Page 911 - Advanced_Engineering_Mathematics o'neil
P. 911
Index 891
Temperature distribution, 612–624, U
633–634, 655–658 Unbounded regions, 649–653, 664–665
boundary conditions, effects of on, Dirichlet problem for, 649–653
622–624 Neumann problem for, 664–665
constants, effects of on, 622–624 Underdamping, 65–67
diffusion in a semi-infinite bar, Undetermined coefficients, method of,
633–634 57–60
diffusivity constant k, 623–624 Unforced spring motion, 62–66
heat equations for, 612–624 Unit normal vector, 352–353
insulated ends, 614–615 Unit tangent vector and, 350–352
radiating ends, 615–617 Unit vector, 150
separation constant λ, 568 Unitary matrix, 286–288
source term for, 619–622 Upper triangular matrix (U), 237
steady-state equation for a sphere,
655–658 V
transformation of problems, 618–619 Vandermark’s determinant, 258
zero, 612–614 Variation of parameters, 55–56,
Terminal point, 367 312–314, 317–318
Terminal velocity, first-order differential exponential matrix solutions using,
equation applications for, 30–31 317–318
Three-point mapping theorem, 762–763 Laplace transform and, 317–318
3-space, 152–154, 410–411 linear system solution using, 312–314
parametric equations for, 152–154 nonhomogeneous differential
potential theory in, 410–411 equations and, 55–56, 312–314
vectors, 152–154 Vector analysis, 343–423
Time convolution, 480 Archimedes’s principle, 404–405
Time-frequency localization, 485 conservative vector fields, 380–387,
Time reversal, Fourier transforms, 476 410–411
Time shifting, Fourier transforms, curl, 362–363, 365, 421–423
475–476 curvature κ(s), 349–354
Torricelli’s law, 12 curves, 349–354, 367–372, 392–393,
Trajectories, 34–37 408–410
orthogonal, 34–35 curvilinear coordinates, 414–423
pursuit problem for, 35–37 del operator ∇ for, 356–357, 362–363
Transfer function, 487 differential calculus, 345–366
Transient solution term, 19–20 divergence, 362–364, 401–407,
Transition matrix, 317 420–421
Translation mapping, 758 Gauss’s divergence theorem, 401–407
Transpose of a matrix, 193–194 gradient field ϕ, 356–361
Triangle inequality, 672 Green’s theorem, 374–380, 399–402
Trigonometric functions, 684–688 heat equation, 405–407
Trivial solution, 219 independence of path, 380–387
Trivial subspace, 165 integral calculus, 367–423
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