Advanced Calculus fi..

IndexOdd function, 480One-to-one transformation, 58, 118-122,237,240,331-336,591-596,617-623Open interval, 76region, 75sets, 74Operational method, 634 (Prob. 13)Order of differential equation, 625,676of pole, 570-573,576,582Ordinary differential equauons, 625458(Chapter 9)existence of solutions, 627428,631,637,65 1-657Orientable surface, 306-307Orientation in space, 5, 364Orthogonal curvilinear coordinates, 189, 196(Prob. 10)basis, 50functions, 495,499,681,696vectors, 3,42,50,672-673 (Prob. 8)Orthonormal, 50,497499Osculating plane, 127 (Prob. 5)Output. See InputOvertone, 468,681integral formula, 257 (Prob. 8), 361,362,603,607,611412(Probs. 5,6)summation of series, 61 1 (Prob. 5)Polar coordinates, 1 19, 122 (Prob. 8)moment of inertia, 229Pole, 570-587Polynomial, 80, 538,547Position vector, 2Positive definite, 45 (Prob. 13), 160 (Probs.13-15), 196 (Prob. 10) ..%Positive direction, 273-275triple of vectors, 5Potential, 340-343Potential energy, 339,670,705theory, 350-364.700Power function, 55 1series, 422-437,441,560-574Primitive. See Indefinite integralPrincipal, normal, 128 (Prob. 6)part, 570,574 (Probs. 2,6), 585value of function, 550-552value of integral, 455-456,463Products of inertia, 235 (Prob. 8)Properly divergent, 384Parabolic equation, 676Parallel, 5axis theorem, 235 (Prob. 7)Parametric equations, 9, 122-123, 129(Prob. 16), 243Parseval's equation, 494 (hob. 2), 500,505Partial derivatives, 83, 135Partial differential equations, 137, 626,659-712 (Chap. lo),Partial fractions, 584-586Partial sums of series, 383Particular solution, 626,63 1Periodic functions, 467Permanence of functional equation, 547Permutations, even or odd, 1 1, 17 (Prob. 16)Perpendicular, 3,50Phase angle, 477Piecewise smooth, 272,307,542Planar sound waves, 676Plane, 8area. See Area of parallelogram, planePoint discontinuity, 250Poisson equation, 320 (Prob. 4), 342,358,362,616,677,708 - ....Quadratic form, 40, 154-156,202,644,670Radius of convergence, 423,44 1,560-565of curvature, 128 (Prob. 6)Range, 58,171Rational functions, 80,532,547,570,574(Prob. 41,584-586,594-596numbers, 167Ratio test, 390,397,460 (Prob. 3)Rayleigh-Ritz method, 706Real number system, 167Real part, 531Rearrangement of series, 406Reciprocal transformation, 595 - .Recursion formula, 509,5 14,648Region, 75Relaxation method, 709 (Prob. 2)Removable singularity, 569,572,574 (Probs.7, 8), 585Residues, 575-583,587 (Probs. 3-8). 587-590Resonance, 668 (Prob. 9)Resonant frequencies, 645,664,670,679,686,696,700,704 'A$ LRiemann integral, 2 15,258-260