Page 899 - Advanced_Engineering_Mathematics o'neil
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Index    879


                                          half-line problems, 629–630              conservative vector fields, 380–387,
                                          heat equations for, 626–630                  410–411
                                          real line problems, 626–628              curvilinear coordinates, 414–423
                                          wave (motion) equations for, 597–584     Gauss’s divergence theorem,
                                        Infinity, mapping point at, 762–763             401–407
                                        Initial-boundary value problem, 566,       Green’s theorem, 374–379, 399–402
                                            594–601, 611–612                       heat equation, 405–407
                                          heat equations, 611–612                  independence of path, 380–387
                                          wave equations, 566, 594–601             line integrals, 367–373
                                        Initial condition, 6, 566, 573–575,        Maxwell’s equations, 411–413
                                            611–612                                potential theory, 380–387
                                        Initial displacement, 570–573, 581–582     Stoke’s theorem, 402, 408–413
                                          nonzero, 572–573                         surface integrals, 388–399
                                          wave motion in an infinite medium,        vector analysis using, 367–423
                                              581–582                            Integral curves, 4–6, 44–45
                                          wave motion over an interval,          Integrals, 367–373, 388–399, 465–471,
                                              570–573                                479–481, 556–561, 695–700,
                                          zero, 570–572, 581–582                     706–709, 713–714, 740–750,
                                        Initial point, 367                           798–799
                                        Initial value problems, 6–8, 40–41,        Bessel’s, 556–560
                                            45–47, 81–84                           Cauchy’s formula, 706–709, 713–714
                                          existence and uniqueness theorem for,    complex functions, 695–700,
                                              40–41                                    706–709, 713–714
                                          first-order differential equations, 6–8,  diffusion in a cylinder, application of,
                                              40–41                                    748–750
                                          Laplace transform solutions, 81–84       eigenfunction expansion and,
                                          second-order differential equations,         556–561
                                              45–47                                Fourier, 465–471
                                          separable differential equations for,    Fourier transform of, 479–481
                                              6–8                                  Hankel’s, 561
                                        Initial velocity, 568–570, 572–573,        inverse Laplace transform and,
                                            579–581                                    746–750
                                          nonzero, 572–573                         line, 367–373
                                          wave motion in an infinite medium,        Lommel’s, 561
                                              579–581                              MAPLE commands for transforms,
                                          wave motion over an interval,                798–799
                                              568–570, 572–573                     Poisson’s, 561
                                          zero, 568–570, 579–581                   rational functions and, 740–745
                                        Insulated ends, heat equation for,         residue theorem evaluation of,
                                            614–615                                    740–750
                                        Insulation conditions, 612                 Sonine’s, 561
                                        Integral calculus, 367–423                 surface, 388–399
                                          Archimedes’s principle, 404–405        Integrating factor, 17




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