimensional Case _t7.2.2 Gram-Schmidt Orthogonalization Procedure _t7.2.3 Rayleigh Quotient _t7.3 Eigenfunction Expansions _t7.3.1 Non-homogeneous Boundary Conditions _t7.3.2 Homogeneous Boundary Conditions _t7.3.3 Hybrid Method _t8 More Separation of Variables _t8.1 Circular Domains _t8.1.1 Initial Boundary Value Problems _t8.1.2 Bessel and Modified Bessel Functions _t8.2 Cylindrical Domains _t8.2.1 Initial Boundary Value Problems _t8.2.2 Laplace Equation _t8.3 Spherical Domains _t8.3.1 Initial Boundary Value Problems _t8.3.2 Legendre Equation _t8.3.3 Laplace Equation _t9 Fourier Transform _t9.1 Delta Functions _t9.1.1 Classical Introduction _t9.1.2 Modern Introduction _t9.2 Fourier Transform _t9.2.1 Complex Form of the Fourier Series _t9.2.2 Fourier Transform and Inverse _t9.3 Properties of Fourier Transform _t9.3.1 Fourier Transform of Derivatives _t9.3.2 Convolution _t9.3.3 Plancherel Formula _t9.4 Applications of Fourier Transform _t9.4.1 Heat Equation _t9.4.2 Wave Equation _t9.4.3 Laplace Equation in a Half Space _t9.4.4 Black-Scholes-Merton Equation _t10 Laplace Transform _t10.1 Laplace Transform and the Inverse _t10.1.1 Laplace Transform _t10.1.2 Inverse Transform _t10.2 Properties of the Laplace Transform _t10.2.1 Laplace Transform of Derivatives _t10.2.2 Convolution Theorem _t10.2.3 Relation with the Fourier Transform _t10.3 Applications to Differential Equations _t10.3.1 Applications to ODE's _t10.3.2 Applications to PDE's _t11 Higher Dimensional Problems - Other Approaches _t11.1 Spherical Means and Method of Descent _t11.1.1 Method of Spherical Means _t11.1.2 The Method of Descent _t11.2 Duhamel's Principle _t11.2.1 Heat Equation _t11.2.2 Wave Equation _t12 Green's Functions _t12.1 Green's Functions for the Laplace Equation _t12.1.1 Eigenfunction Expansion _t12.1.2 Modified Green's Function _t12.2 Green's Functions for the Heat Equation _t12.2.1 Initial Boundary Value Problems _t12.2.2 Initial Value Problems _t12.3 Green's Functions for the Wave Equation _t12.3.1 Initial Boundary Value Problems _t12.3.2 Initial Value Problems _tAppendices _tA.1 Exchanging the Order of Integration and Differentiation _tA.2 Infinite Series _tA.3 Useful Formulas in ODE's _tA.3.1 First Order Linear Equations _tA.3.2 Bernoulli Equations _tA.3.3 Second Order Linear Constant Coefficient Equations _tA.3.4 Variation of Parameters Formula _tA.4 Linear Algebra _tA.4.1 Solutions to Systems of Linear Equations _tA.4.2 Eigenvalues, Eigenvectors, and Diagonalization _tHints and Solutions to Selected Exercises _tBibliography _tIndex
650		0	_aDifferential equations, Partial.
900			_a34873
942			_2lcc _cKT
999			_c32164 _d32164