Preface |
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xiii | |
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1 | (102) |
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Definitions, Elementary Approach |
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1 | (7) |
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Rotation of the Coordinate Axes |
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8 | (5) |
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13 | (6) |
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19 | (8) |
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Triple Scalar Product, Triple Vector Product |
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27 | (8) |
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35 | (5) |
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40 | (4) |
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44 | (7) |
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Successive Applications of ▿ |
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51 | (4) |
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55 | (6) |
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61 | (4) |
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65 | (4) |
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69 | (11) |
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Gauss's Law, Poisson's Equation |
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80 | (4) |
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84 | (12) |
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96 | (7) |
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Curved Coordinates, Tensors |
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103 | (62) |
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103 | (5) |
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Differential Vector Operators |
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108 | (5) |
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Special Coordinate Systems: Introduction |
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113 | (1) |
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Circular Cylindrical Coordinates |
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114 | (7) |
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Spherical Polar Coordinates |
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121 | (10) |
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131 | (6) |
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Contraction, Direct Product |
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137 | (2) |
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139 | (2) |
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Pseudotensors, Dual Tensors |
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141 | (9) |
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150 | (10) |
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Tensor Derivative Operators |
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160 | (5) |
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Determinants and Matrices |
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165 | (72) |
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165 | (9) |
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174 | (18) |
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192 | (14) |
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Determinants Matrices, Unitary Matrices |
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206 | (7) |
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Diagonalization of Matrices |
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213 | (14) |
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227 | (10) |
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237 | (66) |
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Introduction to Group Theory |
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237 | (5) |
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Generators of Continuous Groups |
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242 | (16) |
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258 | (5) |
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Angular Momentum Coupling |
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263 | (12) |
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Homogeneous Lorentz Group |
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275 | (3) |
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Lorentz Covariance of Maxwell's Equations |
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278 | (8) |
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286 | (17) |
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303 | (86) |
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303 | (3) |
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306 | (16) |
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322 | (3) |
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325 | (4) |
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329 | (5) |
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334 | (12) |
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346 | (8) |
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354 | (6) |
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Bernoulli Numbers, Euler-Maclaurin Formula |
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360 | (13) |
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373 | (8) |
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381 | (8) |
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Functions of a Complex Variable I |
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389 | (50) |
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390 | (9) |
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Cauchy-Riemann Conditions |
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399 | (5) |
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Cauchy's Integral Theorem |
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404 | (7) |
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Cauchy's Integral Formula |
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411 | (5) |
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416 | (9) |
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425 | (9) |
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434 | (5) |
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Functions of a Complex Variable II |
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439 | (48) |
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439 | (5) |
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444 | (25) |
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469 | (8) |
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Method of Steepest Descents |
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477 | (10) |
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487 | (88) |
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Partial Differential Equations |
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487 | (9) |
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First-Order Differential Equations |
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496 | (10) |
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506 | (10) |
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516 | (2) |
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Series Solutions---Frobenius's Method |
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518 | (15) |
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533 | (15) |
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Nonhomogeneous Equation---Green's Function |
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548 | (19) |
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567 | (8) |
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575 | (56) |
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575 | (13) |
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588 | (8) |
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Gram-Schmidt Orthogonalization |
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596 | (8) |
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Completeness of Eigenfunctions |
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604 | (12) |
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Green's Function---Eigenfunction Expansion |
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616 | (15) |
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631 | (38) |
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Definitions, Simple Properties |
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631 | (12) |
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Digamma and Polygamma Functions |
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643 | (6) |
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649 | (5) |
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654 | (6) |
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Incomplete Gamma Function |
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660 | (9) |
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669 | (70) |
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Bessel Functions of the First Kind Jv(x) |
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669 | (19) |
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688 | (6) |
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Neumann Functions, Bessel Functions of the Second Kind |
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694 | (8) |
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702 | (7) |
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Modified Bessel Functions Iv(x) and Kv(x) |
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709 | (7) |
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716 | (6) |
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Spherical Bessel Functions |
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722 | (17) |
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739 | (78) |
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739 | (9) |
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748 | (7) |
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755 | (12) |
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767 | (4) |
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Associated Legendre Functions |
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771 | (15) |
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786 | (6) |
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Orbital Angular Momentum Operators |
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792 | (4) |
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The Addition Theorem for Spherical Harmonics |
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796 | (6) |
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802 | (4) |
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Legendre Functions of the Second Kind |
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806 | (7) |
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Vector Spherical Harmonics |
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813 | (4) |
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817 | (46) |
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817 | (11) |
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828 | (11) |
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839 | (11) |
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850 | (5) |
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Confluent Hypergeometric Functions |
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855 | (8) |
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863 | (42) |
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863 | (7) |
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Advantages, Uses of Fourier Series |
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870 | (4) |
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Applications of Fourier Series |
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874 | (12) |
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Properties of Fourier Series |
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886 | (7) |
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893 | (5) |
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Discrete Fourier Transform |
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898 | (7) |
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905 | (78) |
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905 | (4) |
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Development of the Fourier Integral |
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909 | (2) |
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Fourier Transforms---Inversion Theorem |
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911 | (9) |
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Fourier Transform of Derivatives |
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920 | (4) |
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924 | (4) |
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928 | (7) |
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935 | (3) |
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938 | (8) |
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Laplace Transform of Derivatives |
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946 | (7) |
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953 | (12) |
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Convolution or Faltungs Theorem |
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965 | (4) |
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Inverse Laplace Transform |
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969 | (14) |
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983 | (34) |
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983 | (8) |
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Integral Transforms, Generating Functions |
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991 | (6) |
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Neumann Series, Separable Kernels |
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997 | (12) |
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1009 | (8) |
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1017 | (42) |
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A Dependent and an Independent Variable |
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1018 | (5) |
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Applications of the Euler Equation |
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1023 | (8) |
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Several Dependent Variables |
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1031 | (5) |
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Several Independent Variables |
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1036 | (2) |
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Several Dependent and Independent Variables |
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1038 | (1) |
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1039 | (6) |
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Variation With Constraints |
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1045 | (7) |
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Rayleigh-Ritz Variational Technique |
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1052 | (7) |
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Nonlinear Methods and Chaos |
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1059 | (26) |
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1059 | (1) |
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1060 | (4) |
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Sensitivity to Initial Conditions |
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1064 | (4) |
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Nonlinear Differential Equations |
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1068 | (17) |
Appendix 1 Real Zeros of a Function |
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1085 | (4) |
Appendix 2 Gaussian Quadrature |
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1089 | (8) |
Index |
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1097 | |