Page 484 - Numerical Methods for Chemical Engineering

Index 473

QR factorization 130 Search direction 214
Hessenberg matrix 132 Secant condition 224
Householder transformation (reflection) 129 Sequential Quadratic Programming (SQP)
iterative use for eigenvalue analysis 131 240
MATLAB qr 131 Shape function 305
Quadrature (numerical integration) 162 Similarity transformation 118
dynamic simulation (see also Initial value similar matrices 118
problems) 155 Simplex optimization method 213
Gaussian (see also Quadrature) 163–166 Simulated annealing 361–362
Lobatto 166 applied to parameter estimation 417–419
MATLAB dblquad 167 Singular Value Decomposition (SVD) 141–148
MATLAB quad 163 existence and uniqueness of linear systems 143
MATLAB quadl 166 least-squares approximate solution of linear system
MATLAB trapz 140, 163 145
MATLAB triplequad 167 left singular vectors 142
multidimensional integrals 167–169 MATLAB svd 146, 149
Monte Carlo integration 168 pseudo (generalized) matrix inverse 145
Newton-Cotes integration 162 right singular vectors 142
3/8 rule 162 rank of matrix 142
Simpson’s rule 162 singular values 141
Trapezoid rule 162; composite rule Slack variables 239
162 Span
Quantum mechanics 137–141 of set of vectors 29
use of eigenvalue analysis 138 Sparse matrix
Quasi-Steady State Approximation (QSSA) allocation with MATLAB spalloc 52, 56
183 banded 51
BVPs of high dimension 282–294
Random defined 50
number generators fill-in during Gaussian elimination 54
MATLAB normrnd 334 list of available functions with MATLAB sparfun
MATLAB rand 168, 327 57
MATLAB randn 334 storage format 51
variable 322 viewing structure with MATLAB spy 53
conditional expectation 323 Spectral decomposition 122
covariance 336 Stability
expectation 322 dynamic 170
MATLAB mean 364 eigenvalue analysis 171
MATLAB std 364 manifolds 171
MATLAB var 364 Example. stability of steady states of nonlinear
standard deviation 327 dynamic system 172–175
variance 327 numerical stability of ODE-IVP methods
vector A-stability 188
covariance matrix 337 absolute stability 187
walks 328–329 error rejection 190
Rank stiff stability 192
of matrix 44, 142 time step restrictions 190–191
Regression (see Bayesian statistics) Standard deviation 327
Residual function 304 MATLAB std 364
Statistical mechanics
Scalars 3 Boltzmann distribution 337
complex conjugate 3 Example. Monte Carlo simulation of 2-D Ising
complex modulus 3 lattice 356–357
Scattering theory 452–458 Field theory (see also Field theory) 358–360
lattice vectors 457 Lennard-Jones interaction model 368
powder spectrum 458 Maxwell velocity distribution 338
reciprocal lattice vectors 458 statistical field theory 358–360
Small Angle X-ray Scattering (SAXS) 458 Statistics (see Bayesian statistics)
structure factor 455 Steepest descent
Wide Angle X-ray Scattering (WAXS) direction 214
458 optimization method 217
Schr¨odinger equation 138 Stiff dynamical systems 180
Schur decomposition 119 numerical simulation 192
MATLAB schur 119 Stirling’s approximation 331